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nodalBasis.cpp 21.86 KiB
// Gmsh - Copyright (C) 1997-2014 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// bugs and problems to the public mailing list <gmsh@geuz.org>.
#include <limits>
#include <cmath>
#include "nodalBasis.h"
#include "BasisFactory.h"
#include "pointsGenerators.h"
namespace ClosureGen {
inline double pow2(double x)
{
return x * x;
}
void rotateHex(int iFace, int iRot, int iSign, double uI, double vI,
double &uO, double &vO, double &wO)
{
if (iSign<0){
double tmp=uI;
uI=vI;
vI=tmp;
}
for (int i=0; i < iRot; i++){
double tmp=uI;
uI=-vI;
vI=tmp;
}
switch (iFace) {
case 0: uO = vI; vO = uI; wO=-1; break;
case 1: uO = uI; vO = -1; wO=vI; break;
case 2: uO =-1; vO = vI; wO=uI; break;
case 3: uO = 1; vO = uI; wO=vI; break;
case 4: uO =-uI; vO = 1; wO=vI; break;
case 5: uO =uI; vO = vI; wO=1; break;
}
}
void rotateHexFull(int iFace, int iRot, int iSign, double uI, double vI, double wI, double &uO, double &vO, double &wO)
{
switch (iFace) {
case 0: uO = uI; vO = vI; wO = wI; break;
case 1: uO = wI; vO = uI; wO = vI; break;
case 2: uO = vI; vO = wI; wO = uI; break;
case 3: uO = wI; vO = vI; wO =-uI; break;
case 4: uO = wI; vO =-uI; wO =-vI; break;
case 5: uO = vI; vO = uI; wO =-wI; break;
}
for (int i = 0; i < iRot; i++){
double tmp = uO;
uO = -vO;
vO = tmp;
}
if (iSign<0){
double tmp = uO;
uO = vO;
vO = tmp;
}
}
void generate1dVertexClosure(nodalBasis::clCont &closure, int order)
{
closure.clear();
closure.resize(2);
closure[0].push_back(0);
closure[1].push_back(order == 0 ? 0 : 1); closure[0].type = MSH_PNT;
closure[1].type = MSH_PNT;
}
void generate1dVertexClosureFull(nodalBasis::clCont &closure,
std::vector<int> &closureRef, int order)
{
closure.clear();
closure.resize(2);
closure[0].push_back(0);
if (order != 0) {
closure[0].push_back(1);
closure[1].push_back(1);
}
closure[1].push_back(0);
for (int i = 0; i < order - 1; i++) {
closure[0].push_back(2 + i);
closure[1].push_back(2 + order - 2 - i);
}
closureRef.resize(2);
closureRef[0] = 0;
closureRef[1] = 0;
}
void getFaceClosureTet(int iFace, int iSign, int iRotate,
nodalBasis::closure &closure, int order)
{
closure.clear();
closure.resize((order + 1) * (order + 2) / 2);
closure.type = ElementType::getTag(TYPE_TRI, order, false);
switch (order){
case 0:
closure[0] = 0;
break;
default:
int face[4][3] = {{-3, -2, -1}, {1, -6, 4}, {-4, 5, 3}, {6, 2, -5}};
int order1node[4][3] = {{0, 2, 1}, {0, 1, 3}, {0, 3, 2}, {3, 1, 2}};
for (int i = 0; i < 3; ++i){
int k = (3 + (iSign * i) + iRotate) % 3; //- iSign * iRotate
closure[i] = order1node[iFace][k];
}
for (int i = 0;i < 3; ++i){
int edgenumber = iSign *
face[iFace][(6 + i * iSign + (-1 + iSign) / 2 + iRotate) % 3]; //- iSign * iRotate
for (int k = 0; k < (order - 1); k++){
if (edgenumber > 0)
closure[3 + i * (order - 1) + k] =
4 + (edgenumber - 1) * (order - 1) + k;
else
closure[3 + i * (order - 1) + k] =
4 + (-edgenumber) * (order - 1) - 1 - k;
}
}
int fi = 3 + 3 * (order - 1);
int ti = 4 + 6 * (order - 1);
int ndofff = (order - 3 + 2) * (order - 3 + 1) / 2;
ti = ti + iFace * ndofff;
for (int k = 0; k < order / 3; k++){
int orderint = order - 3 - k * 3;
if (orderint > 0){
for (int ci = 0; ci < 3 ; ci++){
int shift = (3 + iSign * ci + iRotate) % 3; //- iSign * iRotate
closure[fi + ci] = ti + shift;
}
fi = fi + 3; ti = ti + 3;
for (int l = 0; l < orderint - 1; l++){
for (int ei = 0; ei < 3; ei++){
int edgenumber = (6 + ei * iSign + (-1 + iSign) / 2 + iRotate) % 3;
//- iSign * iRotate if (iSign > 0)
closure[fi + ei * (orderint - 1) + l] =
ti + edgenumber * (orderint - 1) + l;
else
closure[fi + ei * (orderint - 1) + l] =
ti + (1 + edgenumber) * (orderint - 1) - 1 - l;
}
}
fi = fi + 3 * (orderint - 1); ti = ti + 3 * (orderint - 1);
}
else {
closure[fi] = ti;
ti++;
fi++;
}
}
break;
}
}
void generate2dEdgeClosureFull(nodalBasis::clCont &closure,
std::vector<int> &closureRef,
int order, int nNod, bool serendip)
{
closure.clear();
closure.resize(2*nNod);
closureRef.resize(2*nNod);
int shift = 0;
for (int corder = order; corder>=0; corder -= (nNod == 3 ? 3 : 2)) {
if (corder == 0) {
for (int r = 0; r < nNod ; r++){
closure[r].push_back(shift);
closure[r+nNod].push_back(shift);
}
break;
}
for (int r = 0; r < nNod ; r++){
for (int j = 0; j < nNod; j++) {
closure[r].push_back(shift + (r + j) % nNod);
closure[r + nNod].push_back(shift + (r - j + 1 + nNod) % nNod);
}
}
shift += nNod;
int n = nNod*(corder-1);
for (int r = 0; r < nNod ; r++){
for (int j = 0; j < n; j++){
closure[r].push_back(shift + (j + (corder - 1) * r) % n);
closure[r + nNod].push_back(shift + (n - j - 1 + (corder - 1) * (r + 1)) % n);
}
}
shift += n;
if (serendip) break;
}
for (int r = 0; r < nNod*2 ; r++) {
closure[r].type = ElementType::getTag(TYPE_LIN, order);
closureRef[r] = 0;
}
}
void addEdgeNodes(nodalBasis::clCont &closureFull, const int *edges, int order)
{
if (order < 2)
return;
int numNodes = 0;
for (int i = 0; edges[i] >= 0; ++i) {
numNodes = std::max(numNodes, edges[i] + 1);
}
std::vector<std::vector<int> > nodes2edges(numNodes, std::vector<int>(numNodes, -1));
for (int i = 0; edges[i] >= 0; i += 2) {
nodes2edges[edges[i]][edges[i + 1]] = i; nodes2edges[edges[i + 1]][edges[i]] = i + 1;
}
for (unsigned int iClosure = 0; iClosure < closureFull.size(); iClosure++) {
std::vector<int> &cl = closureFull[iClosure];
for (int iEdge = 0; edges[iEdge] >= 0; iEdge += 2) {
if (cl.empty())
continue;
int n0 = cl[edges[iEdge]];
int n1 = cl[edges[iEdge + 1]];
int oEdge = nodes2edges[n0][n1];
if (oEdge == -1)
Msg::Error("invalid p1 closure or invalid edges list");
for (int i = 0 ; i < order - 1; i++)
cl.push_back(numNodes + oEdge/2 * (order - 1) + ((oEdge % 2) ? order - 2 - i : i));
}
}
}
void generateFaceClosureTet(nodalBasis::clCont &closure, int order)
{
closure.clear();
for (int iRotate = 0; iRotate < 3; iRotate++){
for (int iSign = 1; iSign >= -1; iSign -= 2){
for (int iFace = 0; iFace < 4; iFace++){
nodalBasis::closure closure_face;
getFaceClosureTet(iFace, iSign, iRotate, closure_face, order);
closure.push_back(closure_face);
}
}
}
}
void generateFaceClosureTetFull(nodalBasis::clCont &closureFull,
std::vector<int> &closureRef,
int order, bool serendip)
{
closureFull.clear();
//input :
static const short int faces[4][3] = {{0,1,2}, {0,3,1}, {0,2,3}, {3,2,1}};
static const int edges[] = {0, 1, 1, 2, 2, 0, 3, 0, 3, 2, 3, 1, -1};
static const int faceOrientation[6] = {0,1,2,5,3,4};
closureFull.resize(24);
closureRef.resize(24);
for (int i = 0; i < 24; i ++)
closureRef[i] = 0;
if (order == 0) {
for (int i = 0; i < 24; i ++) {
closureFull[i].push_back(0);
}
return;
}
//Mapping for the p1 nodes
nodalBasis::clCont closure;
generateFaceClosureTet(closure, 1);
for (unsigned int i = 0; i < closureFull.size(); i++) {
std::vector<int> &clFull = closureFull[i];
std::vector<int> &cl = closure[i];
clFull.resize(4, -1);
closureRef[i] = 0;
for (unsigned int j = 0; j < cl.size(); j ++)
clFull[closure[0][j]] = cl[j];
for (int j = 0; j < 4; j ++)
if (clFull[j] == -1)
clFull[j] = (6 - clFull[(j + 1) % 4] - clFull[(j + 2) % 4] - clFull[(j + 3) % 4]);
}
int nodes2Faces[4][4][4];
for (int i = 0; i < 4; i++) {
for (int iRotate = 0; iRotate < 3; iRotate ++) {
short int n0 = faces[i][(3 - iRotate) % 3];
short int n1 = faces[i][(4 - iRotate) % 3]; short int n2 = faces[i][(5 - iRotate) % 3];
nodes2Faces[n0][n1][n2] = i * 6 + iRotate;
nodes2Faces[n0][n2][n1] = i * 6 + iRotate + 3;
}
}
nodalBasis::clCont closureTriangles;
std::vector<int> closureTrianglesRef;
if (order >= 3)
generate2dEdgeClosureFull(closureTriangles, closureTrianglesRef, order - 3, 3, false);
addEdgeNodes(closureFull, edges, order);
for (unsigned int iClosure = 0; iClosure < closureFull.size(); iClosure++) {
//faces
std::vector<int> &cl = closureFull[iClosure];
if (order >= 3) {
for (int iFace = 0; iFace < 4; iFace ++) {
int n0 = cl[faces[iFace][0]];
int n1 = cl[faces[iFace][1]];
int n2 = cl[faces[iFace][2]];
short int id = nodes2Faces[n0][n1][n2];
short int iTriClosure = faceOrientation [id % 6];
short int idFace = id/6;
int nOnFace = closureTriangles[iTriClosure].size();
for (int i = 0; i < nOnFace; i++) {
cl.push_back(4 + 6 * (order - 1) + idFace * nOnFace +
closureTriangles[iTriClosure][i]);
}
}
}
}
if (order >= 4 && !serendip) {
nodalBasis::clCont insideClosure;
std::vector<int> fakeClosureRef;
generateFaceClosureTetFull(insideClosure, fakeClosureRef, order - 4, false);
for (unsigned int i = 0; i < closureFull.size(); i ++) {
unsigned int shift = closureFull[i].size();
for (unsigned int j = 0; j < insideClosure[i].size(); j++)
closureFull[i].push_back(insideClosure[i][j] + shift);
}
}
}
/*
void checkClosure(int tag) {
printf("TYPE = %i\n", tag);
const nodalBasis &fs = *nodalBases::find(tag);
for (int i = 0; i < fs.closures.size(); ++i) {
const std::vector<int> &clRef = fs.closures[fs.closureRef[i]];
const std::vector<int> &cl = fs.closures[i];
const std::vector<int> &clFull = fs.fullClosures[i];
printf("i = %i\n", i);
for (int j = 0; j < cl.size(); ++j) {
printf("%3i ", clFull[clRef[j]]);
}
printf("\n");
for (int j = 0; j < cl.size(); ++j) {
printf("%3i ", cl[j]);
}
printf("\n");
}
}
*/
void generateFaceClosureHex(nodalBasis::clCont &closure, int order,
bool serendip, const fullMatrix<double> &points)
{
closure.clear();
const nodalBasis &fsFace = *BasisFactory::getNodalBasis(ElementType::getTag(TYPE_QUA, order, serendip));
for (int iRotate = 0; iRotate < 4; iRotate++){
for (int iSign = 1; iSign >= -1; iSign -= 2){
for (int iFace = 0; iFace < 6; iFace++) { nodalBasis::closure cl;
cl.type = fsFace.type;
cl.resize(fsFace.points.size1());
for (unsigned int iNode = 0; iNode < cl.size(); ++iNode) {
double u,v,w;
rotateHex(iFace, iRotate, iSign, fsFace.points(iNode, 0),
fsFace.points(iNode, 1), u, v, w);
cl[iNode] = 0;
double D = std::numeric_limits<double>::max();
for (int jNode = 0; jNode < points.size1(); ++jNode) {
double d = pow2(points(jNode, 0) - u) + pow2(points(jNode, 1) - v) +
pow2(points(jNode, 2) - w);
if (d < D) {
cl[iNode] = jNode;
D = d;
}
}
}
closure.push_back(cl);
}
}
}
}
void generateFaceClosureHexFull(nodalBasis::clCont &closure,
std::vector<int> &closureRef,
int order, bool serendip,
const fullMatrix<double> &points)
{
closure.clear();
int clId = 0;
for (int iRotate = 0; iRotate < 4; iRotate++){
for (int iSign = 1; iSign >= -1; iSign -= 2){
for (int iFace = 0; iFace < 6; iFace++) {
nodalBasis::closure cl;
cl.resize(points.size1());
for (int iNode = 0; iNode < points.size1(); ++iNode) {
double u,v,w;
rotateHexFull(iFace, iRotate, iSign, points(iNode, 0), points(iNode, 1),
points(iNode, 2), u, v, w);
int J = 0;
double D = std::numeric_limits<double>::max();
for (int jNode = 0; jNode < points.size1(); ++jNode) {
double d = pow2(points(jNode, 0) - u) + pow2(points(jNode, 1) - v) +
pow2(points(jNode, 2) - w);
if (d < D) {
J = jNode;
D = d;
}
}
cl[J] = iNode;
}
closure.push_back(cl);
closureRef.push_back(0);
clId ++;
}
}
}
}
void getFaceClosurePrism(int iFace, int iSign, int iRotate,
nodalBasis::closure &closure, int order)
{
//if (order > 2)
// Msg::Error("FaceClosure not implemented for prisms of order %d",order);
bool isTriangle = iFace<2;
int nNodes = isTriangle ? (order+1)*(order+2)/2 : (order+1)*(order+1);
closure.clear();
if (isTriangle && iRotate > 2) return;
closure.resize(nNodes); if (order==0) {
closure[0] = 0;
return;
}
int order1node[5][4] = {{0, 2, 1, -1}, {3, 4, 5, -1}, {0, 1, 4, 3}, {0, 3, 5, 2},
{1, 2, 5, 4}};
int order2node[5][5] = {{7, 9, 6, -1, -1}, {12, 14, 13, -1, -1}, {6, 10, 12, 8, 15},
{8, 13, 11, 7, 16}, {9, 11, 14, 10, 17}};
// int order2node[5][4] = {{7, 9, 6, -1}, {12, 14, 13, -1}, {6, 10, 12, 8},
// {8, 13, 11, 7}, {9, 11, 14, 10}};
int nVertex = isTriangle ? 3 : 4;
closure.type = ElementType::getTag(isTriangle ? TYPE_TRI : TYPE_QUA, order);
for (int i = 0; i < nVertex; ++i){
int k = (nVertex + (iSign * i) + iRotate) % nVertex; //- iSign * iRotate
closure[i] = order1node[iFace][k];
}
if (order==2) {
for (int i = 0; i < nVertex; ++i){
int k = (nVertex + (iSign==-1?-1:0) + (iSign * i) + iRotate) % nVertex;
//- iSign * iRotate
closure[nVertex+i] = order2node[iFace][k];
}
if (!isTriangle)
closure[nNodes-1] = order2node[iFace][4]; // center
}
}
void generateFaceClosurePrism(nodalBasis::clCont &closure, int order)
{
if (order > 2)
Msg::Error("FaceClosure not implemented for prisms of order %d",order);
closure.clear();
for (int iRotate = 0; iRotate < 4; iRotate++){
for (int iSign = 1; iSign >= -1; iSign -= 2){
for (int iFace = 0; iFace < 5; iFace++){
nodalBasis::closure closure_face;
getFaceClosurePrism(iFace, iSign, iRotate, closure_face, order);
closure.push_back(closure_face);
}
}
}
}
void generateFaceClosurePrismFull(nodalBasis::clCont &closureFull,
std::vector<int> &closureRef, int order)
{
nodalBasis::clCont closure;
closureFull.clear();
closureFull.resize(40);
closureRef.resize(40);
generateFaceClosurePrism(closure, 1);
int ref3 = -1, ref4a = -1, ref4b = -1;
for (unsigned int i = 0; i < closure.size(); i++) {
std::vector<int> &clFull = closureFull[i];
std::vector<int> &cl = closure[i];
if (cl.size() == 0)
continue;
clFull.resize(6, -1);
int &ref = cl.size() == 3 ? ref3 : (cl[0] / 3 + cl[1] / 3) % 2 ? ref4b : ref4a;
if (ref == -1)
ref = i;
closureRef[i] = ref;
for (unsigned int j = 0; j < cl.size(); j ++)
clFull[closure[ref][j]] = cl[j];
for (int j = 0; j < 6; j ++) {
if (clFull[j] == -1) {
int k = ((j / 3) + 1) % 2 * 3;
int sum = (clFull[k + (j + 1) % 3] + clFull[k + (j + 2) % 3]);
clFull[j] = ((sum / 6 + 1) % 2) * 3 + (12 - sum) % 3;
} }
}
static const int edges[] = {0, 1, 0, 2, 0, 3, 1, 2, 1, 4, 2, 5,
3, 4, 3, 5, 4, 5, -1};
addEdgeNodes(closureFull, edges, order);
if ( order < 2 )
return;
// face center nodes for p2 prism
static const int faces[5][4] = {{0, 2, 1, -1}, {3, 4, 5, -1}, {0, 1, 4, 3},
{0, 3, 5, 2}, {1, 2, 5, 4}};
if ( order == 2 ) {
int nextFaceNode = 15;
int numFaces = 5;
int numFaceNodes = 4;
std::map<int,int> nodeSum2Face;
for (int iFace = 0; iFace < numFaces ; iFace ++) {
int nodeSum = 0;
for (int iNode = 0; iNode < numFaceNodes; iNode++ ) {
nodeSum += faces[iFace][iNode];
}
nodeSum2Face[nodeSum] = iFace;
}
for (unsigned int i = 0; i < closureFull.size(); i++ ) {
if (closureFull[i].empty())
continue;
for (int iFace = 0; iFace < numFaces; iFace++ ) {
int nodeSum = 0;
for (int iNode = 0; iNode < numFaceNodes; iNode++)
nodeSum += faces[iFace][iNode] < 0 ? faces[iFace][iNode] :
closureFull[i][ faces[iFace][iNode] ];
std::map<int,int>::iterator it = nodeSum2Face.find(nodeSum);
if (it == nodeSum2Face.end() )
Msg::Error("Prism face not found");
int mappedFaceId = it->second;
if ( mappedFaceId > 1) {
closureFull[i].push_back(nextFaceNode + mappedFaceId - 2);
}
}
}
} else {
Msg::Error("FaceClosureFull not implemented for prisms of order %d",order);
}
}
void generate2dEdgeClosure(nodalBasis::clCont &closure, int order, int nNod = 3)
{
closure.clear();
closure.resize(2*nNod);
for (int j = 0; j < nNod ; j++){
closure[j].push_back(j);
closure[j].push_back((j+1)%nNod);
closure[nNod+j].push_back((j+1)%nNod);
closure[nNod+j].push_back(j);
for (int i=0; i < order-1; i++){
closure[j].push_back( nNod + (order-1)*j + i );
closure[nNod+j].push_back(nNod + (order-1)*(j+1) -i -1);
}
closure[j].type = closure[nNod+j].type = ElementType::getTag(TYPE_LIN, order);
}
}
void generateClosureOrder0(nodalBasis::clCont &closure, int nb)
{
closure.clear();
closure.resize(nb);
for (int i=0; i < nb; i++) {
closure[i].push_back(0);
closure[i].type = MSH_PNT; }
}
}
nodalBasis::nodalBasis(int tag)
{
using namespace ClosureGen;
type = tag;
parentType = ElementType::ParentTypeFromTag(tag);
order = ElementType::OrderFromTag(tag);
serendip = ElementType::SerendipityFromTag(tag) > 1;
dimension = ElementType::DimensionFromTag(tag);
switch (parentType) {
case TYPE_PNT :
numFaces = 1;
points = gmshGeneratePointsLine(0);
break;
case TYPE_LIN :
numFaces = 2;
points = gmshGeneratePointsLine(order);
generate1dVertexClosure(closures, order);
generate1dVertexClosureFull(fullClosures, closureRef, order);
break;
case TYPE_TRI :
numFaces = 3;
points = gmshGeneratePointsTriangle(order, serendip);
if (order == 0) {
generateClosureOrder0(closures, 6);
generateClosureOrder0(fullClosures, 6);
closureRef.resize(6, 0);
}
else {
generate2dEdgeClosure(closures, order);
generate2dEdgeClosureFull(fullClosures, closureRef, order, 3, serendip);
}
break;
case TYPE_QUA :
numFaces = 4;
points = gmshGeneratePointsQuadrangle(order, serendip);
if (order == 0) {
generateClosureOrder0(closures, 8);
generateClosureOrder0(fullClosures, 8);
closureRef.resize(8, 0);
}
else {
generate2dEdgeClosure(closures, order, 4);
generate2dEdgeClosureFull(fullClosures, closureRef, order, 4, serendip);
}
break;
case TYPE_TET :
numFaces = 4;
points = gmshGeneratePointsTetrahedron(order, serendip);
if (order == 0) {
generateClosureOrder0(closures,24);
generateClosureOrder0(fullClosures, 24);
closureRef.resize(24, 0);
}
else {
generateFaceClosureTet(closures, order);
generateFaceClosureTetFull(fullClosures, closureRef, order, serendip);
}
break;
case TYPE_PRI :
numFaces = 5;
points = gmshGeneratePointsPrism(order, serendip);
if (order == 0) {
generateClosureOrder0(closures,48);
generateClosureOrder0(fullClosures,48);
closureRef.resize(48, 0); }
else {
generateFaceClosurePrism(closures, order);
generateFaceClosurePrismFull(fullClosures, closureRef, order);
}
break;
case TYPE_HEX :
numFaces = 6;
points = gmshGeneratePointsHexahedron(order, serendip);
generateFaceClosureHex(closures, order, serendip, points);
generateFaceClosureHexFull(fullClosures, closureRef, order, serendip, points);
break;
case TYPE_PYR :
numFaces = 5;
points = gmshGeneratePointsPyramid(order, serendip);
break;
}
}
void nodalBasis::getReferenceNodesForBezier(fullMatrix<double> &nodes) const {
if (parentType != TYPE_PYR && !serendip) {
nodes = points;
}
else {
const bool serendipSpace = false;
if (parentType != TYPE_PYR) {
FuncSpaceData data(true, type, order, &serendipSpace);
gmshGeneratePoints(data, nodes);
}
else {
FuncSpaceData data(true, type, false, order, order, &serendipSpace);
gmshGeneratePoints(data, nodes);
}
}
}