diff --git a/CMakeLists.txt b/CMakeLists.txt
index 75934f7c0f3025853c4c0bd44c1e358abb8f52ad..c598830685321a7c8a8a2587e25f819a1567d2d5 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -2,6 +2,9 @@ cmake_minimum_required(VERSION 3.0 FATAL_ERROR)
project(gmshddm CXX)
+include(CTest)
+enable_testing()
+
set(GMSHDDM_MAJOR_VERSION 1)
set(GMSHDDM_MINOR_VERSION 0)
set(GMSHDDM_PATCH_VERSION 0)
@@ -142,6 +145,9 @@ add_subdirectory(src/problem)
include_directories(src/common src/domain src/field src/problem)
include_directories(contrib/eigen)
+add_subdirectory(examples)
+add_subdirectory(tutorials)
+
#----------------------------------
#
# O T H E R L I B S
diff --git a/demos/helmholtz/scattering/pml/main.cpp b/demos/helmholtz/scattering/pml/main.cpp
deleted file mode 100644
index 33d688d38b64e131fcb9a93a596c0116ef8257ca..0000000000000000000000000000000000000000
--- a/demos/helmholtz/scattering/pml/main.cpp
+++ /dev/null
@@ -1,853 +0,0 @@
-#include "GmshDdm.h"
-
-#include "FormulationDDM.h"
-
-#include "Message.h"
-#include "AnalyticalFunction.h"
-
-#include "gmsh.h"
-
-using namespace gmshddm;
-using namespace gmshddm::common;
-using namespace gmshddm::domain;
-using namespace gmshddm::problem;
-using namespace gmshddm::field;
-
-using namespace gmshfem;
-using namespace gmshfem::analytics;
-using namespace gmshfem::domain;
-using namespace gmshfem::problem;
-using namespace gmshfem::field;
-using namespace gmshfem::function;
-using namespace gmshfem::post;
-
-gmshfem::function::TensorFunction< std::complex< double > > getPmlDParameter(const double k, const double pmlSize, const double pos, const bool onX);
-gmshfem::function::ScalarFunction< std::complex< double > > getPmlEParameter(const double k, const double pmlSize, const double pos, const bool onX);
-
-void checkerboard(const unsigned int nDomX, const unsigned int nDomY, const double xSize, const double ySize, const double circleSize, const double pmlSize, const double lc, const bool pml = true, const unsigned int circlePosX = 0, const unsigned int circlePosY = 0)
-{
- std::vector< std::vector< int > > omega(nDomX);
- for(unsigned int i = 0; i < nDomX; ++i) {
- omega[i].resize(nDomY);
- }
-
- // ******************
- // borders
- // ******************
-
- // ****(2)****
- // * *
- // (3) (1)
- // * *
- // ****(0)****
- std::vector< std::vector< std::vector< int > > > borders(nDomX);
- for(unsigned int i = 0; i < nDomX; ++i) {
- borders[i].resize(nDomY);
- for(unsigned int j = 0; j < nDomY; ++j) {
- borders[i][j].resize(4);
- }
- }
-
- // ******************
- // pmls
- // ******************
-
- // 1 0
- // 0 ****(2)**** 1
- // * *
- // (3) (1)
- // * *
- // 1 ****(0)**** 0
- // 0 1
-
- std::vector< std::vector< std::vector< int > > > pmls(nDomX);
- std::vector< std::vector< std::vector< int > > > pmlsInf(nDomX);
- std::vector< std::vector< std::vector< std::vector< int > > > > pmlsBnd(nDomX);
- for(unsigned int i = 0; i < nDomX; ++i) {
- pmls[i].resize(nDomY);
- pmlsInf[i].resize(nDomY);
- pmlsBnd[i].resize(nDomY);
- for(unsigned int j = 0; j < nDomY; ++j) {
- pmls[i][j].resize(4);
- pmlsInf[i][j].resize(4);
- pmlsBnd[i][j].resize(4);
- for(unsigned int k = 0; k < 4; ++k) {
- pmlsBnd[i][j][k].resize(2);
- }
- }
- }
-
- // ******************
- // pmlsSquare
- // ******************
-
- // (2)*******(1)
- // * *
- // * *
- // * *
- // (3)*******(0)
-
- std::vector< std::vector< std::vector< int > > > pmlsSquare(nDomX);
- for(unsigned int i = 0; i < nDomX; ++i) {
- pmlsSquare[i].resize(nDomY);
- for(unsigned int j = 0; j < nDomY; ++j) {
- pmlsSquare[i][j].resize(4);
- }
- }
-
- std::vector< int > left(nDomY);
- int bottom = 0;
- for(unsigned int i = 0; i < nDomX; ++i) {
- for(unsigned int j = 0; j < nDomY; ++j) {
- int p[4];
- p[0] = gmsh::model::geo::addPoint(i * xSize, j * ySize, 0., lc);
- p[1] = gmsh::model::geo::addPoint((i + 1) * xSize, j * ySize, 0., lc);
- p[2] = gmsh::model::geo::addPoint((i + 1) * xSize, (j + 1) * ySize, 0., lc);
- p[3] = gmsh::model::geo::addPoint(i * xSize, (j + 1) * ySize, 0., lc);
-
- int l[4];
- borders[i][j][0] = l[0] = gmsh::model::geo::addLine(p[0], p[1]);
- borders[i][j][1] = l[1] = gmsh::model::geo::addLine(p[1], p[2]);
- borders[i][j][2] = l[2] = gmsh::model::geo::addLine(p[2], p[3]);
- borders[i][j][3] = l[3] = gmsh::model::geo::addLine(p[3], p[0]);
-
- if(i == 0) {
- left[j] = l[1];
- }
- else {
- borders[i][j][3] = left[j];
- left[j] = l[1];
- }
-
- if(j == 0) {
- bottom = l[2];
- }
- else {
- borders[i][j][0] = bottom;
- bottom = l[2];
- }
-
- int ll = gmsh::model::geo::addCurveLoop({l[0], l[1], l[2], l[3]});
-
- int surface = 0;
- if(i == circlePosX && j == circlePosY) {
- // circle
- int pC[5];
- pC[0] = gmsh::model::geo::addPoint(circlePosX * i + xSize / 2., circlePosY * j + ySize / 2., 0., lc);
- pC[1] = gmsh::model::geo::addPoint(circlePosX * i + xSize / 2. + circleSize, circlePosY * j + ySize / 2., 0., lc);
- pC[2] = gmsh::model::geo::addPoint(circlePosX * i + xSize / 2., circlePosY * j + ySize / 2. + circleSize, 0., lc);
- pC[3] = gmsh::model::geo::addPoint(circlePosX * i + xSize / 2. - circleSize, circlePosY * j + ySize / 2., 0., lc);
- pC[4] = gmsh::model::geo::addPoint(circlePosX * i + xSize / 2., circlePosY * j + ySize / 2. - circleSize, 0., lc);
-
- int lC[4];
- lC[0] = gmsh::model::geo::addCircleArc(pC[1], pC[0], pC[2]);
- lC[1] = gmsh::model::geo::addCircleArc(pC[2], pC[0], pC[3]);
- lC[2] = gmsh::model::geo::addCircleArc(pC[3], pC[0], pC[4]);
- lC[3] = gmsh::model::geo::addCircleArc(pC[4], pC[0], pC[1]);
-
- // surface
- int llC;
- llC = gmsh::model::geo::addCurveLoop({lC[0], lC[1], lC[2], lC[3]});
-
- surface = gmsh::model::geo::addPlaneSurface({ll, llC});
-
- gmsh::model::addPhysicalGroup(1, {lC[0], lC[1], lC[2], lC[3]}, 1);
- gmsh::model::setPhysicalName(1, 1, "gammaScat");
- }
- else {
- surface = gmsh::model::geo::addPlaneSurface({ll});
- }
- omega[i][j] = surface;
-
- if(pml) {
- // pmls
- double extrudeX[4] = {0., pmlSize, 0., -pmlSize};
- double extrudeY[4] = {-pmlSize, 0., pmlSize, 0.};
- for(unsigned int k = 0; k < 4; ++k) {
- std::vector< std::pair< int, int > > extrudeEntities;
- gmsh::model::geo::extrude({std::make_pair(1, ((k == 3 && i != 0) || (k == 0 && j != 0) ? 1 : -1) * borders[i][j][k])}, extrudeX[k], extrudeY[k], 0., extrudeEntities, {static_cast< int >(pmlSize / lc)}, std::vector< double >(), true);
- pmlsInf[i][j][k] = extrudeEntities[0].second;
- pmls[i][j][k] = extrudeEntities[1].second;
- if((k == 3 && i != 0) || (k == 0 && j != 0)) {
- pmlsBnd[i][j][k][0] = extrudeEntities[2].second;
- pmlsBnd[i][j][k][1] = extrudeEntities[3].second;
- }
- else {
- pmlsBnd[i][j][k][0] = extrudeEntities[3].second;
- pmlsBnd[i][j][k][1] = extrudeEntities[4].second;
- }
- }
-
- // pmlsSquare
- double extrudeSquareX[4] = {pmlSize, pmlSize, -pmlSize, -pmlSize};
- int side[4] = {0, 2, 2, 0};
- int sideBnd[4] = {1, 0, 1, 0};
- for(unsigned int k = 0; k < 4; ++k) {
- std::vector< std::pair< int, int > > extrudeEntities;
- gmsh::model::geo::extrude({std::make_pair(1, -pmlsBnd[i][j][side[k]][sideBnd[k]])}, extrudeSquareX[k], 0., 0., extrudeEntities, {static_cast< int >(pmlSize / lc)}, std::vector< double >(), true);
- pmlsSquare[i][j][k] = extrudeEntities[1].second;
- }
- }
- }
- }
-
- gmsh::model::geo::synchronize();
-
- // ******************
- // physicals
- // ******************
-
- for(unsigned int i = 0; i < nDomX; ++i) {
- for(unsigned int j = 0; j < nDomY; ++j) {
- gmsh::model::addPhysicalGroup(2, {omega[i][j]}, i * nDomY + j + 1);
- gmsh::model::setPhysicalName(2, i * nDomY + j + 1, "omega_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(1, {borders[i][j][0]}, 10000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 10000 + i * nDomY + j + 1, "sigmaS_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(1, {borders[i][j][1]}, 20000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 20000 + i * nDomY + j + 1, "sigmaE_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(1, {borders[i][j][2]}, 30000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 30000 + i * nDomY + j + 1, "sigmaN_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(1, {borders[i][j][3]}, 40000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 40000 + i * nDomY + j + 1, "sigmaW_" + std::to_string(i) + "_" + std::to_string(j));
-
- if(pml) {
- // PMLs
- gmsh::model::addPhysicalGroup(2, {pmls[i][j][0]}, 10000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(2, 10000 + i * nDomY + j + 1, "pmlS_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(2, {pmls[i][j][1]}, 20000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(2, 20000 + i * nDomY + j + 1, "pmlE_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(2, {pmls[i][j][2]}, 30000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(2, 30000 + i * nDomY + j + 1, "pmlN_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(2, {pmls[i][j][3]}, 40000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(2, 40000 + i * nDomY + j + 1, "pmlW_" + std::to_string(i) + "_" + std::to_string(j));
-
- // PMLs square
- gmsh::model::addPhysicalGroup(2, {pmlsSquare[i][j][0]}, 100000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(2, 100000 + i * nDomY + j + 1, "pmlSE_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(2, {pmlsSquare[i][j][1]}, 200000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(2, 200000 + i * nDomY + j + 1, "pmlNE_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(2, {pmlsSquare[i][j][2]}, 300000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(2, 300000 + i * nDomY + j + 1, "pmlNW_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(2, {pmlsSquare[i][j][3]}, 400000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(2, 400000 + i * nDomY + j + 1, "pmlSW_" + std::to_string(i) + "_" + std::to_string(j));
-
- // Sigmas in PMLs
- gmsh::model::addPhysicalGroup(1, {pmlsBnd[i][j][3][1]}, 100000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 100000 + i * nDomY + j + 1, "sigmaS_W_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(1, {pmlsBnd[i][j][1][0]}, 150000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 150000 + i * nDomY + j + 1, "sigmaS_E_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(1, {pmlsBnd[i][j][0][1]}, 200000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 200000 + i * nDomY + j + 1, "sigmaE_S_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(1, {pmlsBnd[i][j][2][0]}, 250000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 250000 + i * nDomY + j + 1, "sigmaE_N_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(1, {pmlsBnd[i][j][1][1]}, 300000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 300000 + i * nDomY + j + 1, "sigmaN_E_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(1, {pmlsBnd[i][j][3][0]}, 350000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 350000 + i * nDomY + j + 1, "sigmaN_W_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(1, {pmlsBnd[i][j][2][1]}, 400000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 400000 + i * nDomY + j + 1, "sigmaW_N_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(1, {pmlsBnd[i][j][0][0]}, 450000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 450000 + i * nDomY + j + 1, "sigmaW_S_" + std::to_string(i) + "_" + std::to_string(j));
-
- }
- }
- }
-
- gmsh::model::addPhysicalGroup(0, {3}, 1);
- gmsh::model::setPhysicalName(0, 1, "crossPoint");
-
- gmsh::model::geo::synchronize();
- gmsh::model::mesh::generate();
-}
-
-int main(int argc, char **argv)
-{
- GmshDdm gmshDdm(argc, argv);
-
- double pi = 3.14159265359;
-
- int nDomX = 2, nDomY = 2;
- gmshDdm.userDefinedParameter(nDomX, "nDomX");
- gmshDdm.userDefinedParameter(nDomY, "nDomY");
- double xSize = 1., ySize = 1.;
- gmshDdm.userDefinedParameter(xSize, "xSize");
- gmshDdm.userDefinedParameter(ySize, "ySize");
- double circleSize = 0.1;
- gmshDdm.userDefinedParameter(circleSize, "circleSize");
- double pmlSize = 0.1;
- gmshDdm.userDefinedParameter(pmlSize, "pmlSize");
- double k = 10. * pi + 0.3;
- gmshDdm.userDefinedParameter(k, "k");
- double lc = 0.02;
- gmshDdm.userDefinedParameter(lc, "lc");
- std::string gauss = "Gauss3";
- gmshDdm.userDefinedParameter(gauss, "gauss");
- int circlePosX = 0, circlePosY = 0;
- gmshDdm.userDefinedParameter(circlePosX, "circlePosX");
- gmshDdm.userDefinedParameter(circlePosY, "circlePosY");
- bool errorMono = false;
- gmshDdm.userDefinedParameter(errorMono, "errorMono");
- bool withSquarePML = true;
- gmshDdm.userDefinedParameter(withSquarePML, "withSquarePML");
-
- // Build geometry and mesh using gmsh API
- checkerboard(nDomX, nDomY, xSize, ySize, circleSize, pmlSize, lc, true, circlePosX, circlePosY);
-
- unsigned int nDom = nDomX * nDomY;
-
- // | |
- // NW | N | NE
- // ----**************----
- // * *
- // * *
- // W * * E
- // * *
- // * *
- // ----**************----
- // SW | S | SE
- // | |
-
- // Define domain
- Subdomain omega(nDom);
- Subdomain gammaDir(nDom);
-
- Subdomain pmlS(nDom);
- Subdomain pmlE(nDom);
- Subdomain pmlN(nDom);
- Subdomain pmlW(nDom);
-
- Subdomain pmlSE(nDom);
- Subdomain pmlNE(nDom);
- Subdomain pmlNW(nDom);
- Subdomain pmlSW(nDom);
-
- InterfaceDomain sigmaS(nDom);
- InterfaceDomain sigmaE(nDom);
- InterfaceDomain sigmaN(nDom);
- InterfaceDomain sigmaW(nDom);
-
- InterfaceDomain sigmaS_W(nDom);
- InterfaceDomain sigmaS_E(nDom);
- InterfaceDomain sigmaE_S(nDom);
- InterfaceDomain sigmaE_N(nDom);
- InterfaceDomain sigmaN_E(nDom);
- InterfaceDomain sigmaN_W(nDom);
- InterfaceDomain sigmaW_N(nDom);
- InterfaceDomain sigmaW_S(nDom);
-
- InterfaceDomain pmlS_W(nDom);
- InterfaceDomain pmlS_E(nDom);
- InterfaceDomain pmlE_S(nDom);
- InterfaceDomain pmlE_N(nDom);
- InterfaceDomain pmlN_E(nDom);
- InterfaceDomain pmlN_W(nDom);
- InterfaceDomain pmlW_N(nDom);
- InterfaceDomain pmlW_S(nDom);
-
- InterfaceDomain crossPoint(nDom);
-
- // Define topology
- std::vector< std::vector< unsigned int > > topology(nDom);
- for(unsigned int i = 0; i < static_cast< unsigned int >(nDomX); ++i) {
- for(unsigned int j = 0; j < static_cast< unsigned int >(nDomY); ++j) {
- unsigned int index = i * nDomY + j;
-
- omega(index) = Domain(2, index + 1);
-
- pmlS(index) = Domain(2, 10000 + index + 1);
- pmlE(index) = Domain(2, 20000 + index + 1);
- pmlN(index) = Domain(2, 30000 + index + 1);
- pmlW(index) = Domain(2, 40000 + index + 1);
-
- if(withSquarePML || i == static_cast< unsigned int >(nDomX) - 1 || j == 0) {
- pmlSE(index) = Domain(2, 100000 + index + 1);
- }
-
- if(withSquarePML || i == static_cast< unsigned int >(nDomX) - 1 || j == static_cast< unsigned int >(nDomY) - 1) {
- pmlNE(index) = Domain(2, 200000 + index + 1);
- }
-
- if(withSquarePML || i == 0 || j == static_cast< unsigned int >(nDomY) - 1) {
- pmlNW(index) = Domain(2, 300000 + index + 1);
- }
-
- if(withSquarePML || i == 0 || j == 0) {
- pmlSW(index) = Domain(2, 400000 + index + 1);
- }
-
- if(i == circlePosX && j == circlePosY) {
- gammaDir(index) = Domain(1, 1);
- }
-
- if(i != 0) {
- sigmaW(index, (i-1) * nDomY + j) = Domain(1, 40000 + i * nDomY + j + 1);
-
- crossPoint(index, (i-1) * nDomY + j) = Domain(0, 1);
-
- if(withSquarePML || j == static_cast< unsigned int >(nDomY) - 1) sigmaW_N(index, (i-1) * nDomY + j) = Domain(1, 400000 + i * nDomY + j + 1);
- if(withSquarePML || j == 0) sigmaW_S(index, (i-1) * nDomY + j) = Domain(1, 450000 + i * nDomY + j + 1);
-
- if(j != static_cast< unsigned int >(nDomY) - 1) pmlW_N(index, (i-1) * nDomY + j) = Domain(1, 350000 + i * nDomY + j + 1);
- if(j != 0) pmlW_S(index, (i-1) * nDomY + j) = Domain(1, 100000 + i * nDomY + j + 1);
-
- topology[index].push_back((i-1) * nDomY + j);
- }
- if(i != static_cast< unsigned int >(nDomX) - 1) {
- sigmaE(index, (i+1) * nDomY + j) = Domain(1, 20000 + i * nDomY + j + 1);
-
- crossPoint(index, (i+1) * nDomY + j) = Domain(0, 1);
-
- if(withSquarePML || j == 0) sigmaE_S(index, (i+1) * nDomY + j) = Domain(1, 200000 + i * nDomY + j + 1);
- if(withSquarePML || j == static_cast< unsigned int >(nDomY) - 1) sigmaE_N(index, (i+1) * nDomY + j) = Domain(1, 250000 + i * nDomY + j + 1);
-
- if(j != 0) pmlE_S(index, (i+1) * nDomY + j) = Domain(1, 150000 + i * nDomY + j + 1);
- if(j != static_cast< unsigned int >(nDomY) - 1) pmlE_N(index, (i+1) * nDomY + j) = Domain(1, 300000 + i * nDomY + j + 1);
-
- topology[index].push_back((i+1) * nDomY + j);
- }
-
- if(j != 0) {
- sigmaS(index, i * nDomY + (j-1)) = Domain(1, 10000 + i * nDomY + j + 1);
-
- crossPoint(index, i * nDomY + (j-1)) = Domain(0, 1);
-
- if(withSquarePML || i == 0) sigmaS_W(index, i * nDomY + (j-1)) = Domain(1, 100000 + i * nDomY + j + 1);
- if(withSquarePML || i == static_cast< unsigned int >(nDomX) - 1) sigmaS_E(index, i * nDomY + (j-1)) = Domain(1, 150000 + i * nDomY + j + 1);
-
- if(i != 0) pmlS_W(index, i * nDomY + (j-1)) = Domain(1, 450000 + i * nDomY + j + 1);
- if(i != static_cast< unsigned int >(nDomX) - 1) pmlS_E(index, i * nDomY + (j-1)) = Domain(1, 200000 + i * nDomY + j + 1);
-
- topology[index].push_back(i * nDomY + (j-1));
- }
- if(j != static_cast< unsigned int >(nDomY) - 1) {
- sigmaN(index, i * nDomY + (j+1)) = Domain(1, 30000 + i * nDomY + j + 1);
-
- crossPoint(index, i * nDomY + (j+1)) = Domain(0, 1);
-
- if(withSquarePML || i == static_cast< unsigned int >(nDomX) - 1) sigmaN_E(index, i * nDomY + (j+1)) = Domain(1, 300000 + i * nDomY + j + 1);
- if(withSquarePML || i == 0) sigmaN_W(index, i * nDomY + (j+1)) = Domain(1, 350000 + i * nDomY + j + 1);
-
- if(i != static_cast< unsigned int >(nDomX) - 1) pmlN_E(index, i * nDomY + (j+1)) = Domain(1, 250000 + i * nDomY + j + 1);
- if(i != 0) pmlN_W(index, i * nDomY + (j+1)) = Domain(1, 400000 + i * nDomY + j + 1);
-
- topology[index].push_back(i * nDomY + (j+1));
- }
- }
- }
-
- // Create resolution
- Resolution< std::complex< double > > resolution("DDM");
-
- // Create DDM formulation
- FormulationDDM< std::complex< double > > formulation("Helmholtz", resolution, topology);
-
- // Create fields
- SubdomainField< std::complex< double >, Form::Form0 > u(resolution, "u", omega | gammaDir | pmlS | pmlE | pmlN | pmlW | pmlSE | pmlNE | pmlNW | pmlSW, FunctionSpaceType::Lagrange);
- SubdomainField< std::complex< double >, Form::Form0 > lambda(resolution, "lambda", gammaDir, FunctionSpaceType::Lagrange);
-
- InterfaceField< std::complex< double >, Form::Form0 > gS(resolution, "gS", sigmaS | sigmaS_W | sigmaS_E, FunctionSpaceType::Lagrange);
- InterfaceField< std::complex< double >, Form::Form0 > &gS_W = gS;
- InterfaceField< std::complex< double >, Form::Form0 > &gS_E = gS;
-// InterfaceField< std::complex< double >, Form::Form0 > gS_W(resolution, "gS_W", sigmaS_W, FunctionSpaceType::Lagrange);
-// InterfaceField< std::complex< double >, Form::Form0 > gS_E(resolution, "gS_E", sigmaS_E, FunctionSpaceType::Lagrange);
-
- InterfaceField< std::complex< double >, Form::Form0 > gE(resolution, "gE", sigmaE | sigmaE_S | sigmaE_N, FunctionSpaceType::Lagrange);
- InterfaceField< std::complex< double >, Form::Form0 > &gE_S = gE;
- InterfaceField< std::complex< double >, Form::Form0 > &gE_N = gE;
-// InterfaceField< std::complex< double >, Form::Form0 > gE_S(resolution, "gE_S", sigmaE_S, FunctionSpaceType::Lagrange);
-// InterfaceField< std::complex< double >, Form::Form0 > gE_N(resolution, "gE_N", sigmaE_N, FunctionSpaceType::Lagrange);
-
- InterfaceField< std::complex< double >, Form::Form0 > gN(resolution, "gN", sigmaN | sigmaN_E | sigmaN_W, FunctionSpaceType::Lagrange);
- InterfaceField< std::complex< double >, Form::Form0 > &gN_E = gN;
- InterfaceField< std::complex< double >, Form::Form0 > &gN_W = gN;
-// InterfaceField< std::complex< double >, Form::Form0 > gN_E(resolution, "gN_E", sigmaN_E, FunctionSpaceType::Lagrange);
-// InterfaceField< std::complex< double >, Form::Form0 > gN_W(resolution, "gN_W", sigmaN_W, FunctionSpaceType::Lagrange);
-
- InterfaceField< std::complex< double >, Form::Form0 > gW(resolution, "gW", sigmaW | sigmaW_N | sigmaW_S, FunctionSpaceType::Lagrange);
- InterfaceField< std::complex< double >, Form::Form0 > &gW_N = gW;
- InterfaceField< std::complex< double >, Form::Form0 > &gW_S = gW;
-// InterfaceField< std::complex< double >, Form::Form0 > gW_N(resolution, "gW_N", sigmaW_N, FunctionSpaceType::Lagrange);
-// InterfaceField< std::complex< double >, Form::Form0 > gW_S(resolution, "gW_S", sigmaW_S, FunctionSpaceType::Lagrange);
-
- std::complex< double > im(0., 1.);
- AnalyticalFunction< helmholtz2D::SoftScatteringByACylinder< std::complex< double > > > solution(k, circleSize, xSize / 2., ySize / 2., 2 * k);
-
- // Tell to the formulation that g is field that have to be exchanged between subdomains
- formulation.addInterfaceField(gS);
-// formulation.addInterfaceField(gS_W);
-// formulation.addInterfaceField(gS_E);
-
- formulation.addInterfaceField(gE);
-// formulation.addInterfaceField(gE_S);
-// formulation.addInterfaceField(gE_N);
-
- formulation.addInterfaceField(gN);
-// formulation.addInterfaceField(gN_E);
-// formulation.addInterfaceField(gN_W);
-
- formulation.addInterfaceField(gW);
-// formulation.addInterfaceField(gW_N);
-// formulation.addInterfaceField(gW_S);
-
- // Add terms to the formulation
- for(unsigned int i = 0; i < nDom; ++i) {
- // Compute PML parameters
- gmshfem::function::ScalarFunction< std::complex< double > > distSigmaS = abs(y< std::complex< double > >() - (y< std::complex< double > >(omega(i)) - ySize / 2.));
- gmshfem::function::ScalarFunction< std::complex< double > > distSigmaE = abs(x< std::complex< double > >() - (x< std::complex< double > >(omega(i)) + xSize / 2.));
- gmshfem::function::ScalarFunction< std::complex< double > > distSigmaN = abs(y< std::complex< double > >() - (y< std::complex< double > >(omega(i)) + ySize / 2.));
- gmshfem::function::ScalarFunction< std::complex< double > > distSigmaW = abs(x< std::complex< double > >() - (x< std::complex< double > >(omega(i)) - xSize / 2.));
-
- gmshfem::function::ScalarFunction< std::complex< double > > sigS = 1. / (pmlSize - distSigmaS) - 1./ pmlSize;
- gmshfem::function::ScalarFunction< std::complex< double > > sigE = 1. / (pmlSize - distSigmaE) - 1./ pmlSize;
- gmshfem::function::ScalarFunction< std::complex< double > > sigN = 1. / (pmlSize - distSigmaN) - 1./ pmlSize;
- gmshfem::function::ScalarFunction< std::complex< double > > sigW = 1. / (pmlSize - distSigmaW) - 1./ pmlSize;
-
- gmshfem::function::ScalarFunction< std::complex< double > > kyS = 1. + im * sigS / k;
- gmshfem::function::ScalarFunction< std::complex< double > > kxE = 1. + im * sigE / k;
- gmshfem::function::ScalarFunction< std::complex< double > > kyN = 1. + im * sigN / k;
- gmshfem::function::ScalarFunction< std::complex< double > > kxW = 1. + im * sigW / k;
-
- gmshfem::function::TensorFunction< std::complex< double > > DS = tensorDiag< std::complex< double > >(kyS, 1. / kyS, kyS);
- gmshfem::function::ScalarFunction< std::complex< double > > ES = kyS;
-
- gmshfem::function::TensorFunction< std::complex< double > > DE = tensorDiag< std::complex< double > >(1. / kxE, kxE, kxE);
- gmshfem::function::ScalarFunction< std::complex< double > > EE = kxE;
-
- gmshfem::function::TensorFunction< std::complex< double > > DN = tensorDiag< std::complex< double > >(kyN, 1. / kyN, kyN);
- gmshfem::function::ScalarFunction< std::complex< double > > EN = kyN;
-
- gmshfem::function::TensorFunction< std::complex< double > > DW = tensorDiag< std::complex< double > >(1. / kxW, kxW, kxW);
- gmshfem::function::ScalarFunction< std::complex< double > > EW = kxW;
-
- // VOLUME TERMS
-
- formulation(i).integral(grad(dof(u(i))), grad(tf(u(i))), omega(i), gauss);
- formulation(i).integral(- k * k * dof(u(i)), tf(u(i)), omega(i), gauss);
-
- // Physical source
- formulation(i).integral(dof(lambda(i)), tf(u(i)), gammaDir(i), gauss);
- formulation(i).integral(dof(u(i)), tf(lambda(i)), gammaDir(i), gauss);
- formulation(i).integral(formulation.physicalSource(-solution), tf(lambda(i)), gammaDir(i), gauss);
-
- // S
- formulation(i).integral(DS * grad(dof(u(i))), grad(tf(u(i))), pmlS(i), gauss);
- formulation(i).integral(- ES * k * k * dof(u(i)), tf(u(i)), pmlS(i), gauss);
-
- // E
- formulation(i).integral(DE * grad(dof(u(i))), grad(tf(u(i))), pmlE(i), gauss);
- formulation(i).integral(- EE * k * k * dof(u(i)), tf(u(i)), pmlE(i), gauss);
-
- // N
- formulation(i).integral(DN * grad(dof(u(i))), grad(tf(u(i))), pmlN(i), gauss);
- formulation(i).integral(- EN * k * k * dof(u(i)), tf(u(i)), pmlN(i), gauss);
-
- // W
- formulation(i).integral(DW * grad(dof(u(i))), grad(tf(u(i))), pmlW(i), gauss);
- formulation(i).integral(- EW * k * k * dof(u(i)), tf(u(i)), pmlW(i), gauss);
-
- // SE
- formulation(i).integral(DS * DE * grad(dof(u(i))), grad(tf(u(i))), pmlSE(i), gauss);
- formulation(i).integral(- ES * EE * k * k * dof(u(i)), tf(u(i)), pmlSE(i), gauss);
-
- // NE
- formulation(i).integral(DN * DE * grad(dof(u(i))), grad(tf(u(i))), pmlNE(i), gauss);
- formulation(i).integral(- EN * EE * k * k * dof(u(i)), tf(u(i)), pmlNE(i), gauss);
-
- // NW
- formulation(i).integral(DN * DW * grad(dof(u(i))), grad(tf(u(i))), pmlNW(i), gauss);
- formulation(i).integral(- EN * EW * k * k * dof(u(i)), tf(u(i)), pmlNW(i), gauss);
-
- // SW
- formulation(i).integral(DS * DW * grad(dof(u(i))), grad(tf(u(i))), pmlSW(i), gauss);
- formulation(i).integral(- ES * EW * k * k * dof(u(i)), tf(u(i)), pmlSW(i), gauss);
-
- // Artificial sources
- for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
- const unsigned int j = topology[i][jj];
- if(!sigmaS(i,j).isEmpty()) {
- formulation(i).integral(formulation.artificialSource( -gN(j,i) ), tf(u(i)), sigmaS(i,j), gauss);
- formulation(i).integral(formulation.artificialSource( -gN_W(j,i) ), tf(u(i)), sigmaS_W(i,j), gauss);
- formulation(i).integral(formulation.artificialSource( -gN_E(j,i) ), tf(u(i)), sigmaS_E(i,j), gauss);
- }
- if(!sigmaE(i,j).isEmpty()) {
- formulation(i).integral(formulation.artificialSource( -gW(j,i) ), tf(u(i)), sigmaE(i,j), gauss);
- formulation(i).integral(formulation.artificialSource( -gW_S(j,i) ), tf(u(i)), sigmaE_S(i,j), gauss);
- formulation(i).integral(formulation.artificialSource( -gW_N(j,i) ), tf(u(i)), sigmaE_N(i,j), gauss);
- }
- if(!sigmaN(i,j).isEmpty()) {
- formulation(i).integral(formulation.artificialSource( -gS(j,i) ), tf(u(i)), sigmaN(i,j), gauss);
- formulation(i).integral(formulation.artificialSource( -gS_E(j,i) ), tf(u(i)), sigmaN_E(i,j), gauss);
- formulation(i).integral(formulation.artificialSource( -gS_W(j,i) ), tf(u(i)), sigmaN_W(i,j), gauss);
- }
- if(!sigmaW(i,j).isEmpty()) {
- formulation(i).integral(formulation.artificialSource( -gE(j,i) ), tf(u(i)), sigmaW(i,j), gauss);
- formulation(i).integral(formulation.artificialSource( -gE_N(j,i) ), tf(u(i)), sigmaW_N(i,j), gauss);
- formulation(i).integral(formulation.artificialSource( -gE_S(j,i) ), tf(u(i)), sigmaW_S(i,j), gauss);
- }
- }
-
- // INTERFACE TERMS
- for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
- const unsigned int j = topology[i][jj];
- // S
- if(!sigmaS(i,j).isEmpty()) {
- formulation(i,j).integral(dof(gS(i,j)), tf(gS(i,j)), sigmaS(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( gN(j,i) ), tf(gS(i,j)), sigmaS(i,j), gauss);
-
- formulation(i,j).integral(dof(gS_W(i,j)), tf(gS_W(i,j)), sigmaS_W(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( gN_W(j,i) ), tf(gS_W(i,j)), sigmaS_W(i,j), gauss);
-
- formulation(i,j).integral(dof(gS_E(i,j)), tf(gS_E(i,j)), sigmaS_E(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( gN_E(j,i) ), tf(gS_E(i,j)), sigmaS_E(i,j), gauss);
-
- if(!pmlS_W(i,j).isEmpty() && withSquarePML) formulation(i,j).integral(formulation.artificialSource( 2. * gE_S(i - nDomY,i) ), tf(gS(i,j)), pmlS_W(i,j), gauss);
- if(!pmlS_E(i,j).isEmpty() && withSquarePML) formulation(i,j).integral(formulation.artificialSource( 2. * gW_S(i + nDomY,i) ), tf(gS(i,j)), pmlS_E(i,j), gauss);
-
- formulation(i,j).integral(- 2. * DS * grad(u(i)), grad(tf(gS(i,j))), pmlS(i), gauss);
- formulation(i,j).integral(2. * ES * k * k * u(i), tf(gS(i,j)), pmlS(i), gauss);
-
- formulation(i,j).integral(- 2. * DS * DW * grad(u(i)), grad(tf(gS_W(i,j))), pmlSW(i), gauss);
- formulation(i,j).integral(2. * ES * EW * k * k * u(i), tf(gS_W(i,j)), pmlSW(i), gauss);
-
- formulation(i,j).integral(- 2. * DS * DE * grad(u(i)), grad(tf(gS_E(i,j))), pmlSE(i), gauss);
- formulation(i,j).integral(2. * ES * EE * k * k * u(i), tf(gS_E(i,j)), pmlSE(i), gauss);
- }
-
- // E
- if(!sigmaE(i,j).isEmpty()) {
- formulation(i,j).integral(dof(gE(i,j)), tf(gE(i,j)), sigmaE(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( gW(j,i) ), tf(gE(i,j)), sigmaE(i,j), gauss);
-
- formulation(i,j).integral(dof(gE_S(i,j)), tf(gE_S(i,j)), sigmaE_S(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( gW_S(j,i) ), tf(gE_S(i,j)), sigmaE_S(i,j), gauss);
-
- formulation(i,j).integral(dof(gE_N(i,j)), tf(gE_N(i,j)), sigmaE_N(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( gW_N(j,i) ), tf(gE_N(i,j)), sigmaE_N(i,j), gauss);
-
- if(!pmlE_S(i,j).isEmpty() && withSquarePML) formulation(i,j).integral(formulation.artificialSource( 2. * gN_E(i - 1,i) ), tf(gE(i,j)), pmlE_S(i,j), gauss);
- if(!pmlE_N(i,j).isEmpty() && withSquarePML) formulation(i,j).integral(formulation.artificialSource( 2. * gS_E(i + 1,i) ), tf(gE(i,j)), pmlE_N(i,j), gauss);
-
- formulation(i,j).integral(- 2. * DE * grad(u(i)), grad(tf(gE(i,j))), pmlE(i), gauss);
- formulation(i,j).integral(2. * EE * k * k * u(i), tf(gE(i,j)), pmlE(i), gauss);
-
- formulation(i,j).integral(- 2. * DS * DE * grad(u(i)), grad(tf(gE_S(i,j))), pmlSE(i), gauss);
- formulation(i,j).integral(2. * ES * EE * k * k * u(i), tf(gE_S(i,j)), pmlSE(i), gauss);
-
- formulation(i,j).integral(- 2. * DN * DE * grad(u(i)), grad(tf(gE_N(i,j))), pmlNE(i), gauss);
- formulation(i,j).integral(2. * EN * EE * k * k * u(i), tf(gE_N(i,j)), pmlNE(i), gauss);
- }
-
- // N
- if(!sigmaN(i,j).isEmpty()) {
- formulation(i,j).integral(dof(gN(i,j)), tf(gN(i,j)), sigmaN(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( gS(j,i) ), tf(gN(i,j)), sigmaN(i,j), gauss);
-
- formulation(i,j).integral(dof(gN_E(i,j)), tf(gN_E(i,j)), sigmaN_E(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( gS_E(j,i) ), tf(gN_E(i,j)), sigmaN_E(i,j), gauss);
-
- formulation(i,j).integral(dof(gN_W(i,j)), tf(gN_W(i,j)), sigmaN_W(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( gS_W(j,i) ), tf(gN_W(i,j)), sigmaN_W(i,j), gauss);
-
- if(!pmlN_E(i,j).isEmpty() && withSquarePML) formulation(i,j).integral(formulation.artificialSource( 2. * gW_N(i + nDomY,i) ), tf(gN(i,j)), pmlN_E(i,j), gauss);
- if(!pmlN_W(i,j).isEmpty() && withSquarePML) formulation(i,j).integral(formulation.artificialSource( 2. * gE_N(i - nDomY,i) ), tf(gN(i,j)), pmlN_W(i,j), gauss);
-
- formulation(i,j).integral(- 2. * DN * grad(u(i)), grad(tf(gN(i,j))), pmlN(i), gauss);
- formulation(i,j).integral(2. * EN * k * k * u(i), tf(gN(i,j)), pmlN(i), gauss);
-
- formulation(i,j).integral(- 2. * DN * DE * grad(u(i)), grad(tf(gN_E(i,j))), pmlNE(i), gauss);
- formulation(i,j).integral(2. * EN * EE * k * k * u(i), tf(gN_E(i,j)), pmlNE(i), gauss);
-
- formulation(i,j).integral(- 2. * DN * DW * grad(u(i)), grad(tf(gN_W(i,j))), pmlNW(i), gauss);
- formulation(i,j).integral(2. * EN * EW * k * k * u(i), tf(gN_W(i,j)), pmlNW(i), gauss);
- }
-
- // W
- if(!sigmaW(i,j).isEmpty()) {
- formulation(i,j).integral(dof(gW(i,j)), tf(gW(i,j)), sigmaW(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( gE(j,i) ), tf(gW(i,j)), sigmaW(i,j), gauss);
-
- formulation(i,j).integral(dof(gW_N(i,j)), tf(gW_N(i,j)), sigmaW_N(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( gE_N(j,i) ), tf(gW_N(i,j)), sigmaW_N(i,j), gauss);
-
- formulation(i,j).integral(dof(gW_S(i,j)), tf(gW_S(i,j)), sigmaW_S(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( gE_S(j,i) ), tf(gW_S(i,j)), sigmaW_S(i,j), gauss);
-
- if(!pmlW_N(i,j).isEmpty() && withSquarePML) formulation(i,j).integral(formulation.artificialSource( 2. * gS_W(i + 1,i) ), tf(gW(i,j)), pmlW_N(i,j), gauss);
- if(!pmlW_S(i,j).isEmpty() && withSquarePML) formulation(i,j).integral(formulation.artificialSource( 2. * gN_W(i - 1,i) ), tf(gW(i,j)), pmlW_S(i,j), gauss);
-
- formulation(i,j).integral(- 2. * DW * grad(u(i)), grad(tf(gW(i,j))), pmlW(i), gauss);
- formulation(i,j).integral(2. * EW * k * k * u(i), tf(gW(i,j)), pmlW(i), gauss);
-
- formulation(i,j).integral(- 2. * DN * DW * grad(u(i)), grad(tf(gW_N(i,j))), pmlNW(i), gauss);
- formulation(i,j).integral(2. * EN * EW * k * k * u(i), tf(gW_N(i,j)), pmlNW(i), gauss);
-
- formulation(i,j).integral(- 2. * DS * DW * grad(u(i)), grad(tf(gW_S(i,j))), pmlSW(i), gauss);
- formulation(i,j).integral(2. * ES * EW * k * k * u(i), tf(gW_S(i,j)), pmlSW(i), gauss);
- }
- }
- }
-
- // Solve the DDM formulation
- formulation.pre();
- formulation.solve("gmres", 1e-6, 1000);
-
- if(errorMono) {
- gmshfem::domain::Domain omegaMono, pmlSMono, pmlEMono, pmlNMono, pmlWMono, pmlSEMono, pmlNEMono, pmlNWMono, pmlSWMono;
- for(unsigned int i = 0; i < static_cast< unsigned int >(nDom); ++i) {
- omegaMono |= omega(i);
- }
-
- for(unsigned int i = 0; i < static_cast< unsigned int >(nDomX); ++i) {
- pmlSMono |= pmlS(i * nDomY + 0);
- pmlNMono |= pmlN(i * nDomY + nDomY - 1);
- }
- for(unsigned int j = 0; j < static_cast< unsigned int >(nDomY); ++j) {
- pmlEMono |= pmlE((nDomX - 1) * nDomY + j);
- pmlWMono |= pmlW(0 * nDomY + j);
- }
- pmlSEMono = pmlSE((nDomX - 1) * nDomY + 0);
- pmlNEMono = pmlNE((nDomX - 1) * nDomY + nDomY - 1);
- pmlNWMono = pmlNW(0 * nDomY + nDomY - 1);
- pmlSWMono = pmlSW(0);
-
- gmshfem::function::TensorFunction< std::complex< double > > DSmono = getPmlDParameter(k, pmlSize, 0., false);
- gmshfem::function::TensorFunction< std::complex< double > > DEmono = getPmlDParameter(k, pmlSize, nDomX * xSize, true);
- gmshfem::function::TensorFunction< std::complex< double > > DNmono = getPmlDParameter(k, pmlSize, nDomY * ySize, false);
- gmshfem::function::TensorFunction< std::complex< double > > DWmono = getPmlDParameter(k, pmlSize, 0., true);
-
- gmshfem::function::ScalarFunction< std::complex< double > > ESmono = getPmlEParameter(k, pmlSize, 0., false);
- gmshfem::function::ScalarFunction< std::complex< double > > EEmono = getPmlEParameter(k, pmlSize, nDomX * xSize, true);
- gmshfem::function::ScalarFunction< std::complex< double > > ENmono = getPmlEParameter(k, pmlSize, nDomY * ySize, false);
- gmshfem::function::ScalarFunction< std::complex< double > > EWmono = getPmlEParameter(k, pmlSize, 0., true);
-
- gmshfem::field::Field< std::complex< double >, gmshfem::field::Form::Form0 > uMono(resolution, "uMono", gammaDir(circlePosX * nDomY + circlePosY) | omegaMono | pmlSMono | pmlEMono | pmlNMono | pmlWMono | pmlSEMono | pmlNEMono | pmlNWMono | pmlSWMono, FunctionSpaceType::Lagrange);
- gmshfem::field::Field< std::complex< double >, gmshfem::field::Form::Form0 > lambdaMono(resolution, "lambdaMono", gammaDir(circlePosX * nDomY + circlePosY), FunctionSpaceType::Lagrange);
-
- Formulation< std::complex< double > > monodomain("HelmholtzMono", resolution);
-
- monodomain.integral(grad(dof(uMono)), grad(tf(uMono)), omegaMono, gauss);
- monodomain.integral(- k * k * dof(uMono), tf(uMono), omegaMono, gauss);
-
- monodomain.integral(dof(lambdaMono), tf(uMono), gammaDir(circlePosX * nDomY + circlePosY), gauss);
- monodomain.integral(dof(uMono), tf(lambdaMono), gammaDir(circlePosX * nDomY + circlePosY), gauss);
- monodomain.integral(- solution, tf(lambdaMono), gammaDir(circlePosX * nDomY + circlePosY), gauss);
-
- monodomain.integral(DSmono * grad(dof(uMono)), grad(tf(uMono)), pmlSMono, gauss);
- monodomain.integral(- k * k * ESmono * dof(uMono), tf(uMono), pmlSMono, gauss);
-
- monodomain.integral(DEmono * grad(dof(uMono)), grad(tf(uMono)), pmlEMono, gauss);
- monodomain.integral(- k * k * EEmono * dof(uMono), tf(uMono), pmlEMono, gauss);
-
- monodomain.integral(DNmono * grad(dof(uMono)), grad(tf(uMono)), pmlNMono, gauss);
- monodomain.integral(- k * k * ENmono * dof(uMono), tf(uMono), pmlNMono, gauss);
-
- monodomain.integral(DWmono * grad(dof(uMono)), grad(tf(uMono)), pmlWMono, gauss);
- monodomain.integral(- k * k * EWmono * dof(uMono), tf(uMono), pmlWMono, gauss);
-
- monodomain.integral(DSmono * DEmono * grad(dof(uMono)), grad(tf(uMono)), pmlSEMono, gauss);
- monodomain.integral(- k * k * ESmono * EEmono * dof(uMono), tf(uMono), pmlSEMono, gauss);
-
- monodomain.integral(DNmono * DEmono * grad(dof(uMono)), grad(tf(uMono)), pmlNEMono, gauss);
- monodomain.integral(- k * k * ENmono * EEmono * dof(uMono), tf(uMono), pmlNEMono, gauss);
-
- monodomain.integral(DNmono * DWmono * grad(dof(uMono)), grad(tf(uMono)), pmlNWMono, gauss);
- monodomain.integral(- k * k * ENmono * EWmono * dof(uMono), tf(uMono), pmlNWMono, gauss);
-
- monodomain.integral(DSmono * DWmono * grad(dof(uMono)), grad(tf(uMono)), pmlSWMono, gauss);
- monodomain.integral(- k * k * ESmono * EWmono * dof(uMono), tf(uMono), pmlSWMono, gauss);
-
- monodomain.pre();
- monodomain.assemble();
- monodomain.solve();
-
- save(uMono);
-
- for(unsigned int i = 0; i < nDom; ++i) {
- save(uMono - u(i), omega(i), "eMono_" + std::to_string(i));
- }
-
- // L2 error
- double num = 0., den = 0.;
- for(unsigned int i = 0; i < nDom; ++i) {
- std::complex< double > denLocal = integrate(pow(abs(uMono), 2), omega(i), gauss);
- std::complex< double > numLocal = integrate(pow(abs(uMono - u(i)), 2), omega(i), gauss);
- num += numLocal.real();
- den += denLocal.real();
- }
- msg::info << "L2 mono domain error = " << std::sqrt(num / den) << msg::endl;
- }
-
- for(unsigned int i = 0; i < nDom; ++i) {
- save(+u(i), omega(i), "u_" + std::to_string(i));
- //save(u(i));
- save(solution - u(i), omega(i), "e_" + std::to_string(i));
- for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
- const unsigned int j = topology[i][jj];
- if(!sigmaS(i,j).isEmpty()) save(gS(i,j));
- if(!sigmaE(i,j).isEmpty()) save(gE(i,j));
- if(!sigmaN(i,j).isEmpty()) save(gN(i,j));
- if(!sigmaW(i,j).isEmpty()) save(gW(i,j));
- }
- }
-
- return 0;
-}
-
-gmshfem::function::TensorFunction< std::complex< double > > getPmlDParameter(const double k, const double pmlSize, const double pos, const bool onX)
-{
- gmshfem::function::ScalarFunction< std::complex< double > > kx = 1.;
- gmshfem::function::ScalarFunction< std::complex< double > > ky = 1.;
- gmshfem::function::ScalarFunction< std::complex< double > > kz = 1.;
-
- std::complex< double > I(0., 1.);
- if(onX) {
- gmshfem::function::ScalarFunction< std::complex< double > > distSigma = abs(x< std::complex< double > >() - pos);
- gmshfem::function::ScalarFunction< std::complex< double > > sigmaX = 1. / (pmlSize - distSigma) - 1./ pmlSize;
- kx = 1. + I * sigmaX / k;
- }
- else { // onY
- gmshfem::function::ScalarFunction< std::complex< double > > distSigma = abs(y< std::complex< double > >() - pos);
- gmshfem::function::ScalarFunction< std::complex< double > > sigmaY = 1. / (pmlSize - distSigma) - 1./ pmlSize;
- ky = 1. + I * sigmaY / k;
- }
-
- return tensorDiag< std::complex< double > >(ky * kz / kx, kx * kz / ky, kx * ky / kz);
-}
-
-gmshfem::function::ScalarFunction< std::complex< double > > getPmlEParameter(const double k, const double pmlSize, const double pos, const bool onX)
-{
- gmshfem::function::ScalarFunction< std::complex< double > > kx = 1.;
- gmshfem::function::ScalarFunction< std::complex< double > > ky = 1.;
- gmshfem::function::ScalarFunction< std::complex< double > > kz = 1.;
-
- std::complex< double > I(0., 1.);
- if(onX) {
- gmshfem::function::ScalarFunction< std::complex< double > > distSigma = abs(x< std::complex< double > >() - pos);
- gmshfem::function::ScalarFunction< std::complex< double > > sigmaX = 1. / (pmlSize - distSigma) - 1./ pmlSize;
- kx = 1. + I * sigmaX / k;
- }
- else { // onY
- gmshfem::function::ScalarFunction< std::complex< double > > distSigma = abs(y< std::complex< double > >() - pos);
- gmshfem::function::ScalarFunction< std::complex< double > > sigmaY = 1. / (pmlSize - distSigma) - 1./ pmlSize;
- ky = 1. + I * sigmaY / k;
- }
-
- return kx * ky * kz;
-}
diff --git a/demos/helmholtz/scattering/testWithoutGInPML/main.cpp b/demos/helmholtz/scattering/testWithoutGInPML/main.cpp
deleted file mode 100644
index 8a35635126531b1be69c9b5a12122c9bf0455616..0000000000000000000000000000000000000000
--- a/demos/helmholtz/scattering/testWithoutGInPML/main.cpp
+++ /dev/null
@@ -1,767 +0,0 @@
-#include "GmshDdm.h"
-
-#include "FormulationDDM.h"
-
-#include "Message.h"
-#include "AnalyticalFunction.h"
-
-#include "gmsh.h"
-
-using namespace gmshddm;
-using namespace gmshddm::common;
-using namespace gmshddm::domain;
-using namespace gmshddm::problem;
-using namespace gmshddm::field;
-
-using namespace gmshfem;
-using namespace gmshfem::analytics;
-using namespace gmshfem::domain;
-using namespace gmshfem::problem;
-using namespace gmshfem::field;
-using namespace gmshfem::function;
-using namespace gmshfem::post;
-
-gmshfem::function::TensorFunction< std::complex< double > > getPmlDParameter(const double k, const double pmlSize, const double pos, const bool onX);
-gmshfem::function::ScalarFunction< std::complex< double > > getPmlEParameter(const double k, const double pmlSize, const double pos, const bool onX);
-
-void checkerboard(const unsigned int nDomX, const unsigned int nDomY, const double xSize, const double ySize, const double circleSize, const double pmlSize, const double lc, const bool pml = true, const unsigned int circlePosX = 0, const unsigned int circlePosY = 0)
-{
- std::vector< std::vector< int > > omega(nDomX);
- for(unsigned int i = 0; i < nDomX; ++i) {
- omega[i].resize(nDomY);
- }
-
- // ******************
- // borders
- // ******************
-
- // ****(2)****
- // * *
- // (3) (1)
- // * *
- // ****(0)****
- std::vector< std::vector< std::vector< int > > > borders(nDomX);
- for(unsigned int i = 0; i < nDomX; ++i) {
- borders[i].resize(nDomY);
- for(unsigned int j = 0; j < nDomY; ++j) {
- borders[i][j].resize(4);
- }
- }
-
- // ******************
- // pmls
- // ******************
-
- // 1 0
- // 0 ****(2)**** 1
- // * *
- // (3) (1)
- // * *
- // 1 ****(0)**** 0
- // 0 1
-
- std::vector< std::vector< std::vector< int > > > pmls(nDomX);
- std::vector< std::vector< std::vector< int > > > pmlsInf(nDomX);
- std::vector< std::vector< std::vector< std::vector< int > > > > pmlsBnd(nDomX);
- for(unsigned int i = 0; i < nDomX; ++i) {
- pmls[i].resize(nDomY);
- pmlsInf[i].resize(nDomY);
- pmlsBnd[i].resize(nDomY);
- for(unsigned int j = 0; j < nDomY; ++j) {
- pmls[i][j].resize(4);
- pmlsInf[i][j].resize(4);
- pmlsBnd[i][j].resize(4);
- for(unsigned int k = 0; k < 4; ++k) {
- pmlsBnd[i][j][k].resize(2);
- }
- }
- }
-
- // ******************
- // pmlsSquare
- // ******************
-
- // (2)*******(1)
- // * *
- // * *
- // * *
- // (3)*******(0)
-
- std::vector< std::vector< std::vector< int > > > pmlsSquare(nDomX);
- for(unsigned int i = 0; i < nDomX; ++i) {
- pmlsSquare[i].resize(nDomY);
- for(unsigned int j = 0; j < nDomY; ++j) {
- pmlsSquare[i][j].resize(4);
- }
- }
-
- std::vector< int > left(nDomY);
- int bottom = 0;
- for(unsigned int i = 0; i < nDomX; ++i) {
- for(unsigned int j = 0; j < nDomY; ++j) {
- int p[4];
- p[0] = gmsh::model::geo::addPoint(i * xSize, j * ySize, 0., lc);
- p[1] = gmsh::model::geo::addPoint((i + 1) * xSize, j * ySize, 0., lc);
- p[2] = gmsh::model::geo::addPoint((i + 1) * xSize, (j + 1) * ySize, 0., lc);
- p[3] = gmsh::model::geo::addPoint(i * xSize, (j + 1) * ySize, 0., lc);
-
- int l[4];
- borders[i][j][0] = l[0] = gmsh::model::geo::addLine(p[0], p[1]);
- borders[i][j][1] = l[1] = gmsh::model::geo::addLine(p[1], p[2]);
- borders[i][j][2] = l[2] = gmsh::model::geo::addLine(p[2], p[3]);
- borders[i][j][3] = l[3] = gmsh::model::geo::addLine(p[3], p[0]);
-
- if(i == 0) {
- left[j] = l[1];
- }
- else {
- borders[i][j][3] = left[j];
- left[j] = l[1];
- }
-
- if(j == 0) {
- bottom = l[2];
- }
- else {
- borders[i][j][0] = bottom;
- bottom = l[2];
- }
-
- int ll = gmsh::model::geo::addCurveLoop({l[0], l[1], l[2], l[3]});
-
- int surface = 0;
- if(i == circlePosX && j == circlePosY) {
- // circle
- int pC[5];
- pC[0] = gmsh::model::geo::addPoint(circlePosX * i + xSize / 2., circlePosY * j + ySize / 2., 0., lc);
- pC[1] = gmsh::model::geo::addPoint(circlePosX * i + xSize / 2. + circleSize, circlePosY * j + ySize / 2., 0., lc);
- pC[2] = gmsh::model::geo::addPoint(circlePosX * i + xSize / 2., circlePosY * j + ySize / 2. + circleSize, 0., lc);
- pC[3] = gmsh::model::geo::addPoint(circlePosX * i + xSize / 2. - circleSize, circlePosY * j + ySize / 2., 0., lc);
- pC[4] = gmsh::model::geo::addPoint(circlePosX * i + xSize / 2., circlePosY * j + ySize / 2. - circleSize, 0., lc);
-
- int lC[4];
- lC[0] = gmsh::model::geo::addCircleArc(pC[1], pC[0], pC[2]);
- lC[1] = gmsh::model::geo::addCircleArc(pC[2], pC[0], pC[3]);
- lC[2] = gmsh::model::geo::addCircleArc(pC[3], pC[0], pC[4]);
- lC[3] = gmsh::model::geo::addCircleArc(pC[4], pC[0], pC[1]);
-
- // surface
- int llC;
- llC = gmsh::model::geo::addCurveLoop({lC[0], lC[1], lC[2], lC[3]});
-
- surface = gmsh::model::geo::addPlaneSurface({ll, llC});
-
- gmsh::model::addPhysicalGroup(1, {lC[0], lC[1], lC[2], lC[3]}, 1);
- gmsh::model::setPhysicalName(1, 1, "gammaScat");
- }
- else {
- surface = gmsh::model::geo::addPlaneSurface({ll});
- }
- omega[i][j] = surface;
-
- if(pml) {
- // pmls
- double extrudeX[4] = {0., pmlSize, 0., -pmlSize};
- double extrudeY[4] = {-pmlSize, 0., pmlSize, 0.};
- for(unsigned int k = 0; k < 4; ++k) {
- std::vector< std::pair< int, int > > extrudeEntities;
- gmsh::model::geo::extrude({std::make_pair(1, ((k == 3 && i != 0) || (k == 0 && j != 0) ? 1 : -1) * borders[i][j][k])}, extrudeX[k], extrudeY[k], 0., extrudeEntities, {static_cast< int >(pmlSize / lc)}, std::vector< double >(), true);
- pmlsInf[i][j][k] = extrudeEntities[0].second;
- pmls[i][j][k] = extrudeEntities[1].second;
- if((k == 3 && i != 0) || (k == 0 && j != 0)) {
- pmlsBnd[i][j][k][0] = extrudeEntities[2].second;
- pmlsBnd[i][j][k][1] = extrudeEntities[3].second;
- }
- else {
- pmlsBnd[i][j][k][0] = extrudeEntities[3].second;
- pmlsBnd[i][j][k][1] = extrudeEntities[4].second;
- }
- }
-
- // pmlsSquare
- double extrudeSquareX[4] = {pmlSize, pmlSize, -pmlSize, -pmlSize};
- int side[4] = {0, 2, 2, 0};
- int sideBnd[4] = {1, 0, 1, 0};
- for(unsigned int k = 0; k < 4; ++k) {
- std::vector< std::pair< int, int > > extrudeEntities;
- gmsh::model::geo::extrude({std::make_pair(1, -pmlsBnd[i][j][side[k]][sideBnd[k]])}, extrudeSquareX[k], 0., 0., extrudeEntities, {static_cast< int >(pmlSize / lc)}, std::vector< double >(), true);
- pmlsSquare[i][j][k] = extrudeEntities[1].second;
- }
- }
- }
- }
-
- gmsh::model::geo::synchronize();
-
- // ******************
- // physicals
- // ******************
-
- for(unsigned int i = 0; i < nDomX; ++i) {
- for(unsigned int j = 0; j < nDomY; ++j) {
- gmsh::model::addPhysicalGroup(2, {omega[i][j]}, i * nDomY + j + 1);
- gmsh::model::setPhysicalName(2, i * nDomY + j + 1, "omega_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(1, {borders[i][j][0]}, 10000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 10000 + i * nDomY + j + 1, "sigmaS_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(1, {borders[i][j][1]}, 20000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 20000 + i * nDomY + j + 1, "sigmaE_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(1, {borders[i][j][2]}, 30000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 30000 + i * nDomY + j + 1, "sigmaN_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(1, {borders[i][j][3]}, 40000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 40000 + i * nDomY + j + 1, "sigmaW_" + std::to_string(i) + "_" + std::to_string(j));
-
- if(pml) {
- // PMLs
- gmsh::model::addPhysicalGroup(2, {pmls[i][j][0]}, 10000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(2, 10000 + i * nDomY + j + 1, "pmlS_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(2, {pmls[i][j][1]}, 20000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(2, 20000 + i * nDomY + j + 1, "pmlE_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(2, {pmls[i][j][2]}, 30000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(2, 30000 + i * nDomY + j + 1, "pmlN_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(2, {pmls[i][j][3]}, 40000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(2, 40000 + i * nDomY + j + 1, "pmlW_" + std::to_string(i) + "_" + std::to_string(j));
-
- // PMLs square
- gmsh::model::addPhysicalGroup(2, {pmlsSquare[i][j][0]}, 100000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(2, 100000 + i * nDomY + j + 1, "pmlSE_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(2, {pmlsSquare[i][j][1]}, 200000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(2, 200000 + i * nDomY + j + 1, "pmlNE_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(2, {pmlsSquare[i][j][2]}, 300000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(2, 300000 + i * nDomY + j + 1, "pmlNW_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(2, {pmlsSquare[i][j][3]}, 400000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(2, 400000 + i * nDomY + j + 1, "pmlSW_" + std::to_string(i) + "_" + std::to_string(j));
-
- // Sigmas in PMLs
- gmsh::model::addPhysicalGroup(1, {pmlsBnd[i][j][3][1]}, 100000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 100000 + i * nDomY + j + 1, "sigmaS_W_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(1, {pmlsBnd[i][j][1][0]}, 150000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 150000 + i * nDomY + j + 1, "sigmaS_E_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(1, {pmlsBnd[i][j][0][1]}, 200000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 200000 + i * nDomY + j + 1, "sigmaE_S_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(1, {pmlsBnd[i][j][2][0]}, 250000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 250000 + i * nDomY + j + 1, "sigmaE_N_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(1, {pmlsBnd[i][j][1][1]}, 300000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 300000 + i * nDomY + j + 1, "sigmaN_E_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(1, {pmlsBnd[i][j][3][0]}, 350000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 350000 + i * nDomY + j + 1, "sigmaN_E_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(1, {pmlsBnd[i][j][2][1]}, 400000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 400000 + i * nDomY + j + 1, "sigmaW_N_" + std::to_string(i) + "_" + std::to_string(j));
-
- gmsh::model::addPhysicalGroup(1, {pmlsBnd[i][j][0][0]}, 450000 + i * nDomY + j + 1);
- gmsh::model::setPhysicalName(1, 450000 + i * nDomY + j + 1, "sigmaW_S_" + std::to_string(i) + "_" + std::to_string(j));
-
- }
- }
- }
-
- gmsh::model::geo::synchronize();
- gmsh::model::mesh::generate();
-}
-
-int main(int argc, char **argv)
-{
- GmshDdm gmshDdm(argc, argv);
-
- double pi = 3.14159265359;
-
- int nDomX = 2, nDomY = 2;
- gmshDdm.userDefinedParameter(nDomX, "nDomX");
- gmshDdm.userDefinedParameter(nDomY, "nDomY");
- double xSize = 1., ySize = 1.;
- gmshDdm.userDefinedParameter(xSize, "xSize");
- gmshDdm.userDefinedParameter(ySize, "ySize");
- double circleSize = 0.1;
- gmshDdm.userDefinedParameter(circleSize, "circleSize");
- double pmlSize = 0.1;
- gmshDdm.userDefinedParameter(pmlSize, "pmlSize");
- double k = 10. * pi;
- gmshDdm.userDefinedParameter(k, "k");
- double lc = 0.02;
- gmshDdm.userDefinedParameter(lc, "lc");
- std::string gauss = "Gauss3";
- gmshDdm.userDefinedParameter(gauss, "gauss");
- int circlePosX = 0, circlePosY = 0;
- gmshDdm.userDefinedParameter(circlePosX, "circlePosX");
- gmshDdm.userDefinedParameter(circlePosY, "circlePosY");
- bool errorMono = false;
- gmshDdm.userDefinedParameter(errorMono, "errorMono");
-
- // Build geometry and mesh using gmsh API
- checkerboard(nDomX, nDomY, xSize, ySize, circleSize, pmlSize, lc, true, circlePosX, circlePosY);
-
- unsigned int nDom = nDomX * nDomY;
-
- // | |
- // NW | N | NE
- // ----**************----
- // * *
- // * *
- // W * * E
- // * *
- // * *
- // ----**************----
- // SW | S | SE
- // | |
-
- // Define domain
- Subdomain omega(nDom);
- Subdomain gammaDir(nDom);
-
- Subdomain pmlS(nDom);
- Subdomain pmlE(nDom);
- Subdomain pmlN(nDom);
- Subdomain pmlW(nDom);
-
- Subdomain pmlSE(nDom);
- Subdomain pmlNE(nDom);
- Subdomain pmlNW(nDom);
- Subdomain pmlSW(nDom);
-
- Interface sigmaS(nDom);
- Interface sigmaE(nDom);
- Interface sigmaN(nDom);
- Interface sigmaW(nDom);
-
- Interface sigmaS_W(nDom);
- Interface sigmaS_E(nDom);
- Interface sigmaE_S(nDom);
- Interface sigmaE_N(nDom);
- Interface sigmaN_E(nDom);
- Interface sigmaN_W(nDom);
- Interface sigmaW_N(nDom);
- Interface sigmaW_S(nDom);
-
- Interface pmlS_W(nDom);
- Interface pmlS_E(nDom);
- Interface pmlE_S(nDom);
- Interface pmlE_N(nDom);
- Interface pmlN_E(nDom);
- Interface pmlN_W(nDom);
- Interface pmlW_N(nDom);
- Interface pmlW_S(nDom);
-
- // Define topology
- std::vector< std::vector< unsigned int > > topology(nDom);
- for(unsigned int i = 0; i < static_cast< unsigned int >(nDomX); ++i) {
- for(unsigned int j = 0; j < static_cast< unsigned int >(nDomY); ++j) {
- unsigned int index = i * nDomY + j;
-
- omega(index) = Domain(2, index + 1);
-
- pmlS(index) = Domain(2, 10000 + index + 1);
- pmlE(index) = Domain(2, 20000 + index + 1);
- pmlN(index) = Domain(2, 30000 + index + 1);
- pmlW(index) = Domain(2, 40000 + index + 1);
-
- if(i == static_cast< unsigned int >(nDomX) - 1 || j == 0) pmlSE(index) = Domain(2, 100000 + index + 1);
- if(i == static_cast< unsigned int >(nDomX) - 1 || j == static_cast< unsigned int >(nDomY) - 1) pmlNE(index) = Domain(2, 200000 + index + 1);
- if(i == 0 || j == static_cast< unsigned int >(nDomY) - 1) pmlNW(index) = Domain(2, 300000 + index + 1);
- if(i == 0 || j == 0) pmlSW(index) = Domain(2, 400000 + index + 1);
-
- if(i == circlePosX && j == circlePosY) {
- gammaDir(index) = Domain(1, 1);
- }
-
- if(i != 0) {
- sigmaW(index, (i-1) * nDomY + j) = Domain(1, 40000 + i * nDomY + j + 1);
-
- if(j == static_cast< unsigned int >(nDomY) - 1) sigmaW_N(index, (i-1) * nDomY + j) = Domain(1, 400000 + i * nDomY + j + 1);
- if(j == 0) sigmaW_S(index, (i-1) * nDomY + j) = Domain(1, 450000 + i * nDomY + j + 1);
-
- if(j != static_cast< unsigned int >(nDomY) - 1) pmlW_N(index, (i-1) * nDomY + j) = Domain(1, 350000 + i * nDomY + j + 1);
- if(j != 0) pmlW_S(index, (i-1) * nDomY + j) = Domain(1, 100000 + i * nDomY + j + 1);
-
- topology[index].push_back((i-1) * nDomY + j);
- }
- if(i != static_cast< unsigned int >(nDomX) - 1) {
- sigmaE(index, (i+1) * nDomY + j) = Domain(1, 20000 + i * nDomY + j + 1);
-
- if(j == 0) sigmaE_S(index, (i+1) * nDomY + j) = Domain(1, 200000 + i * nDomY + j + 1);
- if(j == static_cast< unsigned int >(nDomY) - 1) sigmaE_N(index, (i+1) * nDomY + j) = Domain(1, 250000 + i * nDomY + j + 1);
-
- if(j != 0) pmlE_S(index, (i+1) * nDomY + j) = Domain(1, 150000 + i * nDomY + j + 1);
- if(j != static_cast< unsigned int >(nDomY) - 1) pmlE_N(index, (i+1) * nDomY + j) = Domain(1, 300000 + i * nDomY + j + 1);
-
- topology[index].push_back((i+1) * nDomY + j);
- }
-
- if(j != 0) {
- sigmaS(index, i * nDomY + (j-1)) = Domain(1, 10000 + i * nDomY + j + 1);
-
- if(i == 0) sigmaS_W(index, i * nDomY + (j-1)) = Domain(1, 100000 + i * nDomY + j + 1);
- if(i == static_cast< unsigned int >(nDomX) - 1) sigmaS_E(index, i * nDomY + (j-1)) = Domain(1, 150000 + i * nDomY + j + 1);
-
- if(i != 0) pmlS_W(index, i * nDomY + (j-1)) = Domain(1, 450000 + i * nDomY + j + 1);
- if(i != static_cast< unsigned int >(nDomX) - 1) pmlS_E(index, i * nDomY + (j-1)) = Domain(1, 200000 + i * nDomY + j + 1);
-
- topology[index].push_back(i * nDomY + (j-1));
- }
- if(j != static_cast< unsigned int >(nDomY) - 1) {
- sigmaN(index, i * nDomY + (j+1)) = Domain(1, 30000 + i * nDomY + j + 1);
-
- if(i == static_cast< unsigned int >(nDomX) - 1) sigmaN_E(index, i * nDomY + (j+1)) = Domain(1, 300000 + i * nDomY + j + 1);
- if(i == 0) sigmaN_W(index, i * nDomY + (j+1)) = Domain(1, 350000 + i * nDomY + j + 1);
-
- if(i != static_cast< unsigned int >(nDomX) - 1) pmlN_E(index, i * nDomY + (j+1)) = Domain(1, 250000 + i * nDomY + j + 1);
- if(i != 0) pmlN_W(index, i * nDomY + (j+1)) = Domain(1, 400000 + i * nDomY + j + 1);
-
- topology[index].push_back(i * nDomY + (j+1));
- }
- }
- }
-
- // Create resolution
- Resolution< std::complex< double > > resolution("DDM");
-
- // Create DDM formulation
- FormulationDDM< std::complex< double > > formulation("Helmholtz", resolution, topology);
-
- // Create fields
- SubdomainField< std::complex< double >, Form::Form0 > u(resolution, "u", omega | gammaDir | pmlS | pmlE | pmlN | pmlW | pmlSE | pmlNE | pmlNW | pmlSW, FunctionSpaceType::Lagrange);
- SubdomainField< std::complex< double >, Form::Form0 > lambda(resolution, "lambda", gammaDir, FunctionSpaceType::Lagrange);
- InterfaceField< std::complex< double >, Form::Form0 > gS(resolution, "gS", sigmaS | sigmaS_W | sigmaS_E, FunctionSpaceType::Lagrange);
- InterfaceField< std::complex< double >, Form::Form0 > gE(resolution, "gE", sigmaE | sigmaE_S | sigmaE_N, FunctionSpaceType::Lagrange);
- InterfaceField< std::complex< double >, Form::Form0 > gN(resolution, "gN", sigmaN | sigmaN_E | sigmaN_W, FunctionSpaceType::Lagrange);
- InterfaceField< std::complex< double >, Form::Form0 > gW(resolution, "gW", sigmaW | sigmaW_N | sigmaW_S, FunctionSpaceType::Lagrange);
-
- std::complex< double > im(0., 1.);
- AnalyticalFunction< helmholtz2D::SoftScatteringByACylinder< std::complex< double > > > solution(k, circleSize, xSize / 2., ySize / 2., 2 * k);
-
- // Tell to the formulation that g is field that have to be exchanged between subdomains
- formulation.addInterfaceField(gS);
- formulation.addInterfaceField(gE);
- formulation.addInterfaceField(gN);
- formulation.addInterfaceField(gW);
-
- // Add terms to the formulation
- for(unsigned int i = 0; i < nDom; ++i) {
- // Compute PML parameters
- gmshfem::function::ScalarFunction< std::complex< double > > distSigmaS = abs(y< std::complex< double > >() - (y< std::complex< double > >(omega(i)) - ySize / 2.));
- gmshfem::function::ScalarFunction< std::complex< double > > distSigmaE = abs(x< std::complex< double > >() - (x< std::complex< double > >(omega(i)) + xSize / 2.));
- gmshfem::function::ScalarFunction< std::complex< double > > distSigmaN = abs(y< std::complex< double > >() - (y< std::complex< double > >(omega(i)) + ySize / 2.));
- gmshfem::function::ScalarFunction< std::complex< double > > distSigmaW = abs(x< std::complex< double > >() - (x< std::complex< double > >(omega(i)) - xSize / 2.));
-
- gmshfem::function::ScalarFunction< std::complex< double > > sigS = 1. / (pmlSize - distSigmaS) - 1./ pmlSize;
- gmshfem::function::ScalarFunction< std::complex< double > > sigE = 1. / (pmlSize - distSigmaE) - 1./ pmlSize;
- gmshfem::function::ScalarFunction< std::complex< double > > sigN = 1. / (pmlSize - distSigmaN) - 1./ pmlSize;
- gmshfem::function::ScalarFunction< std::complex< double > > sigW = 1. / (pmlSize - distSigmaW) - 1./ pmlSize;
-
- gmshfem::function::ScalarFunction< std::complex< double > > kyS = 1. + im * sigS / k;
- gmshfem::function::ScalarFunction< std::complex< double > > kxE = 1. + im * sigE / k;
- gmshfem::function::ScalarFunction< std::complex< double > > kyN = 1. + im * sigN / k;
- gmshfem::function::ScalarFunction< std::complex< double > > kxW = 1. + im * sigW / k;
-
- gmshfem::function::TensorFunction< std::complex< double > > DS = tensorDiag< std::complex< double > >(kyS, 1. / kyS, kyS);
- gmshfem::function::ScalarFunction< std::complex< double > > ES = kyS;
-
- gmshfem::function::TensorFunction< std::complex< double > > DE = tensorDiag< std::complex< double > >(1. / kxE, kxE, kxE);
- gmshfem::function::ScalarFunction< std::complex< double > > EE = kxE;
-
- gmshfem::function::TensorFunction< std::complex< double > > DN = tensorDiag< std::complex< double > >(kyN, 1. / kyN, kyN);
- gmshfem::function::ScalarFunction< std::complex< double > > EN = kyN;
-
- gmshfem::function::TensorFunction< std::complex< double > > DW = tensorDiag< std::complex< double > >(1. / kxW, kxW, kxW);
- gmshfem::function::ScalarFunction< std::complex< double > > EW = kxW;
-
- // VOLUME TERMS
-
- formulation(i).integral(grad(dof(u(i))), grad(tf(u(i))), omega(i), gauss);
- formulation(i).integral(- k * k * dof(u(i)), tf(u(i)), omega(i), gauss);
-
- // Physical source
- formulation(i).integral(dof(lambda(i)), tf(u(i)), gammaDir(i), gauss);
- formulation(i).integral(dof(u(i)), tf(lambda(i)), gammaDir(i), gauss);
- formulation(i).integral(formulation.physicalSource(-solution), tf(lambda(i)), gammaDir(i), gauss);
-
- // S
- formulation(i).integral(DS * grad(dof(u(i))), grad(tf(u(i))), pmlS(i), gauss);
- formulation(i).integral(- ES * k * k * dof(u(i)), tf(u(i)), pmlS(i), gauss);
-
- // E
- formulation(i).integral(DE * grad(dof(u(i))), grad(tf(u(i))), pmlE(i), gauss);
- formulation(i).integral(- EE * k * k * dof(u(i)), tf(u(i)), pmlE(i), gauss);
-
- // N
- formulation(i).integral(DN * grad(dof(u(i))), grad(tf(u(i))), pmlN(i), gauss);
- formulation(i).integral(- EN * k * k * dof(u(i)), tf(u(i)), pmlN(i), gauss);
-
- // W
- formulation(i).integral(DW * grad(dof(u(i))), grad(tf(u(i))), pmlW(i), gauss);
- formulation(i).integral(- EW * k * k * dof(u(i)), tf(u(i)), pmlW(i), gauss);
-
- // SE
- formulation(i).integral(DS * DE * grad(dof(u(i))), grad(tf(u(i))), pmlSE(i), gauss);
- formulation(i).integral(- ES * EE * k * k * dof(u(i)), tf(u(i)), pmlSE(i), gauss);
-
- // NE
- formulation(i).integral(DN * DE * grad(dof(u(i))), grad(tf(u(i))), pmlNE(i), gauss);
- formulation(i).integral(- EN * EE * k * k * dof(u(i)), tf(u(i)), pmlNE(i), gauss);
-
- // NW
- formulation(i).integral(DN * DW * grad(dof(u(i))), grad(tf(u(i))), pmlNW(i), gauss);
- formulation(i).integral(- EN * EW * k * k * dof(u(i)), tf(u(i)), pmlNW(i), gauss);
-
- // SW
- formulation(i).integral(DS * DW * grad(dof(u(i))), grad(tf(u(i))), pmlSW(i), gauss);
- formulation(i).integral(- ES * EW * k * k * dof(u(i)), tf(u(i)), pmlSW(i), gauss);
-
- // Artificial sources
- for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
- const unsigned int j = topology[i][jj];
- if(!sigmaS(i,j).isEmpty()) formulation(i).integral(formulation.artificialSource( -gN(j,i) ), tf(u(i)), sigmaS(i,j) | sigmaS_W(i,j) | sigmaS_E(i,j), gauss);
- if(!sigmaE(i,j).isEmpty()) formulation(i).integral(formulation.artificialSource( -gW(j,i) ), tf(u(i)), sigmaE(i,j) | sigmaE_S(i,j) | sigmaE_N(i,j), gauss);
- if(!sigmaN(i,j).isEmpty()) formulation(i).integral(formulation.artificialSource( -gS(j,i) ), tf(u(i)), sigmaN(i,j) | sigmaN_E(i,j) | sigmaN_W(i,j), gauss);
- if(!sigmaW(i,j).isEmpty()) formulation(i).integral(formulation.artificialSource( -gE(j,i) ), tf(u(i)), sigmaW(i,j) | sigmaW_N(i,j) | sigmaW_S(i,j), gauss);
- }
-
- // INTERFACE TERMS
- for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
- const unsigned int j = topology[i][jj];
- // S
- if(!sigmaS(i,j).isEmpty()) {
- formulation(i,j).integral(dof(gS(i,j)), tf(gS(i,j)), sigmaS(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( gN(j,i) ), tf(gS(i,j)), sigmaS(i,j), gauss);
-
- formulation(i,j).integral(dof(gS(i,j)), tf(gS(i,j)), sigmaS_W(i,j) | sigmaS_E(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( gN(j,i) ), tf(gS(i,j)), sigmaS_W(i,j) | sigmaS_E(i,j), gauss);
-
- if(!pmlS_W(i,j).isEmpty()) formulation(i,j).integral(formulation.artificialSource( 2. * gE(i - nDomY,i) ), tf(gS(i,j)), pmlS_W(i,j), gauss);
- if(!pmlS_E(i,j).isEmpty()) formulation(i,j).integral(formulation.artificialSource( 2. * gW(i + nDomY,i) ), tf(gS(i,j)), pmlS_E(i,j), gauss);
-
- formulation(i,j).integral(- 2. * DS * grad(u(i)), grad(tf(gS(i,j))), pmlS(i), gauss);
- formulation(i,j).integral(2. * ES * k * k * u(i), tf(gS(i,j)), pmlS(i), gauss);
-
- formulation(i,j).integral(- 2. * DS * DW * grad(u(i)), grad(tf(gS(i,j))), pmlSW(i), gauss);
- formulation(i,j).integral(2. * ES * EW * k * k * u(i), tf(gS(i,j)), pmlSW(i), gauss);
-
- formulation(i,j).integral(- 2. * DS * DE * grad(u(i)), grad(tf(gS(i,j))), pmlSE(i), gauss);
- formulation(i,j).integral(2. * ES * EE * k * k * u(i), tf(gS(i,j)), pmlSE(i), gauss);
- }
-
- // E
- if(!sigmaE(i,j).isEmpty()) {
- formulation(i,j).integral(dof(gE(i,j)), tf(gE(i,j)), sigmaE(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( gW(j,i) ), tf(gE(i,j)), sigmaE(i,j), gauss);
-
- formulation(i,j).integral(dof(gE(i,j)), tf(gE(i,j)), sigmaE_S(i,j) | sigmaE_N(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( gW(j,i) ), tf(gE(i,j)), sigmaE_S(i,j) | sigmaE_N(i,j), gauss);
-
- if(!pmlE_S(i,j).isEmpty()) formulation(i,j).integral(formulation.artificialSource( 2. * gN(i - 1,i) ), tf(gE(i,j)), pmlE_S(i,j), gauss);
- if(!pmlE_N(i,j).isEmpty()) formulation(i,j).integral(formulation.artificialSource( 2. * gS(i + 1,i) ), tf(gE(i,j)), pmlE_N(i,j), gauss);
-
- formulation(i,j).integral(- 2. * DE * grad(u(i)), grad(tf(gE(i,j))), pmlE(i), gauss);
- formulation(i,j).integral(2. * EE * k * k * u(i), tf(gE(i,j)), pmlE(i), gauss);
-
- formulation(i,j).integral(- 2. * DS * DE * grad(u(i)), grad(tf(gE(i,j))), pmlSE(i), gauss);
- formulation(i,j).integral(2. * ES * EE * k * k * u(i), tf(gE(i,j)), pmlSE(i), gauss);
-
- formulation(i,j).integral(- 2. * DN * DE * grad(u(i)), grad(tf(gE(i,j))), pmlNE(i), gauss);
- formulation(i,j).integral(2. * EN * EE * k * k * u(i), tf(gE(i,j)), pmlNE(i), gauss);
- }
-
- // N
- if(!sigmaN(i,j).isEmpty()) {
- formulation(i,j).integral(dof(gN(i,j)), tf(gN(i,j)), sigmaN(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( gS(j,i) ), tf(gN(i,j)), sigmaN(i,j), gauss);
-
- formulation(i,j).integral(dof(gN(i,j)), tf(gN(i,j)), sigmaN_E(i,j) | sigmaN_W(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( gS(j,i) ), tf(gN(i,j)), sigmaN_E(i,j) | sigmaN_W(i,j), gauss);
-
- if(!pmlN_E(i,j).isEmpty()) formulation(i,j).integral(formulation.artificialSource( 2. * gW(i + nDomY,i) ), tf(gN(i,j)), pmlN_E(i,j), gauss);
- if(!pmlN_W(i,j).isEmpty()) formulation(i,j).integral(formulation.artificialSource( 2. * gE(i - nDomY,i) ), tf(gN(i,j)), pmlN_W(i,j), gauss);
-
- formulation(i,j).integral(- 2. * DN * grad(u(i)), grad(tf(gN(i,j))), pmlN(i), gauss);
- formulation(i,j).integral(2. * EN * k * k * u(i), tf(gN(i,j)), pmlN(i), gauss);
-
- formulation(i,j).integral(- 2. * DN * DE * grad(u(i)), grad(tf(gN(i,j))), pmlNE(i), gauss);
- formulation(i,j).integral(2. * EN * EE * k * k * u(i), tf(gN(i,j)), pmlNE(i), gauss);
-
- formulation(i,j).integral(- 2. * DN * DW * grad(u(i)), grad(tf(gN(i,j))), pmlNW(i), gauss);
- formulation(i,j).integral(2. * EN * EW * k * k * u(i), tf(gN(i,j)), pmlNW(i), gauss);
- }
-
- // W
- if(!sigmaW(i,j).isEmpty()) {
- formulation(i,j).integral(dof(gW(i,j)), tf(gW(i,j)), sigmaW(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( gE(j,i) ), tf(gW(i,j)), sigmaW(i,j), gauss);
-
- formulation(i,j).integral(dof(gW(i,j)), tf(gW(i,j)), sigmaW_N(i,j) | sigmaW_S(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( gE(j,i) ), tf(gW(i,j)), sigmaW_N(i,j) | sigmaW_S(i,j), gauss);
-
- if(!pmlW_N(i,j).isEmpty()) formulation(i,j).integral(formulation.artificialSource( 2. * gS(i + 1,i) ), tf(gW(i,j)), pmlW_N(i,j), gauss);
- if(!pmlW_S(i,j).isEmpty()) formulation(i,j).integral(formulation.artificialSource( 2. * gN(i - 1,i) ), tf(gW(i,j)), pmlW_S(i,j), gauss);
-
- formulation(i,j).integral(- 2. * DW * grad(u(i)), grad(tf(gW(i,j))), pmlW(i), gauss);
- formulation(i,j).integral(2. * EW * k * k * u(i), tf(gW(i,j)), pmlW(i), gauss);
-
- formulation(i,j).integral(- 2. * DN * DW * grad(u(i)), grad(tf(gW(i,j))), pmlNW(i), gauss);
- formulation(i,j).integral(2. * EN * EW * k * k * u(i), tf(gW(i,j)), pmlNW(i), gauss);
-
- formulation(i,j).integral(- 2. * DS * DW * grad(u(i)), grad(tf(gW(i,j))), pmlSW(i), gauss);
- formulation(i,j).integral(2. * ES * EW * k * k * u(i), tf(gW(i,j)), pmlSW(i), gauss);
- }
- }
- }
-
- // Solve the DDM formulation
- formulation.pre();
- formulation.solve("gmres");
-
- if(errorMono) {
- gmshfem::domain::Domain omegaMono, pmlSMono, pmlEMono, pmlNMono, pmlWMono, pmlSEMono, pmlNEMono, pmlNWMono, pmlSWMono;
- for(unsigned int i = 0; i < static_cast< unsigned int >(nDom); ++i) {
- omegaMono |= omega(i);
- }
-
- for(unsigned int i = 0; i < static_cast< unsigned int >(nDomX); ++i) {
- pmlSMono |= pmlS(i * nDomY + 0);
- pmlNMono |= pmlN(i * nDomY + nDomY - 1);
- }
- for(unsigned int j = 0; j < static_cast< unsigned int >(nDomY); ++j) {
- pmlEMono |= pmlE((nDomX - 1) * nDomY + j);
- pmlWMono |= pmlW(0 * nDomY + j);
- }
- pmlSEMono = pmlSE((nDomX - 1) * nDomY + 0);
- pmlNEMono = pmlNE((nDomX - 1) * nDomY + nDomY - 1);
- pmlNWMono = pmlNW(0 * nDomY + nDomY - 1);
- pmlSWMono = pmlSW(0);
-
- gmshfem::function::TensorFunction< std::complex< double > > DSmono = getPmlDParameter(k, pmlSize, 0., false);
- gmshfem::function::TensorFunction< std::complex< double > > DEmono = getPmlDParameter(k, pmlSize, nDomX * xSize, true);
- gmshfem::function::TensorFunction< std::complex< double > > DNmono = getPmlDParameter(k, pmlSize, nDomY * ySize, false);
- gmshfem::function::TensorFunction< std::complex< double > > DWmono = getPmlDParameter(k, pmlSize, 0., true);
-
- gmshfem::function::ScalarFunction< std::complex< double > > ESmono = getPmlEParameter(k, pmlSize, 0., false);
- gmshfem::function::ScalarFunction< std::complex< double > > EEmono = getPmlEParameter(k, pmlSize, nDomX * xSize, true);
- gmshfem::function::ScalarFunction< std::complex< double > > ENmono = getPmlEParameter(k, pmlSize, nDomY * ySize, false);
- gmshfem::function::ScalarFunction< std::complex< double > > EWmono = getPmlEParameter(k, pmlSize, 0., true);
-
- gmshfem::field::Field< std::complex< double >, gmshfem::field::Form::Form0 > uMono(resolution, "uMono", gammaDir(circlePosX * nDomY + circlePosY) | omegaMono | pmlSMono | pmlEMono | pmlNMono | pmlWMono | pmlSEMono | pmlNEMono | pmlNWMono | pmlSWMono, FunctionSpaceType::Lagrange);
- gmshfem::field::Field< std::complex< double >, gmshfem::field::Form::Form0 > lambdaMono(resolution, "lambdaMono", gammaDir(circlePosX * nDomY + circlePosY), FunctionSpaceType::Lagrange);
-
- Formulation< std::complex< double > > monodomain("HelmholtzMono", resolution);
-
- monodomain.integral(grad(dof(uMono)), grad(tf(uMono)), omegaMono, gauss);
- monodomain.integral(- k * k * dof(uMono), tf(uMono), omegaMono, gauss);
-
- monodomain.integral(dof(lambdaMono), tf(uMono), gammaDir(circlePosX * nDomY + circlePosY), gauss);
- monodomain.integral(dof(uMono), tf(lambdaMono), gammaDir(circlePosX * nDomY + circlePosY), gauss);
- monodomain.integral(- solution, tf(lambdaMono), gammaDir(circlePosX * nDomY + circlePosY), gauss);
-
- monodomain.integral(DSmono * grad(dof(uMono)), grad(tf(uMono)), pmlSMono, gauss);
- monodomain.integral(- k * k * ESmono * dof(uMono), tf(uMono), pmlSMono, gauss);
-
- monodomain.integral(DEmono * grad(dof(uMono)), grad(tf(uMono)), pmlEMono, gauss);
- monodomain.integral(- k * k * EEmono * dof(uMono), tf(uMono), pmlEMono, gauss);
-
- monodomain.integral(DNmono * grad(dof(uMono)), grad(tf(uMono)), pmlNMono, gauss);
- monodomain.integral(- k * k * ENmono * dof(uMono), tf(uMono), pmlNMono, gauss);
-
- monodomain.integral(DWmono * grad(dof(uMono)), grad(tf(uMono)), pmlWMono, gauss);
- monodomain.integral(- k * k * EWmono * dof(uMono), tf(uMono), pmlWMono, gauss);
-
- monodomain.integral(DSmono * DEmono * grad(dof(uMono)), grad(tf(uMono)), pmlSEMono, gauss);
- monodomain.integral(- k * k * ESmono * EEmono * dof(uMono), tf(uMono), pmlSEMono, gauss);
-
- monodomain.integral(DNmono * DEmono * grad(dof(uMono)), grad(tf(uMono)), pmlNEMono, gauss);
- monodomain.integral(- k * k * ENmono * EEmono * dof(uMono), tf(uMono), pmlNEMono, gauss);
-
- monodomain.integral(DNmono * DWmono * grad(dof(uMono)), grad(tf(uMono)), pmlNWMono, gauss);
- monodomain.integral(- k * k * ENmono * EWmono * dof(uMono), tf(uMono), pmlNWMono, gauss);
-
- monodomain.integral(DSmono * DWmono * grad(dof(uMono)), grad(tf(uMono)), pmlSWMono, gauss);
- monodomain.integral(- k * k * ESmono * EWmono * dof(uMono), tf(uMono), pmlSWMono, gauss);
-
- monodomain.pre();
- monodomain.assemble();
- monodomain.solve();
-
- save(uMono);
-
- for(unsigned int i = 0; i < nDom; ++i) {
- save(uMono - u(i), omega(i), "eMono_" + std::to_string(i));
- }
-
- // L2 error
- double num = 0., den = 0.;
- for(unsigned int i = 0; i < nDom; ++i) {
- std::complex< double > denLocal = integrate(pow(abs(uMono), 2), omega(i), gauss);
- std::complex< double > numLocal = integrate(pow(abs(uMono - u(i)), 2), omega(i), gauss);
- num += numLocal.real();
- den += denLocal.real();
- }
- msg::info << "L2 mono domain error = " << std::sqrt(num / den) << msg::endl;
- }
-
- for(unsigned int i = 0; i < nDom; ++i) {
- save(+u(i), omega(i), "u_" + std::to_string(i));
- save(solution - u(i), omega(i), "e_" + std::to_string(i));
- for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
- const unsigned int j = topology[i][jj];
- if(!sigmaS(i,j).isEmpty()) save(gS(i,j));
- if(!sigmaE(i,j).isEmpty()) save(gE(i,j));
- if(!sigmaN(i,j).isEmpty()) save(gN(i,j));
- if(!sigmaW(i,j).isEmpty()) save(gW(i,j));
- }
- }
-
- return 0;
-}
-
-gmshfem::function::TensorFunction< std::complex< double > > getPmlDParameter(const double k, const double pmlSize, const double pos, const bool onX)
-{
- gmshfem::function::ScalarFunction< std::complex< double > > kx = 1.;
- gmshfem::function::ScalarFunction< std::complex< double > > ky = 1.;
- gmshfem::function::ScalarFunction< std::complex< double > > kz = 1.;
-
- std::complex< double > I(0., 1.);
- if(onX) {
- gmshfem::function::ScalarFunction< std::complex< double > > distSigma = abs(x< std::complex< double > >() - pos);
- gmshfem::function::ScalarFunction< std::complex< double > > sigmaX = 1. / (pmlSize - distSigma) - 1./ pmlSize;
- kx = 1. + I * sigmaX / k;
- }
- else { // onY
- gmshfem::function::ScalarFunction< std::complex< double > > distSigma = abs(y< std::complex< double > >() - pos);
- gmshfem::function::ScalarFunction< std::complex< double > > sigmaY = 1. / (pmlSize - distSigma) - 1./ pmlSize;
- ky = 1. + I * sigmaY / k;
- }
-
- return tensorDiag< std::complex< double > >(ky * kz / kx, kx * kz / ky, kx * ky / kz);
-}
-
-gmshfem::function::ScalarFunction< std::complex< double > > getPmlEParameter(const double k, const double pmlSize, const double pos, const bool onX)
-{
- gmshfem::function::ScalarFunction< std::complex< double > > kx = 1.;
- gmshfem::function::ScalarFunction< std::complex< double > > ky = 1.;
- gmshfem::function::ScalarFunction< std::complex< double > > kz = 1.;
-
- std::complex< double > I(0., 1.);
- if(onX) {
- gmshfem::function::ScalarFunction< std::complex< double > > distSigma = abs(x< std::complex< double > >() - pos);
- gmshfem::function::ScalarFunction< std::complex< double > > sigmaX = 1. / (pmlSize - distSigma) - 1./ pmlSize;
- kx = 1. + I * sigmaX / k;
- }
- else { // onY
- gmshfem::function::ScalarFunction< std::complex< double > > distSigma = abs(y< std::complex< double > >() - pos);
- gmshfem::function::ScalarFunction< std::complex< double > > sigmaY = 1. / (pmlSize - distSigma) - 1./ pmlSize;
- ky = 1. + I * sigmaY / k;
- }
-
- return kx * ky * kz;
-}
diff --git a/demos/helmholtzflow/freefield/runTests.sh b/demos/helmholtzflow/freefield/runTests.sh
deleted file mode 100644
index 8b4741f05eb05a01dd98340e9114503a4e962603..0000000000000000000000000000000000000000
--- a/demos/helmholtzflow/freefield/runTests.sh
+++ /dev/null
@@ -1,19 +0,0 @@
-cd build
-cmake .. && make
-
-echo "****************************"
-echo " zeroth order TC "
-echo "****************************"
-./demo -transmission T0 -alpha 0 -M 0.8
-echo "****************************"
-echo " zeroth order TC with rotation "
-echo "****************************"
-./demo -transmission T0 -alpha -1 -M 0.8
-echo "****************************"
-echo " second order TC with rotation "
-echo "****************************"
-./demo -transmission T2 -alpha -1 -M 0.8
-echo "****************************"
-echo " Pade TC with rotation "
-echo "****************************"
-./demo -transmission Pade -padeOrder 4 -alpha -1 -M 0.8
diff --git a/demos/navier/scattering/CMakeLists.txt b/demos/navier/scattering/CMakeLists.txt
deleted file mode 100755
index 4d2e4b0c91d2a7e0da5a224e581c56eca24b2f71..0000000000000000000000000000000000000000
--- a/demos/navier/scattering/CMakeLists.txt
+++ /dev/null
@@ -1,8 +0,0 @@
-cmake_minimum_required(VERSION 3.0 FATAL_ERROR)
-
-project(demo CXX)
-
-include(${CMAKE_CURRENT_SOURCE_DIR}/../../demos.cmake)
-
-add_executable(demo main.cpp ${EXTRA_INCS})
-target_link_libraries(demo ${EXTRA_LIBS})
diff --git a/examples/.clang-format b/examples/.clang-format
new file mode 100644
index 0000000000000000000000000000000000000000..d902ab979dca0361bb1b063642225163bda4eb7d
--- /dev/null
+++ b/examples/.clang-format
@@ -0,0 +1,112 @@
+---
+Language: Cpp
+AccessModifierOffset: -1
+AlignAfterOpenBracket: Align
+AlignConsecutiveAssignments: false
+AlignConsecutiveDeclarations: false
+AlignEscapedNewlines: Right
+AlignOperands: true
+AlignTrailingComments: false
+AllowAllParametersOfDeclarationOnNextLine: true
+AllowShortBlocksOnASingleLine: false
+AllowShortCaseLabelsOnASingleLine: true
+AllowShortFunctionsOnASingleLine: Empty
+AllowShortIfStatementsOnASingleLine: true
+AllowShortLoopsOnASingleLine: true
+AlwaysBreakAfterDefinitionReturnType: None
+AlwaysBreakAfterReturnType: None
+AlwaysBreakBeforeMultilineStrings: false
+AlwaysBreakTemplateDeclarations: true
+BinPackArguments: true
+BinPackParameters: true
+BraceWrapping:
+ AfterClass: true
+ AfterControlStatement: false
+ AfterEnum: false
+ AfterFunction: true
+ AfterNamespace: true
+ AfterObjCDeclaration: false
+ AfterStruct: false
+ AfterUnion: false
+ AfterExternBlock: false
+ BeforeCatch: true
+ BeforeElse: true
+ IndentBraces: false
+ SplitEmptyFunction: true
+ SplitEmptyRecord: true
+ SplitEmptyNamespace: true
+BreakBeforeBinaryOperators: None
+BreakBeforeBraces: Custom
+BreakBeforeInheritanceComma: false
+BreakBeforeTernaryOperators: true
+BreakConstructorInitializersBeforeComma: false
+BreakConstructorInitializers: AfterColon
+BreakAfterJavaFieldAnnotations: false
+BreakStringLiterals: true
+ColumnLimit: 0
+CommentPragmas: '^ IWYU pragma:'
+CompactNamespaces: false
+ConstructorInitializerAllOnOneLineOrOnePerLine: false
+ConstructorInitializerIndentWidth: 2
+ContinuationIndentWidth: 2
+Cpp11BracedListStyle: true
+DerivePointerAlignment: false
+DisableFormat: false
+ExperimentalAutoDetectBinPacking: false
+FixNamespaceComments: true
+ForEachMacros:
+ - foreach
+ - Q_FOREACH
+ - BOOST_FOREACH
+IncludeBlocks: Regroup
+IncludeCategories:
+ - Regex: '^"(?!gmsh\.h"|petsc\.h"|Eigen")'
+ Priority: 2
+ - Regex: '"gmsh.h"|"petsc.h"|"Eigen"'
+ Priority: 3
+ - Regex: '^<'
+ Priority: 4
+ - Regex: '.*'
+ Priority: 1
+IncludeIsMainRegex: '$'
+IndentCaseLabels: false
+IndentPPDirectives: None
+IndentWidth: 2
+IndentWrappedFunctionNames: false
+JavaScriptQuotes: Leave
+JavaScriptWrapImports: true
+KeepEmptyLinesAtTheStartOfBlocks: true
+MacroBlockBegin: ''
+MacroBlockEnd: ''
+MaxEmptyLinesToKeep: 2
+NamespaceIndentation: All
+ObjCBlockIndentWidth: 2
+ObjCSpaceAfterProperty: false
+ObjCSpaceBeforeProtocolList: true
+PenaltyBreakAssignment: 2
+PenaltyBreakBeforeFirstCallParameter: 19
+PenaltyBreakComment: 300
+PenaltyBreakFirstLessLess: 120
+PenaltyBreakString: 1000
+PenaltyExcessCharacter: 1000000
+PenaltyReturnTypeOnItsOwnLine: 60
+PointerAlignment: Right
+ReflowComments: false
+SortIncludes: true
+SortUsingDeclarations: true
+SpaceAfterCStyleCast: false
+SpaceAfterTemplateKeyword: false
+SpaceBeforeAssignmentOperators: true
+SpaceBeforeParens: Never
+SpaceInEmptyParentheses: false
+SpacesBeforeTrailingComments: 1
+SpacesInAngles: true
+SpacesInContainerLiterals: true
+SpacesInCStyleCastParentheses: false
+SpacesInParentheses: false
+SpacesInSquareBrackets: false
+Standard: Cpp11
+TabWidth: 4
+UseTab: Never
+...
+
diff --git a/examples/CMakeLists.txt b/examples/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a3b6e79a56fd112f02ac9a3fa15103ccec678000
--- /dev/null
+++ b/examples/CMakeLists.txt
@@ -0,0 +1,14 @@
+set(EXAMPLES
+ helmholtz/checkerboard_bcgs
+ helmholtz/scattering/planeWaveDisk
+ helmholtzflow/freefield
+ helmholtzflow/waveguide
+ maxwell
+ navier/scattering
+)
+
+foreach(EXAMPLE ${EXAMPLES})
+ add_test(NAME "example:${EXAMPLE}:mkdir" COMMAND "${CMAKE_COMMAND}" -E make_directory build WORKING_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR}/${EXAMPLE})
+ add_test(NAME "example:${EXAMPLE}:cmake" COMMAND "${CMAKE_COMMAND}" -DCMAKE_PREFIX_PATH=${CMAKE_INSTALL_PREFIX} .. WORKING_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR}/${EXAMPLE}/build)
+ add_test(NAME "example:${EXAMPLE}:build" COMMAND "${CMAKE_MAKE_PROGRAM}" WORKING_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR}/${EXAMPLE}/build)
+endforeach()
diff --git a/examples/README.md b/examples/README.md
new file mode 100644
index 0000000000000000000000000000000000000000..82741b66daaabf64ca87e4b08fc3b59078bc0483
--- /dev/null
+++ b/examples/README.md
@@ -0,0 +1,4 @@
+# Examples
+> This directory contains the GmsmDDM research codes.
+
+This directory contains research codes based on GmshDDM.
diff --git a/examples/README_template.md b/examples/README_template.md
new file mode 100644
index 0000000000000000000000000000000000000000..a4bf0e06dc73e5da7d4111f01de47222af3005b6
--- /dev/null
+++ b/examples/README_template.md
@@ -0,0 +1,23 @@
+# Project name
+> author 1, author 2, ...
+
+Dependency(ies):
+* GmshDDM : [commit hash]
+* GmshFEM : [commit hash]
+* ...
+
+## Project description
+
+Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
+
+## Installation
+
+Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
+
+## Usage
+
+Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
+
+## References
+
+Papers, proceedings, ...
diff --git a/demos/demos.cmake b/examples/example.cmake
similarity index 97%
rename from demos/demos.cmake
rename to examples/example.cmake
index 38ebee16abc036fb6360ea366bb3cc8d4fb54c25..3e2c7ef61683c3ee4d8e3652f5103ed81c1c80c3 100644
--- a/demos/demos.cmake
+++ b/examples/example.cmake
@@ -50,7 +50,8 @@ if(NOT GMSHFEM_INC)
message(FATAL_ERROR "Could not find GmshFEM header 'gmshfem/GmshFem.h'")
endif(NOT GMSHFEM_INC)
list(APPEND EXTRA_LIBS ${GMSHFEM_LIB})
-list(APPEND EXTRA_INCS ${GMSHFEM_INC}/gmshfem/)
+list(APPEND EXTRA_INCS ${GMSHFEM_INC})
+list(APPEND EXTRA_INCS ${GMSHFEM_INC}/gmshfem/contrib)
# Find GmshDDM
find_library(GMSHDDM_LIB gmshddm)
diff --git a/demos/helmholtz/waveguide/CMakeLists.txt b/examples/helmholtz/checkerboard_bcgs/CMakeLists.txt
similarity index 73%
rename from demos/helmholtz/waveguide/CMakeLists.txt
rename to examples/helmholtz/checkerboard_bcgs/CMakeLists.txt
index 4d2e4b0c91d2a7e0da5a224e581c56eca24b2f71..c368ce59f63aed4e569c1b3e727df6dd0b1d6a45 100644
--- a/demos/helmholtz/waveguide/CMakeLists.txt
+++ b/examples/helmholtz/checkerboard_bcgs/CMakeLists.txt
@@ -2,7 +2,7 @@ cmake_minimum_required(VERSION 3.0 FATAL_ERROR)
project(demo CXX)
-include(${CMAKE_CURRENT_SOURCE_DIR}/../../demos.cmake)
+include(${CMAKE_CURRENT_SOURCE_DIR}/../../example.cmake)
add_executable(demo main.cpp ${EXTRA_INCS})
target_link_libraries(demo ${EXTRA_LIBS})
diff --git a/demos/helmholtz/checkerboard_bcgs/conv_test.txt b/examples/helmholtz/checkerboard_bcgs/conv_test.txt
similarity index 100%
rename from demos/helmholtz/checkerboard_bcgs/conv_test.txt
rename to examples/helmholtz/checkerboard_bcgs/conv_test.txt
diff --git a/demos/helmholtz/checkerboard_bcgs/main.cpp b/examples/helmholtz/checkerboard_bcgs/main.cpp
similarity index 82%
rename from demos/helmholtz/checkerboard_bcgs/main.cpp
rename to examples/helmholtz/checkerboard_bcgs/main.cpp
index 69213f7a905984ab1a6ff5f465eb588f6f527d5c..df7859e44cbccd77b4c8994433ec6d1650e27eba 100644
--- a/demos/helmholtz/checkerboard_bcgs/main.cpp
+++ b/examples/helmholtz/checkerboard_bcgs/main.cpp
@@ -1,10 +1,8 @@
-#include <gmshddm/GmshDdm.h>
+#include <gmsh.h>
#include <gmshddm/Formulation.h>
-
+#include <gmshddm/GmshDdm.h>
#include <gmshfem/Message.h>
-#include <gmsh.h>
-
using gmshfem::equation::dof;
using gmshfem::equation::tf;
using gmshfem::function::operator-;
@@ -51,10 +49,10 @@ void checkerboard(const unsigned int nDomX, const unsigned int nDomY, const doub
// * *
// (p0)*******(p1)
int p[4];
- p[0] = gmsh::model::geo::addPoint(i * xSize, j * ySize, 0., lc);
- p[1] = gmsh::model::geo::addPoint((i + 1) * xSize, j * ySize, 0., lc);
+ p[0] = gmsh::model::geo::addPoint(i * xSize, j * ySize, 0., lc);
+ p[1] = gmsh::model::geo::addPoint((i + 1) * xSize, j * ySize, 0., lc);
p[2] = gmsh::model::geo::addPoint((i + 1) * xSize, (j + 1) * ySize, 0., lc);
- p[3] = gmsh::model::geo::addPoint(i * xSize, (j + 1) * ySize, 0., lc);
+ p[3] = gmsh::model::geo::addPoint(i * xSize, (j + 1) * ySize, 0., lc);
int l[4];
borders[i][j][0] = l[0] = gmsh::model::geo::addLine(p[1], p[2]);
@@ -93,7 +91,6 @@ void checkerboard(const unsigned int nDomX, const unsigned int nDomY, const doub
gmsh::model::addPhysicalGroup(0, {pS}, 1);
gmsh::model::setPhysicalName(0, 1, "source");
}
-
}
}
gmsh::model::geo::removeAllDuplicates();
@@ -109,16 +106,16 @@ void checkerboard(const unsigned int nDomX, const unsigned int nDomY, const doub
gmsh::model::addPhysicalGroup(2, {omega[i][j]}, i * nDomY + j + 1);
gmsh::model::setPhysicalName(2, i * nDomY + j + 1, "omega_" + std::to_string(i) + "_" + std::to_string(j));
- gmsh::model::addPhysicalGroup(1, {borders[i][j][0]}, 10000 + i * nDomY + j + 1);
+ gmsh::model::addPhysicalGroup(1, {borders[i][j][0]}, 10000 + i * nDomY + j + 1);
gmsh::model::setPhysicalName(1, 10000 + i * nDomY + j + 1, "sigmaE_" + std::to_string(i) + "_" + std::to_string(j));
- gmsh::model::addPhysicalGroup(1, {borders[i][j][1]}, 20000 + i * nDomY + j + 1);
+ gmsh::model::addPhysicalGroup(1, {borders[i][j][1]}, 20000 + i * nDomY + j + 1);
gmsh::model::setPhysicalName(1, 20000 + i * nDomY + j + 1, "sigmaN_" + std::to_string(i) + "_" + std::to_string(j));
- gmsh::model::addPhysicalGroup(1, {borders[i][j][2]}, 30000 + i * nDomY + j + 1);
+ gmsh::model::addPhysicalGroup(1, {borders[i][j][2]}, 30000 + i * nDomY + j + 1);
gmsh::model::setPhysicalName(1, 30000 + i * nDomY + j + 1, "sigmaW_" + std::to_string(i) + "_" + std::to_string(j));
- gmsh::model::addPhysicalGroup(1, {borders[i][j][3]}, 40000 + i * nDomY + j + 1);
+ gmsh::model::addPhysicalGroup(1, {borders[i][j][3]}, 40000 + i * nDomY + j + 1);
gmsh::model::setPhysicalName(1, 40000 + i * nDomY + j + 1, "sigmaS_" + std::to_string(i) + "_" + std::to_string(j));
}
}
@@ -175,27 +172,27 @@ int main(int argc, char **argv)
omega(index) = gmshfem::domain::Domain(2, index + 1);
for(unsigned int f = 0; f < 4; ++f) {
- sigma[f](index) = gmshfem::domain::Domain(1, (f+1) * 10000 + i * nDomY + j + 1);
+ sigma[f](index) = gmshfem::domain::Domain(1, (f + 1) * 10000 + i * nDomY + j + 1);
}
if(i != static_cast< unsigned int >(nDomX) - 1) { // E
- sigmaInterface[0](index, (i+1) * nDomY + j) = sigma[0](index);
- topology[index].push_back((i+1) * nDomY + j);
+ sigmaInterface[0](index, (i + 1) * nDomY + j) = sigma[0](index);
+ topology[index].push_back((i + 1) * nDomY + j);
}
if(j != static_cast< unsigned int >(nDomY) - 1) { // N
- sigmaInterface[1](index, i * nDomY + (j+1)) = sigma[1](index);
- topology[index].push_back(i * nDomY + (j+1));
+ sigmaInterface[1](index, i * nDomY + (j + 1)) = sigma[1](index);
+ topology[index].push_back(i * nDomY + (j + 1));
}
if(i != 0) { // W
- sigmaInterface[2](index, (i-1) * nDomY + j) = sigma[2](index);
- topology[index].push_back((i-1) * nDomY + j);
+ sigmaInterface[2](index, (i - 1) * nDomY + j) = sigma[2](index);
+ topology[index].push_back((i - 1) * nDomY + j);
}
if(j != 0) { // S
- sigmaInterface[3](index, i * nDomY + (j-1)) = sigma[3](index);
- topology[index].push_back(i * nDomY + (j-1));
+ sigmaInterface[3](index, i * nDomY + (j - 1)) = sigma[3](index);
+ topology[index].push_back(i * nDomY + (j - 1));
}
}
}
@@ -208,7 +205,7 @@ int main(int argc, char **argv)
gmshfem::field::Field< std::complex< double >, gmshfem::field::Form::Form0 > lambda("lambda", gamma, gmshfem::field::FunctionSpaceTypeForm0::Lagrange);
- const std::vector< std::string > orientation {"E", "N", "W", "S"};
+ const std::vector< std::string > orientation{"E", "N", "W", "S"};
std::vector< gmshddm::field::InterfaceField< std::complex< double >, gmshfem::field::Form::Form0 > > g;
g.reserve(4);
for(unsigned int f = 0; f < 4; ++f) {
@@ -229,7 +226,7 @@ int main(int argc, char **argv)
if(i == sourcePosX * nDomY + sourcePosY) {
formulation(i).integral(dof(lambda), tf(u(i)), gamma, gauss);
formulation(i).integral(dof(u(i)), tf(lambda), gamma, gauss);
- formulation(i).integral(formulation.physicalSource(- 1.), tf(lambda), gamma, gauss);
+ formulation(i).integral(formulation.physicalSource(-1.), tf(lambda), gamma, gauss);
}
// boundary
@@ -245,8 +242,8 @@ int main(int argc, char **argv)
for(unsigned int f = 0; f < 4; ++f) {
for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
const unsigned int j = topology[i][jj];
- if(!sigmaInterface[f](i,j).isEmpty()) {
- formulation(i).integral(formulation.artificialSource( - g[(f+2)%4](j,i) ), tf(u(i)), sigmaInterface[f](i,j), gauss);
+ if(!sigmaInterface[f](i, j).isEmpty()) {
+ formulation(i).integral(formulation.artificialSource(-g[(f + 2) % 4](j, i)), tf(u(i)), sigmaInterface[f](i, j), gauss);
}
}
}
@@ -255,11 +252,10 @@ int main(int argc, char **argv)
for(unsigned int f = 0; f < 4; ++f) {
for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
const unsigned int j = topology[i][jj];
- if(!sigmaInterface[f](i,j).isEmpty()) {
- formulation(i,j).integral(dof(g[f](i,j)), tf(g[f](i,j)), sigmaInterface[f](i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( g[(f+2)%4](j,i) ), tf(g[f](i,j)), sigmaInterface[f](i,j), gauss);
- formulation(i,j).integral(2. * v[f](i), tf(g[f](i,j)), sigmaInterface[f](i,j), gauss);
-
+ if(!sigmaInterface[f](i, j).isEmpty()) {
+ formulation(i, j).integral(dof(g[f](i, j)), tf(g[f](i, j)), sigmaInterface[f](i, j), gauss);
+ formulation(i, j).integral(formulation.artificialSource(g[(f + 2) % 4](j, i)), tf(g[f](i, j)), sigmaInterface[f](i, j), gauss);
+ formulation(i, j).integral(2. * v[f](i), tf(g[f](i, j)), sigmaInterface[f](i, j), gauss);
}
}
}
diff --git a/demos/helmholtz/scattering/planeWaveDisk/CMakeLists.txt b/examples/helmholtz/scattering/planeWaveDisk/CMakeLists.txt
similarity index 72%
rename from demos/helmholtz/scattering/planeWaveDisk/CMakeLists.txt
rename to examples/helmholtz/scattering/planeWaveDisk/CMakeLists.txt
index f01d5714177b61745622f922015d7abd78c1cdcf..78dcc127355d6e26101a160e271312b86d9565ab 100644
--- a/demos/helmholtz/scattering/planeWaveDisk/CMakeLists.txt
+++ b/examples/helmholtz/scattering/planeWaveDisk/CMakeLists.txt
@@ -2,7 +2,7 @@ cmake_minimum_required(VERSION 3.0 FATAL_ERROR)
project(demo CXX)
-include(${CMAKE_CURRENT_SOURCE_DIR}/../../../demos.cmake)
+include(${CMAKE_CURRENT_SOURCE_DIR}/../../../example.cmake)
add_executable(demo main.cpp ${EXTRA_INCS})
target_link_libraries(demo ${EXTRA_LIBS})
diff --git a/demos/helmholtz/scattering/planeWaveDisk/main.cpp b/examples/helmholtz/scattering/planeWaveDisk/main.cpp
similarity index 70%
rename from demos/helmholtz/scattering/planeWaveDisk/main.cpp
rename to examples/helmholtz/scattering/planeWaveDisk/main.cpp
index c58ab82948217de38e5090b2145ddda19fa432c2..22f639c6e792c03b96693e727eeebcae6c58104d 100644
--- a/demos/helmholtz/scattering/planeWaveDisk/main.cpp
+++ b/examples/helmholtz/scattering/planeWaveDisk/main.cpp
@@ -1,8 +1,10 @@
-#include <gmshddm/GmshDdm.h>
+#include "gmsh.h"
+
#include <gmshddm/Formulation.h>
-#include <gmshfem/Message.h>
+#include <gmshddm/GmshDdm.h>
+#include <gmshddm/MPIInterface.h>
#include <gmshfem/AnalyticalFunction.h>
-#include "gmsh.h"
+#include <gmshfem/Message.h>
using namespace gmshddm;
using namespace gmshddm::common;
@@ -27,20 +29,20 @@ void circlesConcentric(const unsigned int nDom, const double r0, const double rI
}
gmsh::model::add("circlesConcentric");
- std::vector< int > tagsCircle(nDom+2);
+ std::vector< int > tagsCircle(nDom + 2);
for(unsigned int i = 0; i <= nDom; ++i) {
tagsCircle[i] = gmsh::model::occ::addCircle(0., 0., 0., std::sqrt(double(i * (rInf * rInf - r0 * r0)) / nDom + r0 * r0));
}
- tagsCircle[nDom+1] = gmsh::model::occ::addCircle(0., 0., 0., std::sqrt(double( nDom * (rPml * rPml - r0 * r0)) / nDom + r0 * r0));
+ tagsCircle[nDom + 1] = gmsh::model::occ::addCircle(0., 0., 0., std::sqrt(double(nDom * (rPml * rPml - r0 * r0)) / nDom + r0 * r0));
std::vector< int > tagsCurve(nDom + 2);
- for(unsigned int i = 0; i <= (nDom+1); ++i) {
+ for(unsigned int i = 0; i <= (nDom + 1); ++i) {
tagsCurve[i] = gmsh::model::occ::addCurveLoop({tagsCircle[i]});
}
-
- std::vector< int > tagsSurface(nDom+1);
+
+ std::vector< int > tagsSurface(nDom + 1);
for(unsigned int i = 0; i <= nDom; ++i) {
- tagsSurface[i] = gmsh::model::occ::addPlaneSurface({tagsCurve[i], tagsCurve[i+1]});
+ tagsSurface[i] = gmsh::model::occ::addPlaneSurface({tagsCurve[i], tagsCurve[i + 1]});
}
gmsh::model::occ::synchronize();
@@ -50,24 +52,24 @@ void circlesConcentric(const unsigned int nDom, const double r0, const double rI
gmsh::model::addPhysicalGroup(1, {tagsCircle[nDom]}, 92);
gmsh::model::setPhysicalName(1, 92, "gammaInf");
-
- gmsh::model::addPhysicalGroup(1, {tagsCircle[nDom+1]}, 93);
+
+ gmsh::model::addPhysicalGroup(1, {tagsCircle[nDom + 1]}, 93);
gmsh::model::setPhysicalName(1, 93, "gammaPml");
-
+
for(unsigned int i = 0; i < nDom; ++i) {
- gmsh::model::addPhysicalGroup(2, {tagsCircle[i]}, i+1);
- gmsh::model::setPhysicalName(2, i+1, "omega_" + std::to_string(i));
+ gmsh::model::addPhysicalGroup(2, {tagsCircle[i]}, i + 1);
+ gmsh::model::setPhysicalName(2, i + 1, "omega_" + std::to_string(i));
if(i != nDom - 1) {
- gmsh::model::addPhysicalGroup(1, {tagsCircle[i+1]}, 200 + i);
+ gmsh::model::addPhysicalGroup(1, {tagsCircle[i + 1]}, 200 + i);
gmsh::model::setPhysicalName(1, 200 + i, "sigma_" + std::to_string(i));
}
}
gmsh::model::addPhysicalGroup(2, {tagsCircle[nDom]}, 1 + nDom);
gmsh::model::setPhysicalName(2, 1 + nDom, "omega_pml");
-
+
std::vector< std::pair< int, int > > out;
gmsh::model::getEntities(out, 0);
gmsh::model::mesh::setSize(out, lc);
@@ -81,21 +83,19 @@ int main(int argc, char **argv)
unsigned int nDom = 3;
//gmshDdm.userDefinedParameter(nDom, "nDom");
- unsigned int MPI_Size = getSize_MPI();
- unsigned int MPI_Rank = getRank_MPI();
-
+
double rInf = 5.;
double r0 = 1;
double lc = 0.1;
int Npml = 4;
- double rPml = rInf+Npml*lc;
-
+ double rPml = rInf + Npml * lc;
+
gmshDdm.userDefinedParameter(rInf, "rInf");
gmshDdm.userDefinedParameter(r0, "r0");
gmshDdm.userDefinedParameter(lc, "lc");
-
- int FEMorder = 3;
+
+ int FEMorder = 3;
std::string gauss = "Gauss10";
gmshDdm.userDefinedParameter(gauss, "gauss");
@@ -103,7 +103,7 @@ int main(int argc, char **argv)
// transmission conditions
std::string Transmission = "Taylor2";
gmshDdm.userDefinedParameter(Transmission, "transmission");
- double alpha = pi/4.;
+ double alpha = pi / 4.;
gmshDdm.userDefinedParameter(alpha, "alpha");
msg::info << " Transmission condition " << Transmission << " with rotation alpha = " << alpha << msg::endl;
// Build geometry and mesh using gmsh API
@@ -112,16 +112,16 @@ int main(int argc, char **argv)
// Define domain
Subdomain omega(nDom);
Subdomain gammaPml(nDom);
- Subdomain gammaInf(nDom);
+ Subdomain gammaInf(nDom);
Subdomain gammaScat(nDom);
Interface sigma(nDom);
for(unsigned int i = 0; i < nDom; ++i) { // ddm entities
-
- if(i == (nDom - 1) ) {
+
+ if(i == (nDom - 1)) {
gammaPml(i) = Domain(1, 93);
gammaInf(i) = Domain(1, 92);
- omega(i) = ( Domain(2, i+1) | Domain (2, i+2) );
+ omega(i) = (Domain(2, i + 1) | Domain(2, i + 2));
}
else {
omega(i) = Domain(2, i + 1);
@@ -154,15 +154,15 @@ int main(int argc, char **argv)
gmshddm::problem::Formulation< std::complex< double > > formulation("helmholtz", topology);
double w = 2 * pi;
- double theta = pi/3.;
+ double theta = pi / 3.;
// Create fields
SubdomainField< std::complex< double >, Form::Form0 > u("u", omega | gammaScat | gammaPml | sigma, FunctionSpaceTypeForm0::HierarchicalH1, FEMorder);
InterfaceField< std::complex< double >, Form::Form0 > g("g", sigma, FunctionSpaceTypeForm0::HierarchicalH1, FEMorder);
Function< std::complex< double >, Degree::Degree0 > *solution = nullptr;
-
- solution = new AnalyticalFunction< helmholtz2D::ScatteringByASoftCylinder< std::complex< double > > >(w, r0, 0., 0., 2*w, theta);
+
+ solution = new AnalyticalFunction< helmholtz2D::ScatteringByASoftCylinder< std::complex< double > > >(w, r0, 0., 0., 2 * w, theta);
for(unsigned int i = 0; i < nDom; ++i) {
// physical source constraint
u(i).addConstraint(gammaScat(i), *solution);
@@ -170,15 +170,15 @@ int main(int argc, char **argv)
solution->activateMemorization();
ScalarFunction< std::complex< double > > S, dS;
- if ( Transmission == "Taylor0" ) {
- S = -im*w*exp(im*alpha/2.);
+ if(Transmission == "Taylor0") {
+ S = -im * w * exp(im * alpha / 2.);
dS = 0.;
}
- else if ( Transmission == "Taylor2" ) {
- S = -im*w*cos(alpha/2.);
- dS = -im*exp(-im*alpha/2.0)/(2.0*w);
+ else if(Transmission == "Taylor2") {
+ S = -im * w * cos(alpha / 2.);
+ dS = -im * exp(-im * alpha / 2.0) / (2.0 * w);
}
-
+
// add interface field
formulation.addInterfaceField(g);
@@ -186,25 +186,25 @@ int main(int argc, char **argv)
const double WPml = rPml - rInf;
ScalarFunction< std::complex< double > > cosT = x< std::complex< double > >() / r2d< std::complex< double > >();
ScalarFunction< std::complex< double > > sinT = y< std::complex< double > >() / r2d< std::complex< double > >();
- ScalarFunction< std::complex< double > > dampingProfileR = heaviside( abs(r2d< std::complex< double > >()) - rInf ) / (WPml - (r2d< std::complex< double > >() - rInf));
- ScalarFunction< std::complex< double > > dampingProfileInt = - heaviside( abs(r2d< std::complex< double > >()) - rInf ) * ln((WPml - (r2d< std::complex< double > >() - rInf)) / WPml);
+ ScalarFunction< std::complex< double > > dampingProfileR = heaviside(abs(r2d< std::complex< double > >()) - rInf) / (WPml - (r2d< std::complex< double > >() - rInf));
+ ScalarFunction< std::complex< double > > dampingProfileInt = -heaviside(abs(r2d< std::complex< double > >()) - rInf) * ln((WPml - (r2d< std::complex< double > >() - rInf)) / WPml);
ScalarFunction< std::complex< double > > cR = 1. + im * dampingProfileR / w;
ScalarFunction< std::complex< double > > cStretch = 1. + im * (1. / r2d< std::complex< double > >()) * dampingProfileInt / w;
ScalarFunction< std::complex< double > > S_PML = cR * cStretch;
- TensorFunction< std::complex< double > > D = tensor< std::complex <double > >(cStretch / cR * cosT * cosT + cR / cStretch * sinT * sinT,
- cStretch / cR * cosT * sinT - cR / cStretch * cosT * sinT,
- 0.,
- cStretch / cR * cosT * sinT - cR / cStretch * cosT * sinT,
- cStretch / cR * sinT * sinT + cR / cStretch * cosT * cosT,
- 0.,
- 0., 0., 0.);
+ TensorFunction< std::complex< double > > D = tensor< std::complex< double > >(cStretch / cR * cosT * cosT + cR / cStretch * sinT * sinT,
+ cStretch / cR * cosT * sinT - cR / cStretch * cosT * sinT,
+ 0.,
+ cStretch / cR * cosT * sinT - cR / cStretch * cosT * sinT,
+ cStretch / cR * sinT * sinT + cR / cStretch * cosT * cosT,
+ 0.,
+ 0., 0., 0.);
// Add terms to the formulation
for(unsigned int i = 0; i < nDom; ++i) {
// VOLUME TERMS
- if ( i == (nDom -1) ) { // pre-processing is slower with the PML formulation
+ if(i == (nDom - 1)) { // pre-processing is slower with the PML formulation
formulation(i).integral(D * grad(dof(u(i))), grad(tf(u(i))), omega(i), gauss);
- formulation(i).integral(- w * w * S_PML * dof(u(i)), tf(u(i)), omega(i), gauss);
+ formulation(i).integral(-w * w * S_PML * dof(u(i)), tf(u(i)), omega(i), gauss);
}
else {
formulation(i).integral(grad(dof(u(i))), grad(tf(u(i))), omega(i), gauss);
@@ -213,18 +213,18 @@ int main(int argc, char **argv)
// Artificial source
for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
const unsigned int j = topology[i][jj];
- formulation(i).integral(S * dof(u(i)), tf(u(i)), sigma(i,j), gauss);
- formulation(i).integral(- dS * grad( dof(u(i)) ), grad( tf(u(i)) ) , sigma(i,j), gauss);
- formulation(i).integral(formulation.artificialSource( -g(j,i) ), tf(u(i)), sigma(i,j), gauss);
+ formulation(i).integral(S * dof(u(i)), tf(u(i)), sigma(i, j), gauss);
+ formulation(i).integral(-dS * grad(dof(u(i))), grad(tf(u(i))), sigma(i, j), gauss);
+ formulation(i).integral(formulation.artificialSource(-g(j, i)), tf(u(i)), sigma(i, j), gauss);
}
// INTERFACE TERMS
for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
const unsigned int j = topology[i][jj];
- formulation(i,j).integral(dof(g(i,j)), tf(g(i,j)), sigma(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( g(j,i) ), tf(g(i,j)), sigma(i,j), gauss);
- formulation(i,j).integral(-2.0 * S * u(i), tf(g(i,j)), sigma(i,j), gauss);
- formulation(i,j).integral(2.0 * dS * grad( u(i) ), grad ( tf(g(i,j)) ), sigma(i,j), gauss);
+ formulation(i, j).integral(dof(g(i, j)), tf(g(i, j)), sigma(i, j), gauss);
+ formulation(i, j).integral(formulation.artificialSource(g(j, i)), tf(g(i, j)), sigma(i, j), gauss);
+ formulation(i, j).integral(-2.0 * S * u(i), tf(g(i, j)), sigma(i, j), gauss);
+ formulation(i, j).integral(2.0 * dS * grad(u(i)), grad(tf(g(i, j))), sigma(i, j), gauss);
}
}
@@ -235,14 +235,14 @@ int main(int argc, char **argv)
gmshDdm.userDefinedParameter(maxIter, "maxIter");
formulation.pre();
formulation.solve("gmres", tolerence, maxIter);
-
+
// L2 error
double num = 0., den = 0.;
Subdomain omega_err(nDom);
for(unsigned int i = 0; i < static_cast< unsigned int >(nDom); ++i) {
- if ( i % MPI_Size == MPI_Rank ) {
- omega_err(i) = Domain (2, i + 1);
- save(+u(i), omega(i),"u_"+std::to_string(i));
+ if(gmshddm::mpi::isItMySubdomain(i)) {
+ omega_err(i) = Domain(2, i + 1);
+ save(+u(i), omega(i), "u_" + std::to_string(i));
save(*solution, omega_err(i), "uex_" + std::to_string(i));
save(*solution - u(i), omega_err(i), "err_" + std::to_string(i));
diff --git a/demos/helmholtz/checkerboard_bcgs/CMakeLists.txt b/examples/helmholtzflow/freefield/CMakeLists.txt
similarity index 73%
rename from demos/helmholtz/checkerboard_bcgs/CMakeLists.txt
rename to examples/helmholtzflow/freefield/CMakeLists.txt
index 4d2e4b0c91d2a7e0da5a224e581c56eca24b2f71..c368ce59f63aed4e569c1b3e727df6dd0b1d6a45 100644
--- a/demos/helmholtz/checkerboard_bcgs/CMakeLists.txt
+++ b/examples/helmholtzflow/freefield/CMakeLists.txt
@@ -2,7 +2,7 @@ cmake_minimum_required(VERSION 3.0 FATAL_ERROR)
project(demo CXX)
-include(${CMAKE_CURRENT_SOURCE_DIR}/../../demos.cmake)
+include(${CMAKE_CURRENT_SOURCE_DIR}/../../example.cmake)
add_executable(demo main.cpp ${EXTRA_INCS})
target_link_libraries(demo ${EXTRA_LIBS})
diff --git a/demos/helmholtzflow/freefield/main.cpp b/examples/helmholtzflow/freefield/main.cpp
similarity index 63%
rename from demos/helmholtzflow/freefield/main.cpp
rename to examples/helmholtzflow/freefield/main.cpp
index 373429a682c851d3b2f20721cda2fb4ee0f946c3..36a41a07dd2d2fcd3e0f7f2e5c33fc69d58b09a6 100644
--- a/demos/helmholtzflow/freefield/main.cpp
+++ b/examples/helmholtzflow/freefield/main.cpp
@@ -1,8 +1,9 @@
-#include <gmshddm/GmshDdm.h>
-#include <gmshddm/Formulation.h>
-#include <gmshfem/Message.h>
#include "gmsh.h"
+
+#include <gmshddm/Formulation.h>
+#include <gmshddm/GmshDdm.h>
#include <gmshfem/AnalyticalFunction.h>
+#include <gmshfem/Message.h>
using namespace gmshddm;
using namespace gmshddm::common;
@@ -37,9 +38,9 @@ void circlesConcentric(const unsigned int nDom, const double rInf, const double
std::vector< int > tagsCircle(nDom + 1);
for(unsigned int i = 0; i < nDom; ++i) {
- tagsCircle[i] = gmsh::model::occ::addCircle(0., 0., 0., std::sqrt(double( (i+1) * (rInf * rInf)) / nDom ));
+ tagsCircle[i] = gmsh::model::occ::addCircle(0., 0., 0., std::sqrt(double((i + 1) * (rInf * rInf)) / nDom));
}
- tagsCircle[nDom] = gmsh::model::occ::addCircle(0., 0., 0., std::sqrt( double(rPml * rPml) ) );
+ tagsCircle[nDom] = gmsh::model::occ::addCircle(0., 0., 0., std::sqrt(double(rPml * rPml)));
std::vector< int > tagsCurve(nDom + 1);
for(unsigned int i = 0; i < (nDom + 1); ++i) {
@@ -48,12 +49,12 @@ void circlesConcentric(const unsigned int nDom, const double rInf, const double
std::vector< int > tagsSurface(nDom + 1);
tagsSurface[0] = gmsh::model::occ::addPlaneSurface({tagsCurve[0]});
- for(unsigned int i = 1; i < (nDom+1); ++i) {
- tagsSurface[i] = gmsh::model::occ::addPlaneSurface({tagsCurve[i-1], tagsCurve[i]});
+ for(unsigned int i = 1; i < (nDom + 1); ++i) {
+ tagsSurface[i] = gmsh::model::occ::addPlaneSurface({tagsCurve[i - 1], tagsCurve[i]});
}
gmsh::model::occ::synchronize();
- gmsh::model::mesh::embed(0,{tagPoint},2,1);
+ gmsh::model::mesh::embed(0, {tagPoint}, 2, 1);
for(unsigned int i = 0; i < nDom; ++i) {
gmsh::model::addPhysicalGroup(2, {tagsCircle[i]}, 100 + i);
@@ -65,7 +66,7 @@ void circlesConcentric(const unsigned int nDom, const double rInf, const double
}
}
- gmsh::model::addPhysicalGroup(1, {tagsCircle[nDom-1]}, 92);
+ gmsh::model::addPhysicalGroup(1, {tagsCircle[nDom - 1]}, 92);
gmsh::model::setPhysicalName(1, 92, "gammaInf");
gmsh::model::addPhysicalGroup(1, {tagsCircle[nDom]}, 93);
@@ -95,18 +96,18 @@ int main(int argc, char **argv)
unsigned int nDom = 5;
// gmshDdm.userDefinedParameter(nDom, "nDom");
const double pi = 3.14159265358979323846264338327950288;
-
+
// geometry parameters
double r0 = 2.;
double lc = 0.07;
- double rPML = r0+4.*lc;
+ double rPML = r0 + 4. * lc;
gmshDdm.userDefinedParameter(rPML, "rPML");
gmshDdm.userDefinedParameter(r0, "r0");
gmshDdm.userDefinedParameter(lc, "lc");
// souce point location
double xs = -0.1;
double ys = 0.2;
-
+
// numerical parameters
int FEMorder = 4;
gmshDdm.userDefinedParameter(FEMorder, "FEMorder");
@@ -133,13 +134,13 @@ int main(int argc, char **argv)
if(i == (nDom - 1)) {
gammaPml(i) = Domain(1, 93);
gammaInf(i) = Domain(1, 92);
- omega(i) = ( Domain(2, i + 100) | Domain (2, 100 + i + 1) );
+ omega(i) = (Domain(2, i + 100) | Domain(2, 100 + i + 1));
}
else {
omega(i) = Domain(2, i + 100);
}
- if ( i == 0 ) {
+ if(i == 0) {
source(i) = Domain(0, 999);
}
@@ -167,30 +168,30 @@ int main(int argc, char **argv)
const std::complex< double > im(0., 1.);
double M = 0.5; // Mach number
gmshDdm.userDefinedParameter(M, "M");
- double theta = pi/3.; // mean flow orientation
+ double theta = pi / 3.; // mean flow orientation
msg::info << "Mach number " << M << " theta " << theta << msg::endl;
- double Mx = M*std::cos(theta);
- double My = M*std::sin(theta);
+ double Mx = M * std::cos(theta);
+ double My = M * std::sin(theta);
// Parameters for Inverse Lorentz transformation
- double beta = sqrt(1-M*M); // Jacobian
- double Alphax = 1 + Mx*Mx/(beta*(1+beta));
- double Alphay = 1 + My*My/(beta*(1+beta));
- double K = Mx*My/(beta*(1+beta));
+ double beta = sqrt(1 - M * M); // Jacobian
+ double Alphax = 1 + Mx * Mx / (beta * (1 + beta));
+ double Alphay = 1 + My * My / (beta * (1 + beta));
+ double K = Mx * My / (beta * (1 + beta));
// Inverse Lorentz transformation
- TensorFunction< std::complex< double > > Linv = tensor< std::complex <double > > (beta*Alphay, -beta*K, 0., -beta*K, beta*Alphax,0.,0.,0.,0.);
+ TensorFunction< std::complex< double > > Linv = tensor< std::complex< double > >(beta * Alphay, -beta * K, 0., -beta * K, beta * Alphax, 0., 0., 0., 0.);
// Mach-velocity vector
- VectorFunction< std::complex< double > > MM = vector< std::complex< double > > (Mx,My,0.);
- ScalarFunction< std::complex< double > > Mn = MM*normal< std::complex< double > >();
- ScalarFunction< std::complex< double > > Mt = MM*tangent< std::complex< double > >();
- ScalarFunction< std::complex< double > > beta_n = sqrt(1-Mn*Mn); // Jacobian
+ VectorFunction< std::complex< double > > MM = vector< std::complex< double > >(Mx, My, 0.);
+ ScalarFunction< std::complex< double > > Mn = MM * normal< std::complex< double > >();
+ ScalarFunction< std::complex< double > > Mt = MM * tangent< std::complex< double > >();
+ ScalarFunction< std::complex< double > > beta_n = sqrt(1 - Mn * Mn); // Jacobian
// Transmission condition
ScalarFunction< std::complex< double > > Si, Sj, Sti, Stj, dS;
- float pointsByWl = ( 2*pi*FEMorder*( 1 - abs(M) ) ) / (lc*k);
+ float pointsByWl = (2 * pi * FEMorder * (1 - abs(M))) / (lc * k);
msg::info << " - FEM basis order = " << FEMorder << "" << msg::endl;
msg::info << " - Minimum number of dofs by wavelength = " << pointsByWl << msg::endl;
@@ -207,7 +208,7 @@ int main(int argc, char **argv)
Function< std::complex< double >, Degree::Degree0 > *solution = nullptr;
solution = new AnalyticalFunction< helmholtz2D::MonopoleFreeField< std::complex< double > > >(k, M, theta, 1., xs, ys, 0., 0.);
solution->activateMemorization();
-
+
// PML parameters
double Sigma0 = beta;
ScalarFunction< std::complex< double > > det_J;
@@ -216,104 +217,104 @@ int main(int argc, char **argv)
ScalarFunction< std::complex< double > > cosT = x< std::complex< double > >() / r2d< std::complex< double > >();
ScalarFunction< std::complex< double > > sinT = y< std::complex< double > >() / r2d< std::complex< double > >();
- ScalarFunction< std::complex< double > > dampingProfileR = Sigma0*heaviside( abs(r2d< std::complex< double > >()) - r0 ) / (Wpml - (r2d< std::complex< double > >() - r0));
- ScalarFunction< std::complex< double > > dampingProfileInt = -Sigma0*heaviside( abs(r2d< std::complex< double > >()) - r0 ) * ln((Wpml - (r2d< std::complex< double > >() - r0)) / Wpml);
+ ScalarFunction< std::complex< double > > dampingProfileR = Sigma0 * heaviside(abs(r2d< std::complex< double > >()) - r0) / (Wpml - (r2d< std::complex< double > >() - r0));
+ ScalarFunction< std::complex< double > > dampingProfileInt = -Sigma0 * heaviside(abs(r2d< std::complex< double > >()) - r0) * ln((Wpml - (r2d< std::complex< double > >() - r0)) / Wpml);
ScalarFunction< std::complex< double > > gamma = 1. - im * dampingProfileR / k;
ScalarFunction< std::complex< double > > gamma_hat = 1. - im * (1. / r2d< std::complex< double > >()) * dampingProfileInt / k;
det_J = gamma * gamma_hat;
- J_PML_inv_T = tensor< std::complex <double > >(cosT/gamma,sinT/gamma,0.,-sinT/gamma_hat,cosT/gamma_hat,0.,0.,0.,0.);
+ J_PML_inv_T = tensor< std::complex< double > >(cosT / gamma, sinT / gamma, 0., -sinT / gamma_hat, cosT / gamma_hat, 0., 0., 0., 0.);
// build vector and matrix for the weak form
VectorFunction< std::complex< double > > J_PML_inv_T_M = J_PML_inv_T * MM;
- TensorFunction< std::complex< double > > J_PML_Linv = J_PML_inv_T * Linv;
+ TensorFunction< std::complex< double > > J_PML_Linv = J_PML_inv_T * Linv;
msg::info << "Use a PML as radiation condition - circular stable formulation" << msg::endl;
for(unsigned int i = 0; i < nDom; ++i) {
// VOLUME TERMS
- if ( i != (nDom - 1) ) {
+ if(i != (nDom - 1)) {
// convected Helmholz weak form
- formulation(i).integral(vector< std::complex< double > >(1-Mx*Mx, -Mx*My, 0.) * grad(dof(u(i))), vector< std::complex< double > >(1., 0., 0.) * grad(tf(u(i))), omega(i), gauss);
- formulation(i).integral(vector< std::complex< double > >(-Mx*My, 1-My*My, 0.) * grad(dof(u(i))), vector< std::complex< double > >(0., 1., 0.) * grad(tf(u(i))), omega(i), gauss);
- formulation(i).integral(dof(u(i)), vector< std::complex< double > >(-im*k*Mx,-im*k*My, 0.) * grad(tf(u(i))), omega(i), gauss);
- formulation(i).integral(vector< std::complex< double > >(im*k*Mx, im*k*My, 0.) * grad(dof(u(i))), tf(u(i)), omega(i), gauss);
- formulation(i).integral(- k * k * dof(u(i)), tf(u(i)), omega(i), gauss);
+ formulation(i).integral(vector< std::complex< double > >(1 - Mx * Mx, -Mx * My, 0.) * grad(dof(u(i))), vector< std::complex< double > >(1., 0., 0.) * grad(tf(u(i))), omega(i), gauss);
+ formulation(i).integral(vector< std::complex< double > >(-Mx * My, 1 - My * My, 0.) * grad(dof(u(i))), vector< std::complex< double > >(0., 1., 0.) * grad(tf(u(i))), omega(i), gauss);
+ formulation(i).integral(dof(u(i)), vector< std::complex< double > >(-im * k * Mx, -im * k * My, 0.) * grad(tf(u(i))), omega(i), gauss);
+ formulation(i).integral(vector< std::complex< double > >(im * k * Mx, im * k * My, 0.) * grad(dof(u(i))), tf(u(i)), omega(i), gauss);
+ formulation(i).integral(-k * k * dof(u(i)), tf(u(i)), omega(i), gauss);
}
else {
// convected Helmholz weak form with PML
- formulation(i).integral( det_J * J_PML_Linv*grad(dof(u(i))) , J_PML_Linv*grad(tf(u(i))) , omega(i), gauss);
+ formulation(i).integral(det_J * J_PML_Linv * grad(dof(u(i))), J_PML_Linv * grad(tf(u(i))), omega(i), gauss);
- formulation(i).integral(+ k*k/(beta*beta) * det_J * J_PML_inv_T_M * dof(u(i)) , J_PML_inv_T_M * tf(u(i)), omega(i), gauss);
- formulation(i).integral(+ im*k/beta* det_J * J_PML_Linv * grad(dof(u(i))), J_PML_inv_T_M * tf(u(i)), omega(i), gauss);
+ formulation(i).integral(+k * k / (beta * beta) * det_J * J_PML_inv_T_M * dof(u(i)), J_PML_inv_T_M * tf(u(i)), omega(i), gauss);
+ formulation(i).integral(+im * k / beta * det_J * J_PML_Linv * grad(dof(u(i))), J_PML_inv_T_M * tf(u(i)), omega(i), gauss);
- formulation(i).integral(- im*k/beta* det_J * J_PML_inv_T_M * dof(u(i)), J_PML_Linv * grad(tf(u(i))), omega(i), gauss);
- formulation(i).integral(- k*k/(beta*beta) * det_J * dof(u(i)), tf(u(i)), omega(i), gauss);
+ formulation(i).integral(-im * k / beta * det_J * J_PML_inv_T_M * dof(u(i)), J_PML_Linv * grad(tf(u(i))), omega(i), gauss);
+ formulation(i).integral(-k * k / (beta * beta) * det_J * dof(u(i)), tf(u(i)), omega(i), gauss);
}
// point source
formulation(i).integral(formulation.physicalSource(-1.), tf(u(i)), source(i), gauss);
-
+
// Artificial source - Zeroth order transmission condition
for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
const unsigned int j = topology[i][jj];
- formulation(i).integral(formulation.artificialSource( -g(j,i) ), tf(u(i)), sigma(i,j), gauss);
+ formulation(i).integral(formulation.artificialSource(-g(j, i)), tf(u(i)), sigma(i, j), gauss);
// Contribution from the boundary terms
- formulation(i).integral( (im*k*Mn) * dof(u(i)), tf(u(i)), sigma(i,j), gauss);
- formulation(i).integral(Mn * Mt * tangent< std::complex< double > >() * grad( dof(u(i)) ), dof(u(i)), sigma(i,j), gauss);
+ formulation(i).integral((im * k * Mn) * dof(u(i)), tf(u(i)), sigma(i, j), gauss);
+ formulation(i).integral(Mn * Mt * tangent< std::complex< double > >() * grad(dof(u(i))), dof(u(i)), sigma(i, j), gauss);
}
// Interface weak form
for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
const unsigned int j = topology[i][jj];
- formulation(i,j).integral(dof(g(i,j)), tf(g(i,j)), sigma(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( g(j,i) ), tf(g(i,j)), sigma(i,j), gauss);
+ formulation(i, j).integral(dof(g(i, j)), tf(g(i, j)), sigma(i, j), gauss);
+ formulation(i, j).integral(formulation.artificialSource(g(j, i)), tf(g(i, j)), sigma(i, j), gauss);
}
- if ( transmission == "T0" ) {
- Si = im*k*(exp(im*alpha/2.)-Mn); // alpha=0, beta*beta*Si = i*k*(1-Mn)
- Sti = - Mn * Mt;
- Sj = im*k*(exp(im*alpha/2.)+Mn);
+ if(transmission == "T0") {
+ Si = im * k * (exp(im * alpha / 2.) - Mn); // alpha=0, beta*beta*Si = i*k*(1-Mn)
+ Sti = -Mn * Mt;
+ Sj = im * k * (exp(im * alpha / 2.) + Mn);
for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
const unsigned int j = topology[i][jj];
- formulation(i).integral( Si * dof(u(i)), tf(u(i)), sigma(i,j), gauss);
- formulation(i).integral( Sti * tangent< std::complex< double > >() * grad( dof(u(i)) ), dof(u(i)), sigma(i,j), gauss);
- formulation(i,j).integral(- (Si+Sj) * u(i) , tf(g(i,j)), sigma(i,j), gauss);
- }
+ formulation(i).integral(Si * dof(u(i)), tf(u(i)), sigma(i, j), gauss);
+ formulation(i).integral(Sti * tangent< std::complex< double > >() * grad(dof(u(i))), dof(u(i)), sigma(i, j), gauss);
+ formulation(i, j).integral(-(Si + Sj) * u(i), tf(g(i, j)), sigma(i, j), gauss);
+ }
}
- else if ( transmission == "T2" ) {
- Si = im*k*(cos(alpha/2.)-Mn) ;
- Sj = im*k*(cos(alpha/2.)+Mn) ;
- Sti = ( exp(-im*alpha/2.) - Mn ) * Mt ;
- Stj = ( exp(-im*alpha/2.) + Mn ) * Mt ;
- dS = im*(beta*beta)*exp(-im*alpha/2.) / (2.0*k);
-
+ else if(transmission == "T2") {
+ Si = im * k * (cos(alpha / 2.) - Mn);
+ Sj = im * k * (cos(alpha / 2.) + Mn);
+ Sti = (exp(-im * alpha / 2.) - Mn) * Mt;
+ Stj = (exp(-im * alpha / 2.) + Mn) * Mt;
+ dS = im * (beta * beta) * exp(-im * alpha / 2.) / (2.0 * k);
+
for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
const unsigned int j = topology[i][jj];
- formulation(i).integral( Si * dof(u(i)), tf(u(i)), sigma(i,j), gauss);
- formulation(i).integral( Sti * tangent< std::complex< double > >() * grad( dof(u(i)) ), dof(u(i)), sigma(i,j), gauss);
- formulation(i).integral(- dS * grad( dof(u(i)) ), grad( tf(u(i)) ), sigma(i,j), gauss);
-
- formulation(i,j).integral(- (Si+Sj) * u(i) , tf(g(i,j)), sigma(i,j), gauss);
- formulation(i,j).integral(- (Sti+Stj) * tangent< std::complex< double > >() * grad( u(i) ) , tf(g(i,j)), sigma(i,j), gauss);
-
- formulation(i,j).integral( 2. * dS * grad( u(i) ), grad( tf(g(i,j)) ), sigma(i,j), gauss);
+ formulation(i).integral(Si * dof(u(i)), tf(u(i)), sigma(i, j), gauss);
+ formulation(i).integral(Sti * tangent< std::complex< double > >() * grad(dof(u(i))), dof(u(i)), sigma(i, j), gauss);
+ formulation(i).integral(-dS * grad(dof(u(i))), grad(tf(u(i))), sigma(i, j), gauss);
+
+ formulation(i, j).integral(-(Si + Sj) * u(i), tf(g(i, j)), sigma(i, j), gauss);
+ formulation(i, j).integral(-(Sti + Stj) * tangent< std::complex< double > >() * grad(u(i)), tf(g(i, j)), sigma(i, j), gauss);
+
+ formulation(i, j).integral(2. * dS * grad(u(i)), grad(tf(g(i, j))), sigma(i, j), gauss);
}
}
- else if ( transmission == "Pade" ) {
+ else if(transmission == "Pade") {
int padeOrder = 2;
gmshDdm.userDefinedParameter(padeOrder, "padeOrder");
const double Np = 2. * padeOrder + 1.;
- const std::complex< double > exp1 = std::complex<double>(std::cos(alpha),std::sin(alpha));
- const std::complex< double > exp2 = std::complex<double>(std::cos(alpha/2.),std::sin(alpha/2.));
- const std::complex< double > coef = 2./Np;
-
+ const std::complex< double > exp1 = std::complex< double >(std::cos(alpha), std::sin(alpha));
+ const std::complex< double > exp2 = std::complex< double >(std::cos(alpha / 2.), std::sin(alpha / 2.));
+ const std::complex< double > coef = 2. / Np;
+
for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
const unsigned int j = topology[i][jj];
- formulation(i).integral( im * k * exp2 * dof(u(i)), tf(u(i)), sigma(i,j), gauss);
- formulation(i).integral(- (im*Mn*k) * dof(u(i)), tf(u(i)), sigma(i,j), gauss);
- formulation(i).integral(- Mn*Mt * tangent< std::complex< double > >() * grad( dof(u(i)) ), tf(u(i)), sigma(i,j), gauss);
+ formulation(i).integral(im * k * exp2 * dof(u(i)), tf(u(i)), sigma(i, j), gauss);
+ formulation(i).integral(-(im * Mn * k) * dof(u(i)), tf(u(i)), sigma(i, j), gauss);
+ formulation(i).integral(-Mn * Mt * tangent< std::complex< double > >() * grad(dof(u(i))), tf(u(i)), sigma(i, j), gauss);
// interface unknowns
- formulation(i,j).integral(-2.*(im * k * exp2) * u(i), tf(g(i,j)), sigma(i,j), gauss);
-
+ formulation(i, j).integral(-2. * (im * k * exp2) * u(i), tf(g(i, j)), sigma(i, j), gauss);
+
// define Pade coefficients
std::vector< std::complex< double > > c(padeOrder, 0.);
for(int l = 0; l < padeOrder; ++l) {
@@ -322,27 +323,27 @@ int main(int argc, char **argv)
}
// define the auxiliary fields
- std::vector< Field< std::complex< double >, Form::Form0 >* > phi;
+ std::vector< Field< std::complex< double >, Form::Form0 > * > phi;
for(int l = 0; l < padeOrder; ++l) {
- phi.push_back(new Field< std::complex< double >, Form::Form0 >("phi_" + std::to_string(l), sigma(i,j), FunctionSpaceTypeForm0::HierarchicalH1, FEMorder));
+ phi.push_back(new Field< std::complex< double >, Form::Form0 >("phi_" + std::to_string(l), sigma(i, j), FunctionSpaceTypeForm0::HierarchicalH1, FEMorder));
fieldBucket.push_back(phi.back());
}
-
+
// write the augmented weak form
for(int l = 0; l < padeOrder; ++l) {
// boundary integral terms relating the auxiliary fields
- formulation(i).integral(im * k * exp2 * coef * c[l] * dof(*phi[l]), tf(u(i)), sigma(i,j), gauss);
- formulation(i).integral(im * k * exp2 * coef * c[l] * dof(u(i)), tf(u(i)), sigma(i,j), gauss);
+ formulation(i).integral(im * k * exp2 * coef * c[l] * dof(*phi[l]), tf(u(i)), sigma(i, j), gauss);
+ formulation(i).integral(im * k * exp2 * coef * c[l] * dof(u(i)), tf(u(i)), sigma(i, j), gauss);
// coupling of the auxiliary equations
- formulation(i).integral(- (beta*beta) * grad(dof(*phi[l])), grad(tf(*phi[l])), sigma(i,j), gauss);
- formulation(i).integral(- 2. * im * k * Mt * tangent< std::complex< double > >() * grad(dof(*phi[l])), tf(*phi[l]), sigma(i,j), gauss);
- formulation(i).integral( (k*k) * (exp1 * c[l] + 1.) * dof(*phi[l]), tf(*phi[l]), sigma(i,j), gauss);
- formulation(i).integral( (k*k) * exp1 * (c[l] + 1.) * dof(u(i)), tf(*phi[l]), sigma(i,j), gauss);
+ formulation(i).integral(-(beta * beta) * grad(dof(*phi[l])), grad(tf(*phi[l])), sigma(i, j), gauss);
+ formulation(i).integral(-2. * im * k * Mt * tangent< std::complex< double > >() * grad(dof(*phi[l])), tf(*phi[l]), sigma(i, j), gauss);
+ formulation(i).integral((k * k) * (exp1 * c[l] + 1.) * dof(*phi[l]), tf(*phi[l]), sigma(i, j), gauss);
+ formulation(i).integral((k * k) * exp1 * (c[l] + 1.) * dof(u(i)), tf(*phi[l]), sigma(i, j), gauss);
}
// interfaces unknowns
for(int l = 0; l < padeOrder; ++l) {
- formulation(i,j).integral(- 2. * (im * k * exp2) * coef * c[l] * (*phi[l]), tf(g(i,j)), sigma(i,j), gauss);
- formulation(i,j).integral(- 2. * (im * k * exp2) * coef * c[l] * u(i), tf(g(i,j)), sigma(i,j), gauss);
+ formulation(i, j).integral(-2. * (im * k * exp2) * coef * c[l] * (*phi[l]), tf(g(i, j)), sigma(i, j), gauss);
+ formulation(i, j).integral(-2. * (im * k * exp2) * coef * c[l] * u(i), tf(g(i, j)), sigma(i, j), gauss);
}
}
}
@@ -355,8 +356,8 @@ int main(int argc, char **argv)
double num = 0., den = 0.; // L2 error
Subdomain omega_err(nDom);
for(unsigned int i = 0; i < nDom; ++i) {
- omega_err(i) = Domain(2, i+100);
- save(+u(i), omega(i),"u_"+std::to_string(i));
+ omega_err(i) = Domain(2, i + 100);
+ save(+u(i), omega(i), "u_" + std::to_string(i));
save(*solution, omega_err(i), "uex_" + std::to_string(i));
save(*solution - u(i), omega_err(i), "err_" + std::to_string(i));
diff --git a/examples/helmholtzflow/freefield/runTests.sh b/examples/helmholtzflow/freefield/runTests.sh
new file mode 100644
index 0000000000000000000000000000000000000000..5486cd76fcd8942657652e9ad212faaeed70004a
--- /dev/null
+++ b/examples/helmholtzflow/freefield/runTests.sh
@@ -0,0 +1,7 @@
+cd build
+ cmake..&&make
+
+ echo "****************************" echo " zeroth order TC " echo "****************************"
+ ./
+ demo -
+ transmission T0 - alpha 0 - M 0.8 echo "****************************" echo " zeroth order TC with rotation " echo "****************************"./ demo - transmission T0 - alpha - 1 - M 0.8 echo "****************************" echo " second order TC with rotation " echo "****************************"./ demo - transmission T2 - alpha - 1 - M 0.8 echo "****************************" echo " Pade TC with rotation " echo "****************************"./ demo - transmission Pade - padeOrder 4 - alpha - 1 - M 0.8
diff --git a/demos/helmholtzflow/freefield/CMakeLists.txt b/examples/helmholtzflow/waveguide/CMakeLists.txt
similarity index 73%
rename from demos/helmholtzflow/freefield/CMakeLists.txt
rename to examples/helmholtzflow/waveguide/CMakeLists.txt
index 4d2e4b0c91d2a7e0da5a224e581c56eca24b2f71..c368ce59f63aed4e569c1b3e727df6dd0b1d6a45 100644
--- a/demos/helmholtzflow/freefield/CMakeLists.txt
+++ b/examples/helmholtzflow/waveguide/CMakeLists.txt
@@ -2,7 +2,7 @@ cmake_minimum_required(VERSION 3.0 FATAL_ERROR)
project(demo CXX)
-include(${CMAKE_CURRENT_SOURCE_DIR}/../../demos.cmake)
+include(${CMAKE_CURRENT_SOURCE_DIR}/../../example.cmake)
add_executable(demo main.cpp ${EXTRA_INCS})
target_link_libraries(demo ${EXTRA_LIBS})
diff --git a/demos/helmholtzflow/waveguide/main.cpp b/examples/helmholtzflow/waveguide/main.cpp
similarity index 64%
rename from demos/helmholtzflow/waveguide/main.cpp
rename to examples/helmholtzflow/waveguide/main.cpp
index 34e495ea5f12cdfb7913f576b210682c7944c1e6..454510b8861f93faecba63a33f80eafd979ffa62 100644
--- a/demos/helmholtzflow/waveguide/main.cpp
+++ b/examples/helmholtzflow/waveguide/main.cpp
@@ -1,10 +1,11 @@
-#include <gmshddm/GmshDdm.h>
#include <gmshddm/Formulation.h>
+#include <gmshddm/GmshDdm.h>
+#include <gmshddm/MPIInterface.h>
#include <gmshfem/Message.h>
// #include "mpi.h"
// #include "petscsys.h"
-#include "gmsh.h"
-#include "AnalyticalFunction.h"
+#include <gmsh.h>
+#include <gmshfem/AnalyticalFunction.h>
using namespace gmshddm;
using namespace gmshddm::common;
@@ -81,21 +82,16 @@ int main(int argc, char **argv)
{
GmshDdm gmshDdm(argc, argv);
- // rank and size
- unsigned int MPI_Rank = getRank_MPI();
- unsigned int MPI_Size = getSize_MPI();
- printf("I am processor of rank %d out of %d processes \n", MPI_Rank, MPI_Size);
-
double pi = 3.14159265359;
int nDom = 4;
gmshDdm.userDefinedParameter(nDom, "nDom");
-
+
// duct geometry parameters
double L = 0.5;
double H = 0.25;
- double lc = sqrt(L*H)/(40.0);
+ double lc = sqrt(L * H) / (40.0);
gmshDdm.userDefinedParameter(lc, "lc");
-
+
// upper wall boundary condition
std::string wallType = "hard";
gmshDdm.userDefinedParameter(wallType, "wallType");
@@ -104,33 +100,31 @@ int main(int argc, char **argv)
double k = 70;
gmshDdm.userDefinedParameter(k, "k");
int mode = 3;
- double ky = mode*pi/H;
-
+ double ky = mode * pi / H;
+
// relative Mach number
double M = 0.8;
gmshDdm.userDefinedParameter(M, "M");
- double beta = sqrt(1-M*M);
- double beta2 = beta*beta;
-
+ double beta = sqrt(1 - M * M);
+ double beta2 = beta * beta;
+
// transmission conditions
std::string Transmission = "DtN";
gmshDdm.userDefinedParameter(Transmission, "transmission");
// init transmission operators
ScalarFunction< std::complex< double > > Si, Sj, dS;
- double alpha=0.; // rotation branch-cut, in [0, -pi]
+ double alpha = 0.; // rotation branch-cut, in [0, -pi]
gmshDdm.userDefinedParameter(alpha, "alpha");
- if ( MPI_Rank == 0 ) {
- if (Transmission != "DtN") {
- msg::info << " use " << Transmission << " as transmission condition with alpha = " << alpha << msg::endl;
- }
- else {
- msg::info << " use analytical DtN as transmission condition " << msg::endl;
- }
- if ( wallType == "soft" && Transmission == "Pade" ) {
- msg::error << "Pade condition not available yet for Dirichlet wall " << msg::endl;
- }
+ if(Transmission != "DtN") {
+ msg::info << " use " << Transmission << " as transmission condition with alpha = " << alpha << msg::endl;
+ }
+ else {
+ msg::info << " use analytical DtN as transmission condition " << msg::endl;
+ }
+ if(wallType == "soft" && Transmission == "Pade") {
+ msg::error << "Pade condition not available yet for Dirichlet wall " << msg::endl;
}
-
+
// numerical parameters
int FEMorder = 4;
gmshDdm.userDefinedParameter(FEMorder, "FEMorder");
@@ -139,7 +133,7 @@ int main(int argc, char **argv)
// Build geometry and mesh using gmsh API
// for the moment all the procs do the meshing
- waveguide(nDom, H, L, lc);
+ waveguide(nDom, H, L, lc);
// Define domain
Subdomain omega(nDom);
@@ -150,7 +144,7 @@ int main(int argc, char **argv)
for(unsigned int i = 0; i < static_cast< unsigned int >(nDom); ++i) {
omega(i) = Domain(2, i + 1);
- if(i == (static_cast< unsigned int >(nDom-1)) ) {
+ if(i == (static_cast< unsigned int >(nDom - 1))) {
gammaInf(i) = Domain(1, 2); // outgoing boundary
}
@@ -162,7 +156,7 @@ int main(int argc, char **argv)
if(i != 0) {
sigma(i, i - 1) = Domain(1, 200 + i - 1);
}
- if(i != (static_cast< unsigned int >(nDom-1)) ) {
+ if(i != (static_cast< unsigned int >(nDom - 1))) {
sigma(i, i + 1) = Domain(1, 200 + i);
}
}
@@ -174,9 +168,9 @@ int main(int argc, char **argv)
if(i != 0) {
topology[i].push_back(i - 1);
}
- if(i != (static_cast< unsigned int >(nDom-1)) ) {
+ if(i != (static_cast< unsigned int >(nDom - 1))) {
topology[i].push_back(i + 1);
- }
+ }
}
// Create DDM formulation
@@ -186,15 +180,15 @@ int main(int argc, char **argv)
// Create fields
SubdomainField< std::complex< double >, Form::Form0 > u("u", omega | gammaDir | gammaInf | border | sigma, FunctionSpaceTypeForm0::HierarchicalH1, FEMorder);
InterfaceField< std::complex< double >, Form::Form0 > g("g", sigma, FunctionSpaceTypeForm0::HierarchicalH1, FEMorder);
-
+
// define analytical solution
Function< std::complex< double >, Degree::Degree0 > *solution = nullptr;
- if ( wallType == "hard" ) {
+ if(wallType == "hard") {
solution = new AnalyticalFunction< helmholtz2D::DuctModeSolution< std::complex< double > > >(k, M, H, 0., 0., mode, 0);
}
- else if ( wallType == "soft" ) {
+ else if(wallType == "soft") {
solution = new AnalyticalFunction< helmholtz2D::DuctModeSolution< std::complex< double > > >(k, M, H, 0., 0., mode, 1);
- for(unsigned int i = 0; i < static_cast< unsigned int >(nDom); ++i) {
+ for(unsigned int i = 0; i < static_cast< unsigned int >(nDom); ++i) {
u(i).addConstraint(border(i), 0.);
}
}
@@ -202,124 +196,118 @@ int main(int argc, char **argv)
std::complex< double > im(0., 1.);
std::complex< double > kx; // propagative wavenumber
- double Argsqrt = k*k-beta2*ky*ky;
- if (Argsqrt >= 0) {
- kx = (1/(beta2))*(-M*k + sqrt(Argsqrt));
- if ( MPI_Rank == 0 ) {
- msg::info << " propagative mode " << msg::endl;
- }
+ double Argsqrt = k * k - beta2 * ky * ky;
+ if(Argsqrt >= 0) {
+ kx = (1 / (beta2)) * (-M * k + sqrt(Argsqrt));
+ msg::info << " propagative mode " << msg::endl;
}
else {
- kx = (1/(beta2))*(-M*k - im*sqrt(abs(Argsqrt)));
- if ( MPI_Rank == 0 ) {
- msg::info << " evanescent mode " << msg::endl;
- }
+ kx = (1 / (beta2)) * (-M * k - im * sqrt(abs(Argsqrt)));
+ msg::info << " evanescent mode " << msg::endl;
}
- if ( k>(beta*ky) && k<ky ) {
+ if(k > (beta * ky) && k < ky) {
msg::info << " - inverse upstream mode ! " << msg::endl;
}
- float pointsByWl = (2*pi*FEMorder*(1+M)/k) / lc;
- if ( MPI_Rank == 0 ) {
- msg::info << " - Approximate dofs by wavelength = " << pointsByWl << "" << msg::endl;
- msg::info << " - Mach number = " << M << "" << msg::endl;
- }
-
+ float pointsByWl = (2 * pi * FEMorder * (1 + M) / k) / lc;
+ msg::info << " - Approximate dofs by wavelength = " << pointsByWl << "" << msg::endl;
+ msg::info << " - Mach number = " << M << "" << msg::endl;
+
// define output absorbing boundary condition
- std::complex< double > ABC = im*kx;
-
+ std::complex< double > ABC = im * kx;
+
// Tell to the formulation that g is field that have to be exchanged between subdomains
formulation.addInterfaceField(g);
- for(unsigned int i = 0; i < static_cast< unsigned int >(nDom); ++i) {
+ for(unsigned int i = 0; i < static_cast< unsigned int >(nDom); ++i) {
// VOLUME TERMS
formulation(i).integral(vector< std::complex< double > >(beta2, 0., 0.) * grad(dof(u(i))), vector< std::complex< double > >(1., 0., 0.) * grad(tf(u(i))), omega(i), gauss);
formulation(i).integral(vector< std::complex< double > >(0., 1., 0.) * grad(dof(u(i))), vector< std::complex< double > >(0., 1., 0.) * grad(tf(u(i))), omega(i), gauss);
- formulation(i).integral(vector< std::complex< double > >(im*k*M, 0., 0.) * grad(dof(u(i))), tf(u(i)), omega(i), gauss);
- formulation(i).integral(dof(u(i)), vector< std::complex< double > >(-im*k*M, 0., 0.) * grad(tf(u(i))), omega(i), gauss);
- formulation(i).integral(- k * k * dof(u(i)), tf(u(i)), omega(i), gauss);
+ formulation(i).integral(vector< std::complex< double > >(im * k * M, 0., 0.) * grad(dof(u(i))), tf(u(i)), omega(i), gauss);
+ formulation(i).integral(dof(u(i)), vector< std::complex< double > >(-im * k * M, 0., 0.) * grad(tf(u(i))), omega(i), gauss);
+ formulation(i).integral(-k * k * dof(u(i)), tf(u(i)), omega(i), gauss);
// SURFACE TERMS
// artificial boundary condition, use analytical DtN
formulation(i).integral(beta2 * ABC * dof(u(i)), tf(u(i)), gammaInf(i), gauss);
// Contribution from the mass boundary matrix
- formulation(i).integral( (im*k*M) * dof(u(i)), tf(u(i)), gammaInf(i), gauss);
+ formulation(i).integral((im * k * M) * dof(u(i)), tf(u(i)), gammaInf(i), gauss);
// Physical source
- if ( wallType == "soft" ) {
- formulation(i).integral(formulation.physicalSource( -im*kx*beta2*sin< std::complex< double > >(ky * y< std::complex< double > >() ) ), tf(u(i)), gammaDir(i), gauss);
+ if(wallType == "soft") {
+ formulation(i).integral(formulation.physicalSource(-im * kx * beta2 * sin< std::complex< double > >(ky * y< std::complex< double > >())), tf(u(i)), gammaDir(i), gauss);
}
- else if ( wallType == "hard" ) {
- formulation(i).integral(formulation.physicalSource( -im*kx*beta2*cos< std::complex< double > >(ky * y< std::complex< double > >() ) ), tf(u(i)), gammaDir(i), gauss);
+ else if(wallType == "hard") {
+ formulation(i).integral(formulation.physicalSource(-im * kx * beta2 * cos< std::complex< double > >(ky * y< std::complex< double > >())), tf(u(i)), gammaDir(i), gauss);
}
// Contribution from the mass boundary matrix
- formulation(i).integral( (-im*k*M) * dof(u(i)), tf(u(i)), gammaDir(i), gauss);
+ formulation(i).integral((-im * k * M) * dof(u(i)), tf(u(i)), gammaDir(i), gauss);
// Artificial source
for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
const unsigned int j = topology[i][jj];
- formulation(i).integral(formulation.artificialSource( -g(j,i) ), tf(u(i)), sigma(i,j), gauss);
+ formulation(i).integral(formulation.artificialSource(-g(j, i)), tf(u(i)), sigma(i, j), gauss);
// Contribution from the mass boundary matrix
- formulation(i).integral( (im*k*M) * dof(u(i)), tf(u(i)), sigma(i,j), gauss);
+ formulation(i).integral((im * k * M) * dof(u(i)), tf(u(i)), sigma(i, j), gauss);
}
// INTERFACE TERMS
for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
const unsigned int j = topology[i][jj];
- formulation(i,j).integral(dof(g(i,j)), tf(g(i,j)), sigma(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( g(j,i) ), tf(g(i,j)), sigma(i,j), gauss);
+ formulation(i, j).integral(dof(g(i, j)), tf(g(i, j)), sigma(i, j), gauss);
+ formulation(i, j).integral(formulation.artificialSource(g(j, i)), tf(g(i, j)), sigma(i, j), gauss);
}
// Transmission condition
- if ( Transmission == "Taylor0" ) {
- Si = im*k*(exp(im*alpha/2.)-M)/beta2;
- Sj = im*k*(exp(im*alpha/2.)+M)/beta2;
+ if(Transmission == "Taylor0") {
+ Si = im * k * (exp(im * alpha / 2.) - M) / beta2;
+ Sj = im * k * (exp(im * alpha / 2.) + M) / beta2;
for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
const unsigned int j = topology[i][jj];
- formulation(i).integral(beta2 * Si * dof(u(i)), tf(u(i)), sigma(i,j), gauss);
- formulation(i,j).integral(- beta2 * (Si+Sj) * u(i), tf(g(i,j)), sigma(i,j), gauss);
+ formulation(i).integral(beta2 * Si * dof(u(i)), tf(u(i)), sigma(i, j), gauss);
+ formulation(i, j).integral(-beta2 * (Si + Sj) * u(i), tf(g(i, j)), sigma(i, j), gauss);
}
}
- else if ( Transmission == "Taylor2" ) {
- Si = im*k*(cos(alpha/2.)-M)/beta2;
- Sj = im*k*(cos(alpha/2.)+M)/beta2;
- dS = im*exp(-im*alpha/2.0)/(2.0*k);
+ else if(Transmission == "Taylor2") {
+ Si = im * k * (cos(alpha / 2.) - M) / beta2;
+ Sj = im * k * (cos(alpha / 2.) + M) / beta2;
+ dS = im * exp(-im * alpha / 2.0) / (2.0 * k);
for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
const unsigned int j = topology[i][jj];
- formulation(i).integral(beta2 * Si * dof(u(i)), tf(u(i)), sigma(i,j), gauss);
- formulation(i).integral(- beta2 * dS * grad( dof(u(i)) ), grad( tf(u(i)) ), sigma(i,j), gauss);
- formulation(i,j).integral(- beta2 * (Si+Sj) * u(i), tf(g(i,j)), sigma(i,j), gauss);
- formulation(i,j).integral(+ beta2 * (2.*dS) * grad( u(i) ), grad( tf(g(i,j)) ), sigma(i,j), gauss);
+ formulation(i).integral(beta2 * Si * dof(u(i)), tf(u(i)), sigma(i, j), gauss);
+ formulation(i).integral(-beta2 * dS * grad(dof(u(i))), grad(tf(u(i))), sigma(i, j), gauss);
+ formulation(i, j).integral(-beta2 * (Si + Sj) * u(i), tf(g(i, j)), sigma(i, j), gauss);
+ formulation(i, j).integral(+beta2 * (2. * dS) * grad(u(i)), grad(tf(g(i, j))), sigma(i, j), gauss);
}
}
- else if ( Transmission == "DtN" ) { // analytic DtN relative the normal of the artificial boundary, for a given mode
- Si = im*kx;
- Sj = im*( kx + 2*M*k/(beta2) ); // or Sj = im*( (M*k + sqrt(Argsqrt)) / beta2 );
+ else if(Transmission == "DtN") { // analytic DtN relative the normal of the artificial boundary, for a given mode
+ Si = im * kx;
+ Sj = im * (kx + 2 * M * k / (beta2)); // or Sj = im*( (M*k + sqrt(Argsqrt)) / beta2 );
for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
const unsigned int j = topology[i][jj];
- formulation(i).integral(beta2 * Si * dof(u(i)), tf(u(i)), sigma(i,j), gauss);
- formulation(i,j).integral(- beta2 * (Si+Sj) * u(i), tf(g(i,j)), sigma(i,j), gauss);
+ formulation(i).integral(beta2 * Si * dof(u(i)), tf(u(i)), sigma(i, j), gauss);
+ formulation(i, j).integral(-beta2 * (Si + Sj) * u(i), tf(g(i, j)), sigma(i, j), gauss);
}
}
- else if ( Transmission == "Pade" ) {
+ else if(Transmission == "Pade") {
int padeOrder = 4;
gmshDdm.userDefinedParameter(padeOrder, "padeOrder");
- if ( i == 0 && MPI_Rank == 0 ) {
+ if(i == 0) {
msg::info << "Use Pade transmission condition of order " << padeOrder << msg::endl;
}
const double Np = 2. * padeOrder + 1.;
- const std::complex< double > exp1 = std::complex<double>(std::cos(alpha),std::sin(alpha));
- const std::complex< double > exp2 = std::complex<double>(std::cos(alpha/2.),std::sin(alpha/2.));
- const std::complex< double > coef = 2./Np;
-
+ const std::complex< double > exp1 = std::complex< double >(std::cos(alpha), std::sin(alpha));
+ const std::complex< double > exp2 = std::complex< double >(std::cos(alpha / 2.), std::sin(alpha / 2.));
+ const std::complex< double > coef = 2. / Np;
+
for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
const unsigned int j = topology[i][jj];
- formulation(i).integral( im * k * exp2 * dof(u(i)), tf(u(i)), sigma(i,j), gauss);
- formulation(i).integral(- (im*M*k) * dof(u(i)), tf(u(i)), sigma(i,j), gauss);
+ formulation(i).integral(im * k * exp2 * dof(u(i)), tf(u(i)), sigma(i, j), gauss);
+ formulation(i).integral(-(im * M * k) * dof(u(i)), tf(u(i)), sigma(i, j), gauss);
// interface unknowns
- formulation(i,j).integral(- 2. * (im * k * exp2) * u(i), tf(g(i,j)), sigma(i,j), gauss);
-
+ formulation(i, j).integral(-2. * (im * k * exp2) * u(i), tf(g(i, j)), sigma(i, j), gauss);
+
// define Pade coefficients
std::vector< std::complex< double > > c(padeOrder, 0.);
for(int l = 0; l < padeOrder; ++l) {
@@ -328,47 +316,46 @@ int main(int argc, char **argv)
}
// define the auxiliary fields
- std::vector< Field< std::complex< double >, Form::Form0 >* > phi;
+ std::vector< Field< std::complex< double >, Form::Form0 > * > phi;
for(int l = 0; l < padeOrder; ++l) {
- phi.push_back(new Field< std::complex< double >, Form::Form0 >("phi_" + std::to_string(l), sigma(i,j), FunctionSpaceTypeForm0::HierarchicalH1, FEMorder));
+ phi.push_back(new Field< std::complex< double >, Form::Form0 >("phi_" + std::to_string(l), sigma(i, j), FunctionSpaceTypeForm0::HierarchicalH1, FEMorder));
fieldBucket.push_back(phi.back());
}
-
+
// write the augmented weak form
for(int l = 0; l < padeOrder; ++l) {
// boundary integral terms relating the auxiliary fields
- formulation(i).integral(im * k * exp2 * coef * c[l] * dof(*phi[l]), tf(u(i)), sigma(i,j), gauss);
- formulation(i).integral(im * k * exp2 * coef * c[l] * dof(u(i)), tf(u(i)), sigma(i,j), gauss);
+ formulation(i).integral(im * k * exp2 * coef * c[l] * dof(*phi[l]), tf(u(i)), sigma(i, j), gauss);
+ formulation(i).integral(im * k * exp2 * coef * c[l] * dof(u(i)), tf(u(i)), sigma(i, j), gauss);
// coupling of the auxiliary equations
- formulation(i).integral(grad(dof(*phi[l])), grad(tf(*phi[l])), sigma(i,j), gauss);
- formulation(i).integral(- (k*k)/ beta2 * (exp1 * c[l] + 1.) * dof(*phi[l]), tf(*phi[l]), sigma(i,j), gauss);
- formulation(i).integral(- (k*k)/ beta2 * exp1 * (c[l] + 1.) * dof(u(i)), tf(*phi[l]), sigma(i,j), gauss);
+ formulation(i).integral(grad(dof(*phi[l])), grad(tf(*phi[l])), sigma(i, j), gauss);
+ formulation(i).integral(-(k * k) / beta2 * (exp1 * c[l] + 1.) * dof(*phi[l]), tf(*phi[l]), sigma(i, j), gauss);
+ formulation(i).integral(-(k * k) / beta2 * exp1 * (c[l] + 1.) * dof(u(i)), tf(*phi[l]), sigma(i, j), gauss);
}
-
+
// interfaces unknowns
for(int l = 0; l < padeOrder; ++l) {
- formulation(i,j).integral(- 2. * (im * k * exp2) * coef * c[l] * (*phi[l]), tf(g(i,j)), sigma(i,j), gauss);
- formulation(i,j).integral(- 2. * (im * k * exp2) * coef * c[l] * u(i), tf(g(i,j)), sigma(i,j), gauss);
+ formulation(i, j).integral(-2. * (im * k * exp2) * coef * c[l] * (*phi[l]), tf(g(i, j)), sigma(i, j), gauss);
+ formulation(i, j).integral(-2. * (im * k * exp2) * coef * c[l] * u(i), tf(g(i, j)), sigma(i, j), gauss);
}
}
}
- else {
+ else {
msg::error << "Transmission condition not available !" << msg::endl;
exit(0);
}
-
}
// Solve the DDM formulation
formulation.pre();
- formulation.solve("jacobi",1e-6);
+ formulation.solve("jacobi", 1e-6);
//formulation.solve("gmres");
double num = 0., den = 0.;
double local_err; // L2 local error
for(unsigned int i = 0; i < static_cast< unsigned int >(nDom); ++i) {
- if ( i % MPI_Size == MPI_Rank ) {
- save(+u(i),omega(i),"u_"+std::to_string(i));
+ if(gmshddm::mpi::isItMySubdomain(i)) {
+ save(+u(i), omega(i), "u_" + std::to_string(i));
save(*solution, omega(i), "uex_" + std::to_string(i));
save(*solution - u(i), omega(i), "err_" + std::to_string(i));
@@ -390,7 +377,7 @@ int main(int argc, char **argv)
}
*/
- msg::info << "Local L2 error = " << local_err << " on rank " << MPI_Rank <<msg::endl;
+ msg::info << "Local L2 error = " << local_err << " on rank " << gmshddm::mpi::getMPIRank() << msg::endl;
for(unsigned int i = 0; i < fieldBucket.size(); ++i) {
delete fieldBucket[i];
diff --git a/demos/maxwell/CMakeLists.txt b/examples/maxwell/CMakeLists.txt
similarity index 74%
rename from demos/maxwell/CMakeLists.txt
rename to examples/maxwell/CMakeLists.txt
index c78119517ddd374d9663ff309fd250afbcd67ab9..14a0aa41dcb8ea385d1342e3e16ff57ca12f1ea2 100644
--- a/demos/maxwell/CMakeLists.txt
+++ b/examples/maxwell/CMakeLists.txt
@@ -2,7 +2,7 @@ cmake_minimum_required(VERSION 3.0 FATAL_ERROR)
project(demo CXX)
-include(${CMAKE_CURRENT_SOURCE_DIR}/../demos.cmake)
+include(${CMAKE_CURRENT_SOURCE_DIR}/../example.cmake)
add_executable(demo main.cpp ${EXTRA_INCS})
target_link_libraries(demo ${EXTRA_LIBS})
diff --git a/demos/maxwell/main.cpp b/examples/maxwell/main.cpp
similarity index 70%
rename from demos/maxwell/main.cpp
rename to examples/maxwell/main.cpp
index 7bfc36611a4a49a5dcd07d061949d1e1b2b2ee65..9b3e8c39a5c056b8942cea491a8f8bd5073dc43d 100644
--- a/demos/maxwell/main.cpp
+++ b/examples/maxwell/main.cpp
@@ -1,10 +1,9 @@
+#include "gmsh.h"
+
#include <gmshddm/Formulation.h>
#include <gmshddm/GmshDdm.h>
-
#include <gmshfem/Message.h>
-#include "gmsh.h"
-
using namespace gmshddm;
using namespace gmshddm::common;
using namespace gmshddm::domain;
@@ -20,8 +19,9 @@ using namespace gmshfem::function;
using namespace gmshfem::post;
void waveguide(const unsigned int nDom, const double a, const double b,
- const double L, const double lc) {
- if (nDom < 2) {
+ const double L, const double lc)
+{
+ if(nDom < 2) {
gmshfem::msg::error << "nDom should be at least equal to 2."
<< gmshfem::msg::endl;
exit(0);
@@ -30,9 +30,9 @@ void waveguide(const unsigned int nDom, const double a, const double b,
const double domainSize = L / nDom;
- std::vector<std::vector<int>> borders(nDom);
- std::vector<int> omegas(nDom);
- std::vector<int> sigmas(nDom - 1);
+ std::vector< std::vector< int > > borders(nDom);
+ std::vector< int > omegas(nDom);
+ std::vector< int > sigmas(nDom - 1);
int p[4];
@@ -48,7 +48,7 @@ void waveguide(const unsigned int nDom, const double a, const double b,
line[3] = gmsh::model::geo::addLine(p[3], p[0]);
int curveLoop =
- gmsh::model::geo::addCurveLoop({line[3], line[0], -line[1], line[2]});
+ gmsh::model::geo::addCurveLoop({line[3], line[0], -line[1], line[2]});
int tagSurface = gmsh::model::geo::addPlaneSurface({curveLoop});
gmsh::model::geo::mesh::setTransfiniteSurface(tagSurface);
@@ -56,11 +56,11 @@ void waveguide(const unsigned int nDom, const double a, const double b,
gmsh::model::addPhysicalGroup(2, {tagSurface}, 1);
gmsh::model::setPhysicalName(2, 1, "gammaDir");
- for (unsigned int i = 0; i < nDom; ++i) {
- std::vector<std::pair<int, int>> extrudeEntities;
+ for(unsigned int i = 0; i < nDom; ++i) {
+ std::vector< std::pair< int, int > > extrudeEntities;
gmsh::model::geo::extrude(
- {std::make_pair(2, tagSurface)}, domainSize, 0., 0., extrudeEntities,
- {static_cast<int>((domainSize) / lc)}, std::vector<double>(), true);
+ {std::make_pair(2, tagSurface)}, domainSize, 0., 0., extrudeEntities,
+ {static_cast< int >((domainSize) / lc)}, std::vector< double >(), true);
tagSurface = extrudeEntities[0].second;
omegas[i] = extrudeEntities[1].second;
borders[i].push_back(extrudeEntities[2].second);
@@ -73,26 +73,27 @@ void waveguide(const unsigned int nDom, const double a, const double b,
gmsh::model::addPhysicalGroup(2, {tagSurface}, 2);
gmsh::model::setPhysicalName(2, 2, "gammaInf");
- for (unsigned int i = 0; i < borders.size(); ++i) {
+ for(unsigned int i = 0; i < borders.size(); ++i) {
gmsh::model::addPhysicalGroup(2, borders[i], 100 + i);
gmsh::model::setPhysicalName(2, 100 + i, "border_" + std::to_string(i));
}
- for (unsigned int i = 0; i < omegas.size(); ++i) {
+ for(unsigned int i = 0; i < omegas.size(); ++i) {
gmsh::model::addPhysicalGroup(3, {omegas[i]}, i + 1);
gmsh::model::setPhysicalName(3, i + 1, "omega_" + std::to_string(i));
}
- for (unsigned int i = 0; i < sigmas.size(); ++i) {
+ for(unsigned int i = 0; i < sigmas.size(); ++i) {
gmsh::model::addPhysicalGroup(2, {sigmas[i]}, 200 + i);
gmsh::model::setPhysicalName(
- 2, 200 + i, "sigma_" + std::to_string(i) + "_" + std::to_string(i + 1));
+ 2, 200 + i, "sigma_" + std::to_string(i) + "_" + std::to_string(i + 1));
}
gmsh::model::geo::synchronize();
gmsh::model::mesh::generate();
}
-int main(int argc, char **argv) {
+int main(int argc, char **argv)
+{
GmshDdm gmshDdm(argc, argv);
/****
* input Data
@@ -121,34 +122,35 @@ int main(int argc, char **argv) {
double ky = mode_m * pi / a;
double kz = mode_n * pi / b;
double kc = sqrt(ky * ky + kz * kz);
- std::complex<double> im(0., 1.);
- std::complex<double> beta;
- if (-kc * kc + k * k >= 0) {
+ std::complex< double > im(0., 1.);
+ std::complex< double > beta;
+ if(-kc * kc + k * k >= 0) {
beta = sqrt(-kc * kc + k * k);
- } else {
+ }
+ else {
beta = -im * sqrt(kc * kc - k * k);
}
// TM
- VectorFunction<std::complex<double>> Einc = vector<std::complex<double>>(
- sin<std::complex<double>>(ky * y<std::complex<double>>()) *
- sin<std::complex<double>>(kz * z<std::complex<double>>()),
- im * beta * ky / (kc * kc) *
- cos<std::complex<double>>(ky * y<std::complex<double>>()) *
- sin<std::complex<double>>(kz * z<std::complex<double>>()),
- im * beta * kz / (kc * kc) *
- cos<std::complex<double>>(kz * z<std::complex<double>>()) *
- sin<std::complex<double>>(ky * y<std::complex<double>>()));
- /****
+ VectorFunction< std::complex< double > > Einc = vector< std::complex< double > >(
+ sin< std::complex< double > >(ky * y< std::complex< double > >()) *
+ sin< std::complex< double > >(kz * z< std::complex< double > >()),
+ im * beta * ky / (kc * kc) *
+ cos< std::complex< double > >(ky * y< std::complex< double > >()) *
+ sin< std::complex< double > >(kz * z< std::complex< double > >()),
+ im * beta * kz / (kc * kc) *
+ cos< std::complex< double > >(kz * z< std::complex< double > >()) *
+ sin< std::complex< double > >(ky * y< std::complex< double > >()));
+ /****
* FEM
****/
- if (!ddm) {
- /****
+ if(!ddm) {
+ /****
* Gmsh part
****/
gmsh::model::add("waveguide");
const double domainSize = L;
- std::vector<std::vector<int>> borders(1);
- std::vector<int> omegas(1);
+ std::vector< std::vector< int > > borders(1);
+ std::vector< int > omegas(1);
int p[4];
p[0] = gmsh::model::geo::addPoint(0., 0, 0., lc);
p[1] = gmsh::model::geo::addPoint(0, a, 0., lc);
@@ -162,17 +164,17 @@ int main(int argc, char **argv) {
line[3] = gmsh::model::geo::addLine(p[3], p[0]);
int curveLoop =
- gmsh::model::geo::addCurveLoop({line[3], line[0], -line[1], line[2]});
+ gmsh::model::geo::addCurveLoop({line[3], line[0], -line[1], line[2]});
int tagSurface = gmsh::model::geo::addPlaneSurface({curveLoop});
gmsh::model::geo::mesh::setTransfiniteSurface(tagSurface);
gmsh::model::geo::mesh::setRecombine(2, tagSurface);
gmsh::model::addPhysicalGroup(2, {tagSurface}, 1);
gmsh::model::setPhysicalName(2, 1, "gammaDir");
- std::vector<std::pair<int, int>> extrudeEntities;
+ std::vector< std::pair< int, int > > extrudeEntities;
gmsh::model::geo::extrude(
- {std::make_pair(2, tagSurface)}, domainSize, 0., 0., extrudeEntities,
- {static_cast<int>((domainSize) / lc)}, std::vector<double>(), true);
+ {std::make_pair(2, tagSurface)}, domainSize, 0., 0., extrudeEntities,
+ {static_cast< int >((domainSize) / lc)}, std::vector< double >(), true);
tagSurface = extrudeEntities[0].second;
omegas[0] = extrudeEntities[1].second;
borders[0].push_back(extrudeEntities[2].second);
@@ -193,22 +195,22 @@ int main(int argc, char **argv) {
Domain gammaInf(2, 2);
Domain gammaDir(2, 1);
Domain border(2, 100);
- gmshfem::problem::Formulation<std::complex<double>> formulation("maxwell");
+ gmshfem::problem::Formulation< std::complex< double > > formulation("maxwell");
/****
* Create fields
****/
- Field<std::complex<double>, Form::Form1> E(
- "E", omega | gammaDir | gammaInf | border,
- FunctionSpaceTypeForm1::HierarchicalHCurl, FEorder);
- Field<std::complex<double>, Form::Form1> lambda(
- "lambda", gammaDir , FunctionSpaceTypeForm1::HierarchicalHCurl,
- FEorder);
+ Field< std::complex< double >, Form::Form1 > E(
+ "E", omega | gammaDir | gammaInf | border,
+ FunctionSpaceTypeForm1::HierarchicalHCurl, FEorder);
+ Field< std::complex< double >, Form::Form1 > lambda(
+ "lambda", gammaDir, FunctionSpaceTypeForm1::HierarchicalHCurl,
+ FEorder);
// VectorFunction<std::complex<double>> n = normal<std::complex<double>>();
// VOLUME TERMS
- E.addConstraint(border, vector<std::complex<double>>(0.,0.,0.));
- lambda.addConstraint(border, vector<std::complex<double>>(0.,0.,0.));
+ E.addConstraint(border, vector< std::complex< double > >(0., 0., 0.));
+ lambda.addConstraint(border, vector< std::complex< double > >(0., 0., 0.));
formulation.integral(curl(dof(E)), curl(tf(E)), omega, gauss);
formulation.integral(-k * k * dof(E), tf(E), omega, gauss);
@@ -217,7 +219,7 @@ int main(int argc, char **argv) {
// gauss);
formulation.integral(-im * k * dof(E), tf(E), gammaInf, gauss);
// Physical source using Lagrange mutiplier
- formulation.integral(dof(lambda), tf(E), gammaDir , gauss);
+ formulation.integral(dof(lambda), tf(E), gammaDir, gauss);
formulation.integral(dof(E), tf(lambda), gammaDir, gauss);
formulation.integral(Einc, tf(lambda), gammaDir, gauss);
formulation.pre();
@@ -242,69 +244,69 @@ int main(int argc, char **argv) {
Subdomain gammaDir(nDom);
Subdomain border(nDom);
Interface sigma(nDom);
- for (unsigned int i = 0; i < unsigned(nDom); ++i) {
+ for(unsigned int i = 0; i < unsigned(nDom); ++i) {
omega(i) = Domain(3, i + 1);
- if (i == unsigned(nDom) - 1) {
+ if(i == unsigned(nDom) - 1) {
gammaInf(i) = Domain(2, 2);
}
- if (i == 0) {
+ if(i == 0) {
gammaDir(i) = Domain(2, 1);
}
border(i) = Domain(2, 100 + i);
- if (i != 0) {
+ if(i != 0) {
sigma(i, i - 1) = Domain(2, 200 + i - 1);
}
- if (i != unsigned(nDom) - 1) {
+ if(i != unsigned(nDom) - 1) {
sigma(i, i + 1) = Domain(2, 200 + i);
}
}
/****
* Define topology
****/
- std::vector<std::vector<unsigned int>> topology(nDom);
- for (unsigned int i = 0; i < unsigned(nDom); ++i) {
- if (i != 0) {
+ std::vector< std::vector< unsigned int > > topology(nDom);
+ for(unsigned int i = 0; i < unsigned(nDom); ++i) {
+ if(i != 0) {
topology[i].push_back(i - 1);
}
- if (i != unsigned(nDom) - 1) {
+ if(i != unsigned(nDom) - 1) {
topology[i].push_back(i + 1);
}
}
// Create DDM formulation
- gmshddm::problem::Formulation<std::complex<double>> formulation("Maxwell",
- topology);
+ gmshddm::problem::Formulation< std::complex< double > > formulation("Maxwell",
+ topology);
// Create fields
- SubdomainField<std::complex<double>, Form::Form1> E(
- "E", omega | gammaDir | gammaInf | sigma,
- FunctionSpaceTypeForm1::HierarchicalHCurl, FEorder);
- SubdomainField<std::complex<double>, Form::Form1> lambda(
- "lambda", gammaDir, FunctionSpaceTypeForm1::HierarchicalHCurl,
- FEorder);
- InterfaceField<std::complex<double>, Form::Form1> g(
- "g", sigma, FunctionSpaceTypeForm1::HierarchicalHCurl, 0);
+ SubdomainField< std::complex< double >, Form::Form1 > E(
+ "E", omega | gammaDir | gammaInf | sigma,
+ FunctionSpaceTypeForm1::HierarchicalHCurl, FEorder);
+ SubdomainField< std::complex< double >, Form::Form1 > lambda(
+ "lambda", gammaDir, FunctionSpaceTypeForm1::HierarchicalHCurl,
+ FEorder);
+ InterfaceField< std::complex< double >, Form::Form1 > g(
+ "g", sigma, FunctionSpaceTypeForm1::HierarchicalHCurl, 0);
// Tell to the formulation that g is field that have to be exchanged between
// subdomains
formulation.addInterfaceField(g);
- VectorFunction<std::complex<double>> n = normal<std::complex<double>>();
- VectorFunction<std::complex<double>> functionZero =
- vector<std::complex<double>>(0., 0., 0.);
- for (unsigned int i = 0; i < unsigned(nDom); ++i){
+ VectorFunction< std::complex< double > > n = normal< std::complex< double > >();
+ VectorFunction< std::complex< double > > functionZero =
+ vector< std::complex< double > >(0., 0., 0.);
+ for(unsigned int i = 0; i < unsigned(nDom); ++i) {
E(i).addConstraint(border(i), functionZero);
lambda(i).addConstraint(border(i), functionZero);
- for (unsigned int jj = 0; jj < topology[i].size(); ++jj) {
+ for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
const unsigned int j = topology[i][jj];
g(i, j).addConstraint(border(i), functionZero);
}
}
// Add terms to the formulation
- for (unsigned int i = 0; i < unsigned(nDom); ++i) {
+ for(unsigned int i = 0; i < unsigned(nDom); ++i) {
// VOLUME TERMS
formulation(i).integral(curl(dof(E(i))), curl(tf(E(i))), omega(i), gauss);
formulation(i).integral(-k * k * dof(E(i)), tf(E(i)), omega(i), gauss);
@@ -316,13 +318,13 @@ int main(int argc, char **argv) {
// Physical source using Lagrange mutiplier
formulation(i).integral(dof(lambda(i)), tf(E(i)), gammaDir(i),
gauss);
- formulation(i).integral(dof(E(i)), tf(lambda(i)), gammaDir(i) ,
+ formulation(i).integral(dof(E(i)), tf(lambda(i)), gammaDir(i),
gauss);
formulation(i).integral(formulation.physicalSource(Einc), tf(lambda(i)),
gammaDir(i), gauss);
// Artificial source on transmission boundaries
- for (unsigned int jj = 0; jj < topology[i].size(); ++jj) {
+ for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
const unsigned int j = topology[i][jj];
/* formulation(i).integral(-im * k * n % (dof(E(i)) % n), tf(E(i)),
sigma(i, j), gauss);*/
@@ -332,7 +334,7 @@ int main(int argc, char **argv) {
sigma(i, j), gauss);
}
// INTERFACE TERMS
- for (unsigned int jj = 0; jj < topology[i].size(); ++jj) {
+ for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
const unsigned int j = topology[i][jj];
formulation(i, j).integral(dof(g(i, j)), tf(g(i, j)), sigma(i, j),
gauss);
@@ -348,7 +350,7 @@ int main(int argc, char **argv) {
// Solve the DDM formulation
formulation.solve("gmres");
//save field E
- for (int i = 0; i < nDom; ++i) {
+ for(int i = 0; i < nDom; ++i) {
save(E(i), omega(i), "E" + std::to_string(i));
}
}
diff --git a/demos/helmholtzflow/waveguide/CMakeLists.txt b/examples/navier/scattering/CMakeLists.txt
old mode 100644
new mode 100755
similarity index 73%
rename from demos/helmholtzflow/waveguide/CMakeLists.txt
rename to examples/navier/scattering/CMakeLists.txt
index 4d2e4b0c91d2a7e0da5a224e581c56eca24b2f71..c368ce59f63aed4e569c1b3e727df6dd0b1d6a45
--- a/demos/helmholtzflow/waveguide/CMakeLists.txt
+++ b/examples/navier/scattering/CMakeLists.txt
@@ -2,7 +2,7 @@ cmake_minimum_required(VERSION 3.0 FATAL_ERROR)
project(demo CXX)
-include(${CMAKE_CURRENT_SOURCE_DIR}/../../demos.cmake)
+include(${CMAKE_CURRENT_SOURCE_DIR}/../../example.cmake)
add_executable(demo main.cpp ${EXTRA_INCS})
target_link_libraries(demo ${EXTRA_LIBS})
diff --git a/demos/navier/scattering/main.cpp b/examples/navier/scattering/main.cpp
similarity index 68%
rename from demos/navier/scattering/main.cpp
rename to examples/navier/scattering/main.cpp
index d94b532a9331cc24d5eda9c7b2611dbf542a3b70..b717993b57c63bbc36ccf4636bcbe6f59d1cee42 100644
--- a/demos/navier/scattering/main.cpp
+++ b/examples/navier/scattering/main.cpp
@@ -1,10 +1,9 @@
-#include <gmshddm/GmshDdm.h>
-#include <gmshddm/Formulation.h>
+#include "gmsh.h"
+#include <gmshddm/Formulation.h>
+#include <gmshddm/GmshDdm.h>
#include <gmshfem/Message.h>
-#include "gmsh.h"
-
using namespace gmshddm;
using namespace gmshddm::common;
using namespace gmshddm::domain;
@@ -39,7 +38,7 @@ void circlesConcentric(const unsigned int nDom, const double r0, const double rI
std::vector< int > tagsSurface(nDom);
for(unsigned int i = 0; i < nDom; ++i) {
- tagsSurface[i] = gmsh::model::occ::addPlaneSurface({tagsCurve[i], tagsCurve[i+1]});
+ tagsSurface[i] = gmsh::model::occ::addPlaneSurface({tagsCurve[i], tagsCurve[i + 1]});
}
gmsh::model::occ::synchronize();
@@ -55,7 +54,7 @@ void circlesConcentric(const unsigned int nDom, const double r0, const double rI
gmsh::model::setPhysicalName(2, 1 + i, "omega_" + std::to_string(i));
if(i != nDom - 1) {
- gmsh::model::addPhysicalGroup(1, {tagsCircle[i+1]}, 200 + i);
+ gmsh::model::addPhysicalGroup(1, {tagsCircle[i + 1]}, 200 + i);
gmsh::model::setPhysicalName(1, 200 + i, "sigma_" + std::to_string(i));
}
}
@@ -127,20 +126,20 @@ int main(int argc, char **argv)
gmshddm::problem::Formulation< std::complex< double > > formulation("Navier", topology);
const double pi = 3.14159265358979323846264338327950288;
- const double rho = 1.; //.............[kg/m3] masse volumique
- double f = 1.; //.............[Hz] fréquence
- double w = 2 * pi * f; //.............[rad/s] pulsation
- const double lambda = 1.; //.............[Pa] premier coefficient de Lamé
- const double mu = 1.; //.............[Pa] deuxième coefficient de Lamé
- const double cP = sqrt((lambda+2.0*mu)/rho); //.............[m/s] celerite de l'onde P
- const double cS = sqrt(mu/rho); //.............[m/s] celerite de l'onde S
- double kP = w/cP; //.............[1/m] nombre d'onde p
- double kS = w/cS; //.............[1/m] nombre d'onde s
-
- TensorFunction< std::complex< double > > C_xx = tensor< std::complex< double > >((lambda+2.*mu), 0., 0., 0., mu, 0., 0., 0., 0.);
+ const double rho = 1.; //.............[kg/m3] masse volumique
+ double f = 1.; //.............[Hz] fréquence
+ double w = 2 * pi * f; //.............[rad/s] pulsation
+ const double lambda = 1.; //.............[Pa] premier coefficient de Lamé
+ const double mu = 1.; //.............[Pa] deuxième coefficient de Lamé
+ const double cP = sqrt((lambda + 2.0 * mu) / rho); //.............[m/s] celerite de l'onde P
+ const double cS = sqrt(mu / rho); //.............[m/s] celerite de l'onde S
+ double kP = w / cP; //.............[1/m] nombre d'onde p
+ double kS = w / cS; //.............[1/m] nombre d'onde s
+
+ TensorFunction< std::complex< double > > C_xx = tensor< std::complex< double > >((lambda + 2. * mu), 0., 0., 0., mu, 0., 0., 0., 0.);
TensorFunction< std::complex< double > > C_xy = tensor< std::complex< double > >(0., lambda, 0., mu, 0., 0., 0., 0., 0.);
TensorFunction< std::complex< double > > C_yx = tensor< std::complex< double > >(0., mu, 0., lambda, 0., 0., 0., 0., 0.);
- TensorFunction< std::complex< double > > C_yy = tensor< std::complex< double > >(mu, 0., 0., 0., (lambda+2.*mu), 0., 0., 0., 0.);
+ TensorFunction< std::complex< double > > C_yy = tensor< std::complex< double > >(mu, 0., 0., 0., (lambda + 2. * mu), 0., 0., 0., 0.);
// Create fields
SubdomainField< std::complex< double >, Form::Form0 > ux("ux", omega | gammaScat | gammaInf | sigma, FunctionSpaceTypeForm0::Lagrange);
@@ -172,7 +171,7 @@ int main(int argc, char **argv)
// Physical source
formulation(i).integral(dof(lambdax(i)), tf(ux(i)), gammaScat(i), gauss);
formulation(i).integral(dof(ux(i)), tf(lambdax(i)), gammaScat(i), gauss);
- formulation(i).integral(formulation.physicalSource(- (cos(kP * x< std::complex< double > >()) + im * sin(kP * x< std::complex< double > >()))), tf(lambdax(i)), gammaScat(i), gauss);
+ formulation(i).integral(formulation.physicalSource(-(cos(kP * x< std::complex< double > >()) + im * sin(kP * x< std::complex< double > >()))), tf(lambdax(i)), gammaScat(i), gauss);
formulation(i).integral(dof(lambday(i)), tf(uy(i)), gammaScat(i), gauss);
formulation(i).integral(dof(uy(i)), tf(lambday(i)), gammaScat(i), gauss);
@@ -185,45 +184,45 @@ int main(int argc, char **argv)
formulation(i).integral(-im * w * cP * rho * nY * nY * dof(uy(i)), tf(uy(i)), gammaInf(i), gauss);
formulation(i).integral(-im * w * cS * rho * nY * nY * dof(ux(i)), tf(ux(i)), gammaInf(i), gauss);
- formulation(i).integral( im * w * cS * rho * nX * nY * dof(uy(i)), tf(ux(i)), gammaInf(i), gauss);
+ formulation(i).integral(im * w * cS * rho * nX * nY * dof(uy(i)), tf(ux(i)), gammaInf(i), gauss);
formulation(i).integral(-im * w * cS * rho * nX * nX * dof(uy(i)), tf(uy(i)), gammaInf(i), gauss);
- formulation(i).integral( im * w * cS * rho * nX * nY * dof(ux(i)), tf(uy(i)), gammaInf(i), gauss);
+ formulation(i).integral(im * w * cS * rho * nX * nY * dof(ux(i)), tf(uy(i)), gammaInf(i), gauss);
// Artificial source
for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
const unsigned int j = topology[i][jj];
- formulation(i).integral(-im * w * cP * rho * nX * nX * dof(ux(i)), tf(ux(i)), sigma(i,j), gauss);
- formulation(i).integral(-im * w * cP * rho * nX * nY * dof(uy(i)), tf(ux(i)), sigma(i,j), gauss);
- formulation(i).integral(-im * w * cP * rho * nX * nY * dof(ux(i)), tf(uy(i)), sigma(i,j), gauss);
- formulation(i).integral(-im * w * cP * rho * nY * nY * dof(uy(i)), tf(uy(i)), sigma(i,j), gauss);
-
- formulation(i).integral(-im * w * cS * rho * nY * nY * dof(ux(i)), tf(ux(i)), sigma(i,j), gauss);
- formulation(i).integral( im * w * cS * rho * nX * nY * dof(uy(i)), tf(ux(i)), sigma(i,j), gauss);
- formulation(i).integral(-im * w * cS * rho * nX * nX * dof(uy(i)), tf(uy(i)), sigma(i,j), gauss);
- formulation(i).integral( im * w * cS * rho * nX * nY * dof(ux(i)), tf(uy(i)), sigma(i,j), gauss);
-
- formulation(i).integral(formulation.artificialSource( -gx(j,i) ), tf(ux(i)), sigma(i,j), gauss);
- formulation(i).integral(formulation.artificialSource( -gy(j,i) ), tf(uy(i)), sigma(i,j), gauss);
+ formulation(i).integral(-im * w * cP * rho * nX * nX * dof(ux(i)), tf(ux(i)), sigma(i, j), gauss);
+ formulation(i).integral(-im * w * cP * rho * nX * nY * dof(uy(i)), tf(ux(i)), sigma(i, j), gauss);
+ formulation(i).integral(-im * w * cP * rho * nX * nY * dof(ux(i)), tf(uy(i)), sigma(i, j), gauss);
+ formulation(i).integral(-im * w * cP * rho * nY * nY * dof(uy(i)), tf(uy(i)), sigma(i, j), gauss);
+
+ formulation(i).integral(-im * w * cS * rho * nY * nY * dof(ux(i)), tf(ux(i)), sigma(i, j), gauss);
+ formulation(i).integral(im * w * cS * rho * nX * nY * dof(uy(i)), tf(ux(i)), sigma(i, j), gauss);
+ formulation(i).integral(-im * w * cS * rho * nX * nX * dof(uy(i)), tf(uy(i)), sigma(i, j), gauss);
+ formulation(i).integral(im * w * cS * rho * nX * nY * dof(ux(i)), tf(uy(i)), sigma(i, j), gauss);
+
+ formulation(i).integral(formulation.artificialSource(-gx(j, i)), tf(ux(i)), sigma(i, j), gauss);
+ formulation(i).integral(formulation.artificialSource(-gy(j, i)), tf(uy(i)), sigma(i, j), gauss);
}
// INTERFACE TERMS
for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
const unsigned int j = topology[i][jj];
- formulation(i,j).integral(dof(gx(i,j)), tf(gx(i,j)), sigma(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( gx(j,i) ), tf(gx(i,j)), sigma(i,j), gauss);
+ formulation(i, j).integral(dof(gx(i, j)), tf(gx(i, j)), sigma(i, j), gauss);
+ formulation(i, j).integral(formulation.artificialSource(gx(j, i)), tf(gx(i, j)), sigma(i, j), gauss);
- formulation(i,j).integral(dof(gy(i,j)), tf(gy(i,j)), sigma(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( gy(j,i) ), tf(gy(i,j)), sigma(i,j), gauss);
+ formulation(i, j).integral(dof(gy(i, j)), tf(gy(i, j)), sigma(i, j), gauss);
+ formulation(i, j).integral(formulation.artificialSource(gy(j, i)), tf(gy(i, j)), sigma(i, j), gauss);
- formulation(i,j).integral(2. * im * w * cP * rho * nX * nX * ux(i), tf(gx(i,j)), sigma(i,j), gauss);
- formulation(i,j).integral(2. * im * w * cP * rho * nX * nY * uy(i), tf(gx(i,j)), sigma(i,j), gauss);
- formulation(i,j).integral(2. * im * w * cP * rho * nX * nY * ux(i), tf(gy(i,j)), sigma(i,j), gauss);
- formulation(i,j).integral(2. * im * w * cP * rho * nY * nY * uy(i), tf(gy(i,j)), sigma(i,j), gauss);
+ formulation(i, j).integral(2. * im * w * cP * rho * nX * nX * ux(i), tf(gx(i, j)), sigma(i, j), gauss);
+ formulation(i, j).integral(2. * im * w * cP * rho * nX * nY * uy(i), tf(gx(i, j)), sigma(i, j), gauss);
+ formulation(i, j).integral(2. * im * w * cP * rho * nX * nY * ux(i), tf(gy(i, j)), sigma(i, j), gauss);
+ formulation(i, j).integral(2. * im * w * cP * rho * nY * nY * uy(i), tf(gy(i, j)), sigma(i, j), gauss);
- formulation(i,j).integral(2. * im * w * cS * rho * nY * nY * ux(i), tf(gx(i,j)), sigma(i,j), gauss);
- formulation(i,j).integral(-2. * im * w * cS * rho * nX * nY * uy(i), tf(gx(i,j)), sigma(i,j), gauss);
- formulation(i,j).integral(2. * im * w * cS * rho * nX * nX * uy(i), tf(gy(i,j)), sigma(i,j), gauss);
- formulation(i,j).integral(-2. * im * w * cS * rho * nX * nY * ux(i), tf(gy(i,j)), sigma(i,j), gauss);
+ formulation(i, j).integral(2. * im * w * cS * rho * nY * nY * ux(i), tf(gx(i, j)), sigma(i, j), gauss);
+ formulation(i, j).integral(-2. * im * w * cS * rho * nX * nY * uy(i), tf(gx(i, j)), sigma(i, j), gauss);
+ formulation(i, j).integral(2. * im * w * cS * rho * nX * nX * uy(i), tf(gy(i, j)), sigma(i, j), gauss);
+ formulation(i, j).integral(-2. * im * w * cS * rho * nX * nY * ux(i), tf(gy(i, j)), sigma(i, j), gauss);
}
}
diff --git a/tutorials/.clang-format b/tutorials/.clang-format
new file mode 100644
index 0000000000000000000000000000000000000000..d902ab979dca0361bb1b063642225163bda4eb7d
--- /dev/null
+++ b/tutorials/.clang-format
@@ -0,0 +1,112 @@
+---
+Language: Cpp
+AccessModifierOffset: -1
+AlignAfterOpenBracket: Align
+AlignConsecutiveAssignments: false
+AlignConsecutiveDeclarations: false
+AlignEscapedNewlines: Right
+AlignOperands: true
+AlignTrailingComments: false
+AllowAllParametersOfDeclarationOnNextLine: true
+AllowShortBlocksOnASingleLine: false
+AllowShortCaseLabelsOnASingleLine: true
+AllowShortFunctionsOnASingleLine: Empty
+AllowShortIfStatementsOnASingleLine: true
+AllowShortLoopsOnASingleLine: true
+AlwaysBreakAfterDefinitionReturnType: None
+AlwaysBreakAfterReturnType: None
+AlwaysBreakBeforeMultilineStrings: false
+AlwaysBreakTemplateDeclarations: true
+BinPackArguments: true
+BinPackParameters: true
+BraceWrapping:
+ AfterClass: true
+ AfterControlStatement: false
+ AfterEnum: false
+ AfterFunction: true
+ AfterNamespace: true
+ AfterObjCDeclaration: false
+ AfterStruct: false
+ AfterUnion: false
+ AfterExternBlock: false
+ BeforeCatch: true
+ BeforeElse: true
+ IndentBraces: false
+ SplitEmptyFunction: true
+ SplitEmptyRecord: true
+ SplitEmptyNamespace: true
+BreakBeforeBinaryOperators: None
+BreakBeforeBraces: Custom
+BreakBeforeInheritanceComma: false
+BreakBeforeTernaryOperators: true
+BreakConstructorInitializersBeforeComma: false
+BreakConstructorInitializers: AfterColon
+BreakAfterJavaFieldAnnotations: false
+BreakStringLiterals: true
+ColumnLimit: 0
+CommentPragmas: '^ IWYU pragma:'
+CompactNamespaces: false
+ConstructorInitializerAllOnOneLineOrOnePerLine: false
+ConstructorInitializerIndentWidth: 2
+ContinuationIndentWidth: 2
+Cpp11BracedListStyle: true
+DerivePointerAlignment: false
+DisableFormat: false
+ExperimentalAutoDetectBinPacking: false
+FixNamespaceComments: true
+ForEachMacros:
+ - foreach
+ - Q_FOREACH
+ - BOOST_FOREACH
+IncludeBlocks: Regroup
+IncludeCategories:
+ - Regex: '^"(?!gmsh\.h"|petsc\.h"|Eigen")'
+ Priority: 2
+ - Regex: '"gmsh.h"|"petsc.h"|"Eigen"'
+ Priority: 3
+ - Regex: '^<'
+ Priority: 4
+ - Regex: '.*'
+ Priority: 1
+IncludeIsMainRegex: '$'
+IndentCaseLabels: false
+IndentPPDirectives: None
+IndentWidth: 2
+IndentWrappedFunctionNames: false
+JavaScriptQuotes: Leave
+JavaScriptWrapImports: true
+KeepEmptyLinesAtTheStartOfBlocks: true
+MacroBlockBegin: ''
+MacroBlockEnd: ''
+MaxEmptyLinesToKeep: 2
+NamespaceIndentation: All
+ObjCBlockIndentWidth: 2
+ObjCSpaceAfterProperty: false
+ObjCSpaceBeforeProtocolList: true
+PenaltyBreakAssignment: 2
+PenaltyBreakBeforeFirstCallParameter: 19
+PenaltyBreakComment: 300
+PenaltyBreakFirstLessLess: 120
+PenaltyBreakString: 1000
+PenaltyExcessCharacter: 1000000
+PenaltyReturnTypeOnItsOwnLine: 60
+PointerAlignment: Right
+ReflowComments: false
+SortIncludes: true
+SortUsingDeclarations: true
+SpaceAfterCStyleCast: false
+SpaceAfterTemplateKeyword: false
+SpaceBeforeAssignmentOperators: true
+SpaceBeforeParens: Never
+SpaceInEmptyParentheses: false
+SpacesBeforeTrailingComments: 1
+SpacesInAngles: true
+SpacesInContainerLiterals: true
+SpacesInCStyleCastParentheses: false
+SpacesInParentheses: false
+SpacesInSquareBrackets: false
+Standard: Cpp11
+TabWidth: 4
+UseTab: Never
+...
+
diff --git a/tutorials/CMakeLists.txt b/tutorials/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..210187a9649003866f9d32cff8264416605deb81
--- /dev/null
+++ b/tutorials/CMakeLists.txt
@@ -0,0 +1,11 @@
+set(TUTOS
+ helmholtz/waveguide
+ maxwell/waveguide
+)
+
+foreach(TUTO ${TUTOS})
+ add_test(NAME "tuto:${TUTO}:mkdir" COMMAND "${CMAKE_COMMAND}" -E make_directory build WORKING_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR}/${TUTO})
+ add_test(NAME "tuto:${TUTO}:cmake" COMMAND "${CMAKE_COMMAND}" -DCMAKE_PREFIX_PATH=${CMAKE_INSTALL_PREFIX} .. WORKING_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR}/${TUTO}/build)
+ add_test(NAME "tuto:${TUTO}:build" COMMAND "${CMAKE_MAKE_PROGRAM}" WORKING_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR}/${TUTO}/build)
+ add_test(NAME "tuto:${TUTO}:run" COMMAND ./tuto WORKING_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR}/${TUTO}/build)
+endforeach()
diff --git a/tutorials/README.md b/tutorials/README.md
new file mode 100644
index 0000000000000000000000000000000000000000..fc6fff349f9a001d05bf1af2d7fe1e7ec88bf1c9
--- /dev/null
+++ b/tutorials/README.md
@@ -0,0 +1,3 @@
+# GmshDDM tutorials
+
+Todo: Create tutorials based on problems of increasing difficulties that shows first the basic features of GmshDDM ('basic tutorial'), then that presents some more advanced uses ('advanced tutorial') @CGeuzaine ?
diff --git a/tutorials/helmholtz/waveguide/CMakeLists.txt b/tutorials/helmholtz/waveguide/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7481f3ad58dcd475585824c7f40fddf332e191dc
--- /dev/null
+++ b/tutorials/helmholtz/waveguide/CMakeLists.txt
@@ -0,0 +1,8 @@
+cmake_minimum_required(VERSION 3.0 FATAL_ERROR)
+
+project(tuto CXX)
+
+include(${CMAKE_CURRENT_SOURCE_DIR}/../../tutorial.cmake)
+
+add_executable(tuto main.cpp ${EXTRA_INCS})
+target_link_libraries(tuto ${EXTRA_LIBS})
diff --git a/demos/helmholtz/waveguide/main.cpp b/tutorials/helmholtz/waveguide/main.cpp
similarity index 78%
rename from demos/helmholtz/waveguide/main.cpp
rename to tutorials/helmholtz/waveguide/main.cpp
index a19176604364f6c8aa79f9e501051c45ef92468f..0a9b5b028798234adc46d604fa99b4669227eee2 100644
--- a/demos/helmholtz/waveguide/main.cpp
+++ b/tutorials/helmholtz/waveguide/main.cpp
@@ -1,11 +1,10 @@
-#include <gmshddm/GmshDdm.h>
+#include "gmsh.h"
+
#include <gmshddm/Formulation.h>
+#include <gmshddm/GmshDdm.h>
#include <gmshddm/MPIInterface.h>
-
#include <gmshfem/Message.h>
-#include "gmsh.h"
-
using namespace gmshddm;
using namespace gmshddm::common;
using namespace gmshddm::domain;
@@ -44,6 +43,7 @@ void waveguide(const unsigned int nDom, const double l, const double L, const do
gmsh::model::addPhysicalGroup(1, {line}, 1);
gmsh::model::setPhysicalName(1, 1, "gammaDir");
+ std::vector< int > cornerTags;
for(unsigned int i = 0; i < nDom; ++i) {
std::vector< std::pair< int, int > > extrudeEntities;
gmsh::model::geo::extrude({std::make_pair(1, line)}, domainSize, 0., 0., extrudeEntities, {static_cast< int >((domainSize) / lc)}, std::vector< double >(), true);
@@ -52,6 +52,10 @@ void waveguide(const unsigned int nDom, const double l, const double L, const do
borders[i].push_back(extrudeEntities[2].second);
borders[i].push_back(extrudeEntities[3].second);
sigmas[i] = line;
+ if(i != nDom - 1) {
+ cornerTags.push_back(3 + cornerTags.size());
+ cornerTags.push_back(3 + cornerTags.size());
+ }
}
gmsh::model::addPhysicalGroup(1, {line}, 2);
@@ -72,6 +76,9 @@ void waveguide(const unsigned int nDom, const double l, const double L, const do
gmsh::model::setPhysicalName(1, 200 + i, "sigma_" + std::to_string(i) + "_" + std::to_string(i + 1));
}
+ gmsh::model::addPhysicalGroup(0, cornerTags, 1000);
+ gmsh::model::setPhysicalName(0, 1000, "corner");
+
gmsh::model::geo::synchronize();
gmsh::model::mesh::generate();
}
@@ -79,10 +86,7 @@ void waveguide(const unsigned int nDom, const double l, const double L, const do
int main(int argc, char **argv)
{
GmshDdm gmshDdm(argc, argv);
-
- const unsigned int MPI_Size = getMPISize();
- const unsigned int MPI_Rank = getMPIRank();
-
+
double pi = 3.14159265359;
int nDom = 3;
@@ -111,6 +115,7 @@ int main(int argc, char **argv)
Subdomain gammaDir(nDom);
Subdomain border(nDom);
Interface sigma(nDom);
+ Domain corner = Domain("corner");
for(unsigned int i = 0; i < nDom; ++i) {
omega(i) = Domain(2, i + 1);
@@ -150,8 +155,17 @@ int main(int argc, char **argv)
// Create fields
SubdomainField< std::complex< double >, Form::Form0 > u("u", omega | gammaDir | gammaInf | border | sigma, FunctionSpaceTypeForm0::HierarchicalH1, order);
- SubdomainField< std::complex< double >, Form::Form0 > lambda("lambda", gammaDir | border, FunctionSpaceTypeForm0::HierarchicalH1, order);
+ for(unsigned int i = 0; i < nDom; ++i) {
+ u(i).addConstraint(border(i), 0.);
+ }
+ u(0).addConstraint(gammaDir(0), sin< std::complex< double > >(pi * y< std::complex< double > >() / l));
InterfaceField< std::complex< double >, Form::Form0 > g("g", sigma, FunctionSpaceTypeForm0::HierarchicalH1, order);
+ for(unsigned int i = 0; i < nDom; ++i) {
+ for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
+ const unsigned int j = topology[i][jj];
+ g(i, j).addConstraint(corner, 0.);
+ }
+ }
std::complex< double > im(0., 1.);
@@ -161,29 +175,23 @@ int main(int argc, char **argv)
// Add terms to the formulation
for(unsigned int i = 0; i < nDom; ++i) {
// VOLUME TERMS
-
formulation(i).integral(grad(dof(u(i))), grad(tf(u(i))), omega(i), gauss);
- formulation(i).integral(- k * k * dof(u(i)), tf(u(i)), omega(i), gauss);
- formulation(i).integral(- im * k * dof(u(i)), tf(u(i)), gammaInf(i), gauss);
-
- // Physical source
- formulation(i).integral(dof(lambda(i)), tf(u(i)), gammaDir(i) | border(i), gauss);
- formulation(i).integral(dof(u(i)), tf(lambda(i)), gammaDir(i) | border(i), gauss);
- formulation(i).integral(formulation.physicalSource( -sin< std::complex< double > >((kIn * pi / l) * y< std::complex< double > >() ) ), tf(lambda(i)), gammaDir(i), gauss);
+ formulation(i).integral(-k * k * dof(u(i)), tf(u(i)), omega(i), gauss);
+ formulation(i).integral(-im * k * dof(u(i)), tf(u(i)), gammaInf(i), gauss);
// Artificial source
for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
const unsigned int j = topology[i][jj];
- formulation(i).integral(- im * k * dof(u(i)), tf(u(i)), sigma(i,j), gauss);
- formulation(i).integral(formulation.artificialSource( -g(j,i) ), tf(u(i)), sigma(i,j), gauss);
+ formulation(i).integral(-im * k * dof(u(i)), tf(u(i)), sigma(i, j), gauss);
+ formulation(i).integral(formulation.artificialSource(-g(j, i)), tf(u(i)), sigma(i, j), gauss);
}
// INTERFACE TERMS
for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
const unsigned int j = topology[i][jj];
- formulation(i,j).integral(dof(g(i,j)), tf(g(i,j)), sigma(i,j), gauss);
- formulation(i,j).integral(formulation.artificialSource( g(j,i) ), tf(g(i,j)), sigma(i,j), gauss);
- formulation(i,j).integral(2. * im * k * u(i), tf(g(i,j)), sigma(i,j), gauss);
+ formulation(i, j).integral(dof(g(i, j)), tf(g(i, j)), sigma(i, j), gauss);
+ formulation(i, j).integral(formulation.artificialSource(g(j, i)), tf(g(i, j)), sigma(i, j), gauss);
+ formulation(i, j).integral(2. * im * k * u(i), tf(g(i, j)), sigma(i, j), gauss);
}
}
@@ -194,8 +202,8 @@ int main(int argc, char **argv)
formulation.solve("gmres", 1e-6, iterMax);
for(unsigned int i = 0; i < nDom; ++i) {
- if(i % MPI_Size == MPI_Rank) {
- save(u(i), omega(i), "u_" + std::to_string(i));
+ if(isItMySubdomain(i)) {
+ save(u(i), omega(i), "u_" + std::to_string(i));
}
}
diff --git a/tutorials/maxwell/main.cpp b/tutorials/maxwell/main.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..9b3e8c39a5c056b8942cea491a8f8bd5073dc43d
--- /dev/null
+++ b/tutorials/maxwell/main.cpp
@@ -0,0 +1,359 @@
+#include "gmsh.h"
+
+#include <gmshddm/Formulation.h>
+#include <gmshddm/GmshDdm.h>
+#include <gmshfem/Message.h>
+
+using namespace gmshddm;
+using namespace gmshddm::common;
+using namespace gmshddm::domain;
+using namespace gmshddm::problem;
+using namespace gmshddm::field;
+
+using namespace gmshfem;
+using namespace gmshfem::domain;
+using namespace gmshfem::equation;
+using namespace gmshfem::problem;
+using namespace gmshfem::field;
+using namespace gmshfem::function;
+using namespace gmshfem::post;
+
+void waveguide(const unsigned int nDom, const double a, const double b,
+ const double L, const double lc)
+{
+ if(nDom < 2) {
+ gmshfem::msg::error << "nDom should be at least equal to 2."
+ << gmshfem::msg::endl;
+ exit(0);
+ }
+ gmsh::model::add("waveguide");
+
+ const double domainSize = L / nDom;
+
+ std::vector< std::vector< int > > borders(nDom);
+ std::vector< int > omegas(nDom);
+ std::vector< int > sigmas(nDom - 1);
+
+ int p[4];
+
+ p[0] = gmsh::model::geo::addPoint(0., 0, 0., lc);
+ p[1] = gmsh::model::geo::addPoint(0, a, 0., lc);
+ p[2] = gmsh::model::geo::addPoint(0, a, b, lc);
+ p[3] = gmsh::model::geo::addPoint(0, 0., b, lc);
+ int line[4];
+
+ line[0] = gmsh::model::geo::addLine(p[0], p[1]);
+ line[1] = gmsh::model::geo::addLine(p[2], p[1]);
+ line[2] = gmsh::model::geo::addLine(p[2], p[3]);
+ line[3] = gmsh::model::geo::addLine(p[3], p[0]);
+
+ int curveLoop =
+ gmsh::model::geo::addCurveLoop({line[3], line[0], -line[1], line[2]});
+
+ int tagSurface = gmsh::model::geo::addPlaneSurface({curveLoop});
+ gmsh::model::geo::mesh::setTransfiniteSurface(tagSurface);
+ gmsh::model::geo::mesh::setRecombine(2, tagSurface);
+ gmsh::model::addPhysicalGroup(2, {tagSurface}, 1);
+ gmsh::model::setPhysicalName(2, 1, "gammaDir");
+
+ for(unsigned int i = 0; i < nDom; ++i) {
+ std::vector< std::pair< int, int > > extrudeEntities;
+ gmsh::model::geo::extrude(
+ {std::make_pair(2, tagSurface)}, domainSize, 0., 0., extrudeEntities,
+ {static_cast< int >((domainSize) / lc)}, std::vector< double >(), true);
+ tagSurface = extrudeEntities[0].second;
+ omegas[i] = extrudeEntities[1].second;
+ borders[i].push_back(extrudeEntities[2].second);
+ borders[i].push_back(extrudeEntities[3].second);
+ borders[i].push_back(extrudeEntities[4].second);
+ borders[i].push_back(extrudeEntities[5].second);
+ sigmas[i] = tagSurface;
+ }
+
+ gmsh::model::addPhysicalGroup(2, {tagSurface}, 2);
+ gmsh::model::setPhysicalName(2, 2, "gammaInf");
+
+ for(unsigned int i = 0; i < borders.size(); ++i) {
+ gmsh::model::addPhysicalGroup(2, borders[i], 100 + i);
+ gmsh::model::setPhysicalName(2, 100 + i, "border_" + std::to_string(i));
+ }
+
+ for(unsigned int i = 0; i < omegas.size(); ++i) {
+ gmsh::model::addPhysicalGroup(3, {omegas[i]}, i + 1);
+ gmsh::model::setPhysicalName(3, i + 1, "omega_" + std::to_string(i));
+ }
+
+ for(unsigned int i = 0; i < sigmas.size(); ++i) {
+ gmsh::model::addPhysicalGroup(2, {sigmas[i]}, 200 + i);
+ gmsh::model::setPhysicalName(
+ 2, 200 + i, "sigma_" + std::to_string(i) + "_" + std::to_string(i + 1));
+ }
+ gmsh::model::geo::synchronize();
+ gmsh::model::mesh::generate();
+}
+
+int main(int argc, char **argv)
+{
+ GmshDdm gmshDdm(argc, argv);
+ /****
+ * input Data
+ ****/
+ double pi = 3.14159265359;
+ int nDom = 2;
+ double L = 2;
+ double a = 1;
+ double b = 1;
+ double k = 10;
+ double mode_m = 2.;
+ double mode_n = 1.;
+ int FEorder = 0;
+ double lc = 0.5;
+ bool ddm = true;
+ std::string gauss = "Gauss4";
+ gmshDdm.userDefinedParameter(ddm, "ddm");
+ gmshDdm.userDefinedParameter(nDom, "nDom");
+ gmshDdm.userDefinedParameter(L, "L");
+ gmshDdm.userDefinedParameter(a, "a");
+ gmshDdm.userDefinedParameter(b, "b");
+ gmshDdm.userDefinedParameter(lc, "lc");
+ gmshDdm.userDefinedParameter(k, "k");
+ gmshDdm.userDefinedParameter(FEorder, "FEorder");
+ gmshDdm.userDefinedParameter(gauss, "gauss");
+ double ky = mode_m * pi / a;
+ double kz = mode_n * pi / b;
+ double kc = sqrt(ky * ky + kz * kz);
+ std::complex< double > im(0., 1.);
+ std::complex< double > beta;
+ if(-kc * kc + k * k >= 0) {
+ beta = sqrt(-kc * kc + k * k);
+ }
+ else {
+ beta = -im * sqrt(kc * kc - k * k);
+ }
+ // TM
+ VectorFunction< std::complex< double > > Einc = vector< std::complex< double > >(
+ sin< std::complex< double > >(ky * y< std::complex< double > >()) *
+ sin< std::complex< double > >(kz * z< std::complex< double > >()),
+ im * beta * ky / (kc * kc) *
+ cos< std::complex< double > >(ky * y< std::complex< double > >()) *
+ sin< std::complex< double > >(kz * z< std::complex< double > >()),
+ im * beta * kz / (kc * kc) *
+ cos< std::complex< double > >(kz * z< std::complex< double > >()) *
+ sin< std::complex< double > >(ky * y< std::complex< double > >()));
+ /****
+ * FEM
+ ****/
+ if(!ddm) {
+ /****
+ * Gmsh part
+ ****/
+ gmsh::model::add("waveguide");
+ const double domainSize = L;
+ std::vector< std::vector< int > > borders(1);
+ std::vector< int > omegas(1);
+ int p[4];
+ p[0] = gmsh::model::geo::addPoint(0., 0, 0., lc);
+ p[1] = gmsh::model::geo::addPoint(0, a, 0., lc);
+ p[2] = gmsh::model::geo::addPoint(0, a, b, lc);
+ p[3] = gmsh::model::geo::addPoint(0, 0., b, lc);
+ int line[4];
+
+ line[0] = gmsh::model::geo::addLine(p[0], p[1]);
+ line[1] = gmsh::model::geo::addLine(p[2], p[1]);
+ line[2] = gmsh::model::geo::addLine(p[2], p[3]);
+ line[3] = gmsh::model::geo::addLine(p[3], p[0]);
+
+ int curveLoop =
+ gmsh::model::geo::addCurveLoop({line[3], line[0], -line[1], line[2]});
+
+ int tagSurface = gmsh::model::geo::addPlaneSurface({curveLoop});
+ gmsh::model::geo::mesh::setTransfiniteSurface(tagSurface);
+ gmsh::model::geo::mesh::setRecombine(2, tagSurface);
+ gmsh::model::addPhysicalGroup(2, {tagSurface}, 1);
+ gmsh::model::setPhysicalName(2, 1, "gammaDir");
+ std::vector< std::pair< int, int > > extrudeEntities;
+ gmsh::model::geo::extrude(
+ {std::make_pair(2, tagSurface)}, domainSize, 0., 0., extrudeEntities,
+ {static_cast< int >((domainSize) / lc)}, std::vector< double >(), true);
+ tagSurface = extrudeEntities[0].second;
+ omegas[0] = extrudeEntities[1].second;
+ borders[0].push_back(extrudeEntities[2].second);
+ borders[0].push_back(extrudeEntities[3].second);
+ borders[0].push_back(extrudeEntities[4].second);
+ borders[0].push_back(extrudeEntities[5].second);
+
+ gmsh::model::addPhysicalGroup(2, {tagSurface}, 2);
+ gmsh::model::setPhysicalName(2, 2, "gammaInf");
+ gmsh::model::addPhysicalGroup(2, borders[0], 100);
+ gmsh::model::setPhysicalName(2, 100, "border_" + std::to_string(0));
+ gmsh::model::addPhysicalGroup(3, {omegas[0]}, 1);
+ gmsh::model::setPhysicalName(3, 1, "omega_" + std::to_string(0));
+
+ gmsh::model::geo::synchronize();
+ gmsh::model::mesh::generate();
+ Domain omega(3, 1);
+ Domain gammaInf(2, 2);
+ Domain gammaDir(2, 1);
+ Domain border(2, 100);
+ gmshfem::problem::Formulation< std::complex< double > > formulation("maxwell");
+
+ /****
+ * Create fields
+ ****/
+ Field< std::complex< double >, Form::Form1 > E(
+ "E", omega | gammaDir | gammaInf | border,
+ FunctionSpaceTypeForm1::HierarchicalHCurl, FEorder);
+ Field< std::complex< double >, Form::Form1 > lambda(
+ "lambda", gammaDir, FunctionSpaceTypeForm1::HierarchicalHCurl,
+ FEorder);
+ // VectorFunction<std::complex<double>> n = normal<std::complex<double>>();
+ // VOLUME TERMS
+
+ E.addConstraint(border, vector< std::complex< double > >(0., 0., 0.));
+ lambda.addConstraint(border, vector< std::complex< double > >(0., 0., 0.));
+
+ formulation.integral(curl(dof(E)), curl(tf(E)), omega, gauss);
+ formulation.integral(-k * k * dof(E), tf(E), omega, gauss);
+ // Silver Muller
+ // formulation.integral(- im * k * n % (dof(E) % n), tf(E), gammaInf,
+ // gauss);
+ formulation.integral(-im * k * dof(E), tf(E), gammaInf, gauss);
+ // Physical source using Lagrange mutiplier
+ formulation.integral(dof(lambda), tf(E), gammaDir, gauss);
+ formulation.integral(dof(E), tf(lambda), gammaDir, gauss);
+ formulation.integral(Einc, tf(lambda), gammaDir, gauss);
+ formulation.pre();
+ formulation.assemble();
+ formulation.solve();
+ save(E, omega, "E");
+ }
+ /****
+ * DDM
+ ****/
+ else {
+ /****
+ * Build geometry and mesh using gmsh API
+ ****/
+ waveguide(nDom, a, b, L, lc);
+
+ /****
+ * Define domains
+ ****/
+ Subdomain omega(nDom);
+ Subdomain gammaInf(nDom);
+ Subdomain gammaDir(nDom);
+ Subdomain border(nDom);
+ Interface sigma(nDom);
+ for(unsigned int i = 0; i < unsigned(nDom); ++i) {
+ omega(i) = Domain(3, i + 1);
+
+ if(i == unsigned(nDom) - 1) {
+ gammaInf(i) = Domain(2, 2);
+ }
+
+ if(i == 0) {
+ gammaDir(i) = Domain(2, 1);
+ }
+
+ border(i) = Domain(2, 100 + i);
+
+ if(i != 0) {
+ sigma(i, i - 1) = Domain(2, 200 + i - 1);
+ }
+ if(i != unsigned(nDom) - 1) {
+ sigma(i, i + 1) = Domain(2, 200 + i);
+ }
+ }
+ /****
+ * Define topology
+ ****/
+ std::vector< std::vector< unsigned int > > topology(nDom);
+ for(unsigned int i = 0; i < unsigned(nDom); ++i) {
+ if(i != 0) {
+ topology[i].push_back(i - 1);
+ }
+ if(i != unsigned(nDom) - 1) {
+ topology[i].push_back(i + 1);
+ }
+ }
+ // Create DDM formulation
+ gmshddm::problem::Formulation< std::complex< double > > formulation("Maxwell",
+ topology);
+ // Create fields
+ SubdomainField< std::complex< double >, Form::Form1 > E(
+ "E", omega | gammaDir | gammaInf | sigma,
+ FunctionSpaceTypeForm1::HierarchicalHCurl, FEorder);
+ SubdomainField< std::complex< double >, Form::Form1 > lambda(
+ "lambda", gammaDir, FunctionSpaceTypeForm1::HierarchicalHCurl,
+ FEorder);
+ InterfaceField< std::complex< double >, Form::Form1 > g(
+ "g", sigma, FunctionSpaceTypeForm1::HierarchicalHCurl, 0);
+
+
+ // Tell to the formulation that g is field that have to be exchanged between
+ // subdomains
+ formulation.addInterfaceField(g);
+ VectorFunction< std::complex< double > > n = normal< std::complex< double > >();
+ VectorFunction< std::complex< double > > functionZero =
+ vector< std::complex< double > >(0., 0., 0.);
+ for(unsigned int i = 0; i < unsigned(nDom); ++i) {
+ E(i).addConstraint(border(i), functionZero);
+ lambda(i).addConstraint(border(i), functionZero);
+ for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
+ const unsigned int j = topology[i][jj];
+ g(i, j).addConstraint(border(i), functionZero);
+ }
+ }
+
+ // Add terms to the formulation
+ for(unsigned int i = 0; i < unsigned(nDom); ++i) {
+ // VOLUME TERMS
+ formulation(i).integral(curl(dof(E(i))), curl(tf(E(i))), omega(i), gauss);
+ formulation(i).integral(-k * k * dof(E(i)), tf(E(i)), omega(i), gauss);
+ // Silver Muller
+ /* formulation(i).integral(-im * k * n % (dof(E(i)) % n), tf(E(i)),
+ gammaInf(i), gauss);*/
+ formulation(i).integral(-im * k * dof(E(i)), tf(E(i)), gammaInf(i),
+ gauss);
+ // Physical source using Lagrange mutiplier
+ formulation(i).integral(dof(lambda(i)), tf(E(i)), gammaDir(i),
+ gauss);
+ formulation(i).integral(dof(E(i)), tf(lambda(i)), gammaDir(i),
+ gauss);
+ formulation(i).integral(formulation.physicalSource(Einc), tf(lambda(i)),
+ gammaDir(i), gauss);
+
+ // Artificial source on transmission boundaries
+ for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
+ const unsigned int j = topology[i][jj];
+ /* formulation(i).integral(-im * k * n % (dof(E(i)) % n), tf(E(i)),
+ sigma(i, j), gauss);*/
+ formulation(i).integral(-im * k * dof(E(i)), tf(E(i)), sigma(i, j),
+ gauss);
+ formulation(i).integral(formulation.artificialSource(g(j, i)), tf(E(i)),
+ sigma(i, j), gauss);
+ }
+ // INTERFACE TERMS
+ for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
+ const unsigned int j = topology[i][jj];
+ formulation(i, j).integral(dof(g(i, j)), tf(g(i, j)), sigma(i, j),
+ gauss);
+ formulation(i, j).integral(formulation.artificialSource(g(j, i)),
+ tf(g(i, j)), sigma(i, j), gauss);
+ formulation(i, j).integral(-2. * im * k * E(i), tf(g(i, j)),
+ sigma(i, j), gauss);
+ /*formulation(i, j).integral(-2. * im * k * n % (E(i) % n), tf(g(i, j)),
+ sigma(i, j), gauss);*/
+ }
+ }
+ formulation.pre();
+ // Solve the DDM formulation
+ formulation.solve("gmres");
+ //save field E
+ for(int i = 0; i < nDom; ++i) {
+ save(E(i), omega(i), "E" + std::to_string(i));
+ }
+ }
+
+ return 0;
+}
diff --git a/tutorials/maxwell/waveguide/CMakeLists.txt b/tutorials/maxwell/waveguide/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7481f3ad58dcd475585824c7f40fddf332e191dc
--- /dev/null
+++ b/tutorials/maxwell/waveguide/CMakeLists.txt
@@ -0,0 +1,8 @@
+cmake_minimum_required(VERSION 3.0 FATAL_ERROR)
+
+project(tuto CXX)
+
+include(${CMAKE_CURRENT_SOURCE_DIR}/../../tutorial.cmake)
+
+add_executable(tuto main.cpp ${EXTRA_INCS})
+target_link_libraries(tuto ${EXTRA_LIBS})
diff --git a/tutorials/maxwell/waveguide/main.cpp b/tutorials/maxwell/waveguide/main.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..3d9c6310dfd15d8b37b661c0f4e74a89b765be62
--- /dev/null
+++ b/tutorials/maxwell/waveguide/main.cpp
@@ -0,0 +1,213 @@
+#include "gmsh.h"
+
+#include <gmshddm/Formulation.h>
+#include <gmshddm/GmshDdm.h>
+#include <gmshddm/MPIInterface.h>
+#include <gmshfem/Message.h>
+
+using namespace gmshddm;
+using namespace gmshddm::common;
+using namespace gmshddm::domain;
+using namespace gmshddm::problem;
+using namespace gmshddm::field;
+using namespace gmshddm::mpi;
+
+using namespace gmshfem;
+using namespace gmshfem::domain;
+using namespace gmshfem::equation;
+using namespace gmshfem::problem;
+using namespace gmshfem::field;
+using namespace gmshfem::function;
+using namespace gmshfem::post;
+
+void waveguide(const unsigned int nDom, const double l, const double L, const double lc)
+{
+ if(nDom < 2) {
+ gmshfem::msg::error << "nDom should be at least equal to 2." << gmshfem::msg::endl;
+ exit(0);
+ }
+ gmsh::model::add("waveguide");
+
+ const double domainSize = L / nDom;
+
+ std::vector< std::vector< int > > borders(nDom);
+ std::vector< int > omegas(nDom);
+ std::vector< int > sigmas(nDom - 1);
+
+ int p[2];
+
+ p[0] = gmsh::model::geo::addPoint(0., l, 0., lc);
+ p[1] = gmsh::model::geo::addPoint(0., 0., 0., lc);
+
+ int line = gmsh::model::geo::addLine(p[0], p[1]);
+ gmsh::model::addPhysicalGroup(1, {line}, 1);
+ gmsh::model::setPhysicalName(1, 1, "gammaDir");
+
+ std::vector< int > cornerTags;
+ for(unsigned int i = 0; i < nDom; ++i) {
+ std::vector< std::pair< int, int > > extrudeEntities;
+ gmsh::model::geo::extrude({std::make_pair(1, line)}, domainSize, 0., 0., extrudeEntities, {static_cast< int >((domainSize) / lc)}, std::vector< double >(), true);
+ line = extrudeEntities[0].second;
+ omegas[i] = extrudeEntities[1].second;
+ borders[i].push_back(extrudeEntities[2].second);
+ borders[i].push_back(extrudeEntities[3].second);
+ sigmas[i] = line;
+ if(i != nDom - 1) {
+ cornerTags.push_back(3 + cornerTags.size());
+ cornerTags.push_back(3 + cornerTags.size());
+ }
+ }
+
+ gmsh::model::addPhysicalGroup(1, {line}, 2);
+ gmsh::model::setPhysicalName(1, 2, "gammaInf");
+
+ for(unsigned int i = 0; i < borders.size(); ++i) {
+ gmsh::model::addPhysicalGroup(1, borders[i], 100 + i);
+ gmsh::model::setPhysicalName(1, 100 + i, "border_" + std::to_string(i));
+ }
+
+ for(unsigned int i = 0; i < omegas.size(); ++i) {
+ gmsh::model::addPhysicalGroup(2, {omegas[i]}, i + 1);
+ gmsh::model::setPhysicalName(2, i + 1, "omega_" + std::to_string(i));
+ }
+
+ for(unsigned int i = 0; i < sigmas.size(); ++i) {
+ gmsh::model::addPhysicalGroup(1, {sigmas[i]}, 200 + i);
+ gmsh::model::setPhysicalName(1, 200 + i, "sigma_" + std::to_string(i) + "_" + std::to_string(i + 1));
+ }
+
+ gmsh::model::addPhysicalGroup(0, cornerTags, 1000);
+ gmsh::model::setPhysicalName(0, 1000, "corner");
+
+ gmsh::model::geo::synchronize();
+ gmsh::model::mesh::generate();
+}
+
+int main(int argc, char **argv)
+{
+ GmshDdm gmshDdm(argc, argv);
+
+ double pi = 3.14159265359;
+
+ int nDom = 3;
+ gmshDdm.userDefinedParameter(nDom, "nDom");
+ double L = 5;
+ double l = 1;
+ double lc = 0.02;
+ double k = 2 * pi;
+ double kIn = 1.;
+ int order = 1;
+ gmshDdm.userDefinedParameter(L, "L");
+ gmshDdm.userDefinedParameter(l, "l");
+ gmshDdm.userDefinedParameter(lc, "lc");
+ gmshDdm.userDefinedParameter(k, "k");
+ gmshDdm.userDefinedParameter(kIn, "kIn");
+ gmshDdm.userDefinedParameter(order, "order");
+ std::string gauss = "Gauss10";
+ gmshDdm.userDefinedParameter(gauss, "gauss");
+
+ // Build geometry and mesh using gmsh API
+ waveguide(nDom, l, L, lc);
+
+ // Define domain
+ Subdomain omega(nDom);
+ Subdomain gammaInf(nDom);
+ Subdomain gammaDir(nDom);
+ Subdomain border(nDom);
+ Interface sigma(nDom);
+ Domain corner = Domain("corner");
+
+ for(unsigned int i = 0; i < nDom; ++i) {
+ omega(i) = Domain(2, i + 1);
+
+ if(i == nDom - 1) {
+ gammaInf(i) = Domain(1, 2);
+ }
+
+ if(i == 0) {
+ gammaDir(i) = Domain(1, 1);
+ }
+
+ border(i) = Domain(1, 100 + i);
+
+ if(i != 0) {
+ sigma(i, i - 1) = Domain(1, 200 + i - 1);
+ }
+ if(i != nDom - 1) {
+ sigma(i, i + 1) = Domain(1, 200 + i);
+ }
+ }
+
+ // Define topology
+ std::vector< std::vector< unsigned int > > topology(nDom);
+ for(unsigned int i = 0; i < nDom; ++i) {
+ if(i != 0) {
+ topology[i].push_back(i - 1);
+ }
+ if(i != nDom - 1) {
+ topology[i].push_back(i + 1);
+ }
+ }
+
+
+ // Create DDM formulation
+ gmshddm::problem::Formulation< std::complex< double > > formulation("Maxwell", topology);
+
+ // Create fields
+ SubdomainField< std::complex< double >, Form::Form1 > e("e", omega | gammaDir | gammaInf | border | sigma, FunctionSpaceTypeForm1::HierarchicalHCurl, order);
+ for(unsigned int i = 0; i < nDom; ++i) {
+ e(i).addConstraint(border(i), vector< std::complex< double > >(0., 0., 0.));
+ }
+ e(0).addConstraint(gammaDir(0), sin< std::complex< double > >(2. * pi * y< std::complex< double > >() / l) * vector< std::complex< double > >(0., 1., 0.));
+ InterfaceField< std::complex< double >, Form::Form1 > g("g", sigma, FunctionSpaceTypeForm1::HierarchicalHCurl, order);
+ for(unsigned int i = 0; i < nDom; ++i) {
+ for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
+ const unsigned int j = topology[i][jj];
+ g(i, j).addConstraint(border(i), vector< std::complex< double > >(0., 0., 0.));
+ }
+ }
+
+ std::complex< double > im(0., 1.);
+
+ // Tell to the formulation that g is field that have to be exchanged between subdomains
+ formulation.addInterfaceField(g);
+
+ VectorFunction< std::complex< double > > n = normal< std::complex< double > >();
+
+ // Add terms to the formulation
+ for(unsigned int i = 0; i < nDom; ++i) {
+ // VOLUME TERMS
+ formulation(i).integral(curl(dof(e(i))), curl(tf(e(i))), omega(i), gauss);
+ formulation(i).integral(-k * k * dof(e(i)), tf(e(i)), omega(i), gauss);
+ formulation(i).integral(-im * k * n % (dof(e(i)) % n), tf(e(i)), gammaInf(i), gauss);
+
+ // Artificial source
+ for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
+ const unsigned int j = topology[i][jj];
+ formulation(i).integral(-im * k * n % (dof(e(i)) % n), tf(e(i)), sigma(i, j), gauss);
+ formulation(i).integral(formulation.artificialSource(-g(j, i)), tf(e(i)), sigma(i, j), gauss);
+ }
+
+ // INTERFACE TERMS
+ for(unsigned int jj = 0; jj < topology[i].size(); ++jj) {
+ const unsigned int j = topology[i][jj];
+ formulation(i, j).integral(dof(g(i, j)), tf(g(i, j)), sigma(i, j), gauss);
+ formulation(i, j).integral(formulation.artificialSource(g(j, i)), tf(g(i, j)), sigma(i, j), gauss);
+ formulation(i, j).integral(2. * im * k * n % (e(i) % n), tf(g(i, j)), sigma(i, j), gauss);
+ }
+ }
+
+ // Solve the DDM formulation
+ formulation.pre();
+ int iterMax = 1000;
+ gmshDdm.userDefinedParameter(iterMax, "iter");
+ formulation.solve("gmres", 1e-6, iterMax);
+
+ for(unsigned int i = 0; i < nDom; ++i) {
+ if(isItMySubdomain(i)) {
+ save(e(i), omega(i), "e_" + std::to_string(i));
+ }
+ }
+
+ return 0;
+}
diff --git a/tutorials/tutorial.cmake b/tutorials/tutorial.cmake
new file mode 100644
index 0000000000000000000000000000000000000000..3e2c7ef61683c3ee4d8e3652f5103ed81c1c80c3
--- /dev/null
+++ b/tutorials/tutorial.cmake
@@ -0,0 +1,98 @@
+# The following commands are useful for the demos, and can be included in each
+# demos's CMakeLists.txt; they fill the EXTRA_INCS and EXTRA_LIBS variables.
+
+# Detect if we use the MinGW compilers on Cygwin - if we do, handle the build as
+# a pure Windows build
+if(CYGWIN OR MSYS)
+ if(CMAKE_CXX_COMPILER_ID MATCHES "GNU" OR
+ CMAKE_CXX_COMPILER_ID MATCHES "Clang")
+ execute_process(COMMAND ${CMAKE_CXX_COMPILER} -dumpmachine
+ OUTPUT_VARIABLE CXX_COMPILER_MACHINE
+ OUTPUT_STRIP_TRAILING_WHITESPACE)
+ if(CXX_COMPILER_MACHINE MATCHES "mingw")
+ set(WIN32 1)
+ add_definitions(-DWIN32)
+ set(CMAKE_FIND_LIBRARY_PREFIXES "lib" "")
+ set(CMAKE_FIND_LIBRARY_SUFFIXES ".a" ".so" ".lib" ".LIB" ".dll" ".DLL")
+ endif()
+ endif()
+endif()
+
+# Make sure we have C++11 support
+set(CMAKE_CXX_STANDARD 11)
+
+# Enable all warnings
+include(CheckCXXCompilerFlag)
+check_cxx_compiler_flag("-Wall" HAVE_WALL)
+if(HAVE_WALL)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Wall")
+endif()
+
+# Find Gmsh
+find_library(GMSH_LIB gmsh)
+if(NOT GMSH_LIB)
+ message(FATAL_ERROR "Could not find Gmsh library")
+endif(NOT GMSH_LIB)
+find_path(GMSH_INC gmsh.h)
+if(NOT GMSH_INC)
+ message(FATAL_ERROR "Could not find Gmsh header 'gmsh.h'")
+endif(NOT GMSH_INC)
+list(APPEND EXTRA_INCS ${GMSH_INC})
+list(APPEND EXTRA_LIBS ${GMSH_LIB})
+
+# Find GmshFEM
+find_library(GMSHFEM_LIB gmshfem)
+if(NOT GMSHFEM_LIB)
+ message(FATAL_ERROR "Could not find GmshFEM library")
+endif(NOT GMSHFEM_LIB)
+find_path(GMSHFEM_INC gmshfem/GmshFem.h)
+if(NOT GMSHFEM_INC)
+ message(FATAL_ERROR "Could not find GmshFEM header 'gmshfem/GmshFem.h'")
+endif(NOT GMSHFEM_INC)
+list(APPEND EXTRA_LIBS ${GMSHFEM_LIB})
+list(APPEND EXTRA_INCS ${GMSHFEM_INC})
+list(APPEND EXTRA_INCS ${GMSHFEM_INC}/gmshfem/contrib)
+
+# Find GmshDDM
+find_library(GMSHDDM_LIB gmshddm)
+if(NOT GMSHDDM_LIB)
+ message(FATAL_ERROR "Could not find GmshDDM library")
+endif(NOT GMSHDDM_LIB)
+
+find_path(GMSHDDM_INC gmshddm/GmshDdm.h)
+if(NOT GMSHDDM_INC)
+ message(FATAL_ERROR "Could not find GmshDDM header 'gmshddm/GmshDdm.h'")
+endif(NOT GMSHDDM_INC)
+list(APPEND EXTRA_LIBS ${GMSHDDM_LIB})
+list(APPEND EXTRA_INCS ${GMSHDDM_INC})
+
+# OpenMP
+find_package(OpenMP)
+if(OPENMP_FOUND)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${OpenMP_CXX_FLAGS}")
+endif()
+
+if(APPLE AND EXISTS "/usr/local/opt/libomp")
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Xpreprocessor -fopenmp -I/usr/local/opt/libomp/include")
+ list(APPEND EXTRA_LIBS "-L/usr/local/opt/libomp/lib -lomp")
+ message(STATUS "Found OpenMP[Homebrew]")
+elseif(APPLE AND EXISTS "/opt/local/lib/libomp")
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Xpreprocessor -fopenmp -I/opt/local/include/libomp")
+ list(APPEND EXTRA_LIBS "-L/opt/local/lib/libomp -lomp")
+ message(STATUS "Found OpenMP[MacPorts]")
+endif()
+
+# MPI
+find_package(MPI)
+if(MPI_FOUND)
+ list(APPEND EXTRA_INCS ${MPI_CXX_INCLUDE_PATH})
+ list(APPEND EXTRA_LIBS ${MPI_CXX_LIBRARIES})
+ set(CMAKE_C_COMPILER ${MPI_C_COMPILER})
+ set(CMAKE_CXX_COMPILER ${MPI_CXX_COMPILER})
+ set(CMAKE_Fortran_COMPILER ${MPI_Fortran_COMPILER})
+endif()
+
+# Eigen
+list(APPEND EXTRA_INCS ${CMAKE_CURRENT_LIST_DIR}/../contrib/eigen)
+
+include_directories(${EXTRA_INCS})