From 7dbd7f7c610c1bc8a99cbe9fcc2b53c5ab086cbd Mon Sep 17 00:00:00 2001
From: Axel Modave <axel.modave@ensta-paris.fr>
Date: Sun, 8 Mar 2020 21:43:15 +0100
Subject: [PATCH] add model HelmholtzDDMwithCrosspoints
---
HelmholtzDDMwithCrosspoints/.DS_Store | Bin 0 -> 6148 bytes
HelmholtzDDMwithCrosspoints/README.txt | 11 +
HelmholtzDDMwithCrosspoints/circularDom.dat | 40 +
HelmholtzDDMwithCrosspoints/circularDom.geo | 159 +
HelmholtzDDMwithCrosspoints/circularDom.pro | 217 +
.../ddmHelmholtzCrossPoints.pro | 954 +
HelmholtzDDMwithCrosspoints/main.dat | 45 +
HelmholtzDDMwithCrosspoints/main.geo | 11 +
HelmholtzDDMwithCrosspoints/main.pro | 68 +
.../rectangularDom.dat | 97 +
.../rectangularDom.geo | 161 +
.../rectangularDom.pro | 222 +
.../rectangularDomMarmousi.dat | 125 +
.../rectangularDomMarmousiGmsh.dat | 46851 ++++++++++++++++
14 files changed, 48961 insertions(+)
create mode 100644 HelmholtzDDMwithCrosspoints/.DS_Store
create mode 100644 HelmholtzDDMwithCrosspoints/README.txt
create mode 100644 HelmholtzDDMwithCrosspoints/circularDom.dat
create mode 100644 HelmholtzDDMwithCrosspoints/circularDom.geo
create mode 100644 HelmholtzDDMwithCrosspoints/circularDom.pro
create mode 100644 HelmholtzDDMwithCrosspoints/ddmHelmholtzCrossPoints.pro
create mode 100644 HelmholtzDDMwithCrosspoints/main.dat
create mode 100644 HelmholtzDDMwithCrosspoints/main.geo
create mode 100644 HelmholtzDDMwithCrosspoints/main.pro
create mode 100644 HelmholtzDDMwithCrosspoints/rectangularDom.dat
create mode 100644 HelmholtzDDMwithCrosspoints/rectangularDom.geo
create mode 100644 HelmholtzDDMwithCrosspoints/rectangularDom.pro
create mode 100644 HelmholtzDDMwithCrosspoints/rectangularDomMarmousi.dat
create mode 100644 HelmholtzDDMwithCrosspoints/rectangularDomMarmousiGmsh.dat
diff --git a/HelmholtzDDMwithCrosspoints/.DS_Store b/HelmholtzDDMwithCrosspoints/.DS_Store
new file mode 100644
index 0000000000000000000000000000000000000000..c88dfc4a587783c61188c27a35d535a5b045cec6
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diff --git a/HelmholtzDDMwithCrosspoints/README.txt b/HelmholtzDDMwithCrosspoints/README.txt
new file mode 100644
index 0000000..bcbb68c
--- /dev/null
+++ b/HelmholtzDDMwithCrosspoints/README.txt
@@ -0,0 +1,11 @@
+A non-overlapping HABC-based domain decomposition method with cross-point treatment for 2D Helmholtz problems.
+
+A. Modave, A. Royer, X. Antoine, X. Geuzaine. An optimized Schwarz domain decomposition method with cross-point treatment for time-harmonic acoustic scattering. https://hal.archives-ouvertes.fr/hal-02432422
+
+Model developed by Axel Modave, based on GetDDM codes.
+
+
+Quick start
+-----------
+
+Open `main.pro' with Gmsh.
\ No newline at end of file
diff --git a/HelmholtzDDMwithCrosspoints/circularDom.dat b/HelmholtzDDMwithCrosspoints/circularDom.dat
new file mode 100644
index 0000000..da60356
--- /dev/null
+++ b/HelmholtzDDMwithCrosspoints/circularDom.dat
@@ -0,0 +1,40 @@
+BC_Dir = 1;
+BC_Neu = 2;
+
+DefineConstant[
+ BC_SCATT = {BC_Dir, Highlight "Blue",
+ Choices {BC_Dir = "Sound-soft scat. (Dirichlet BC)",
+ BC_Neu = "Sound-hard scat. (Neumann BC)"},
+ Name "Input/01Type of solution"},
+
+ // Geometry
+ R_INT = {1, Min 0.01, Step 0.01, Name "Input/1Model/40Internal radius"},
+ R_EXT = {4, Min 0.01, Step 0.01, Name "Input/1Model/41External radius"},
+
+ // Subdomains
+ Npie_DOM = {5, Min 3, Max 20, Step 1, Name "Input/1Model/50Number of azimutal divisions"},
+ Nlay_DOM = {3, Min 3, Max 20, Step 1, Name "Input/1Model/51Number of radial divisions"},
+ THETA_INC = {0, Min 0., Max 2*Pi, Step 0.1, Name "Input/1Model/52Rotation of pie"},
+ TWIST = {0, Min 0, Max 0.3, Step 0.1, Name "Input/1Model/52 TWIST"},
+
+ // Frequency
+ WAVENUMBER = {4*Pi, Min 1, Max 24, Step 1, Name "Input/03Wavenumber"},
+ N_LAMBDA = {10, Min 5, Max 30, Step 1, Name "Input/04Points per wavelength"}
+];
+
+LAMBDA = (2*Pi)/WAVENUMBER;
+FREQ = WAVENUMBER/(2*Pi);
+LC = LAMBDA/N_LAMBDA;
+
+N_DOM = Npie_DOM*Nlay_DOM;
+R_SCA = R_INT;
+
+For iDom In {0:N_DOM-1}
+ TAG_DOM~{iDom} = 1000 + iDom;
+For iEdge In {0:3}
+ TAG_BND~{iDom}~{iEdge} = 2000 + 4*iDom + iEdge;
+EndFor
+For iCorner In {0:3}
+ TAG_CRN~{iDom}~{iCorner} = 3000 + 4*iDom + iCorner;
+EndFor
+EndFor
diff --git a/HelmholtzDDMwithCrosspoints/circularDom.geo b/HelmholtzDDMwithCrosspoints/circularDom.geo
new file mode 100644
index 0000000..9ef7fed
--- /dev/null
+++ b/HelmholtzDDMwithCrosspoints/circularDom.geo
@@ -0,0 +1,159 @@
+Include "circularDom.dat";
+
+Mesh.CharacteristicLengthMin = LC;
+Mesh.CharacteristicLengthMax = LC;
+
+// =================================================================================================
+// Build POINTS, RADIAL LINES, CIRCULAR LINES and SURFACES
+// =================================================================================================
+
+If(Npie_DOM == 1)
+
+ // Circular lines
+ pCenter = newp;
+ Point(pCenter) = {0,0,0};
+ For iLay In {0:Nlay_DOM}
+ radius = R_INT + iLay * (R_EXT-R_INT)/Nlay_DOM;
+ p~{iLay}~{0} = newp;
+ Point(p~{iLay}~{0}) = { radius, 0, 0};
+ p~{iLay}~{1} = newp;
+ Point(p~{iLay}~{1}) = {-radius, 0, 0};
+ l_curve~{iLay}~{0} = newl;
+ Circle(l_curve~{iLay}~{0}) = {p~{iLay}~{0}, pCenter, p~{iLay}~{1}};
+ l_curve~{iLay}~{1} = newl;
+ Circle(l_curve~{iLay}~{1}) = {p~{iLay}~{1}, pCenter, p~{iLay}~{0}};
+ EndFor
+
+ // Surfaces
+ For iLay In {0:Nlay_DOM-1}
+ ll = newll;
+ Line Loop(ll) = {l_curve~{iLay+1}~{0}, l_curve~{iLay+1}~{1}, -l_curve~{iLay}~{0}, -l_curve~{iLay}~{1} };
+ omega~{iLay}~{0} = news;
+ Plane Surface(omega~{iLay}~{0}) = {ll};
+ EndFor
+
+Else
+
+ // Points
+
+ radiusTwist~{0} = -TWIST;
+ radiusTwist~{1} = TWIST;
+ radiusTwist~{2} = -TWIST;
+ radiusTwist~{3} = TWIST;
+ radiusTwist~{4} = -TWIST;
+ radiusTwist~{5} = TWIST;
+ radiusTwist~{6} = -TWIST;
+ radiusTwist~{7} = TWIST;
+
+ pCenter = newp;
+ Point(pCenter) = {0,0,0};
+ For iPie In {0:Npie_DOM-1}
+ For iLay In {0:Nlay_DOM}
+ theta = iPie * (2*Pi/Npie_DOM) - THETA_INC + radiusTwist~{iLay};
+ radius = R_INT + iLay * (R_EXT-R_INT)/Nlay_DOM;
+ p~{iLay}~{iPie} = newp;
+ Point(p~{iLay}~{iPie}) = {radius*Cos(theta), radius*Sin(theta), 0};
+ EndFor
+ EndFor
+
+ // Radial lines
+ For iPie In {0:Npie_DOM-1}
+ For iLay In {0:Nlay_DOM-1}
+ l_straight~{iLay}~{iPie} = newl;
+ Line(l_straight~{iLay}~{iPie}) = {p~{iLay}~{iPie}, p~{iLay+1}~{iPie}};
+ EndFor
+ EndFor
+
+ // Circular lines
+ For iPie In {0:Npie_DOM-1}
+ For iLay In {0:Nlay_DOM}
+ iPieNext = (iPie+1)%Npie_DOM;
+ l_curve~{iLay}~{iPie} = newl;
+ Circle(l_curve~{iLay}~{iPie}) = {p~{iLay}~{iPie}, pCenter, p~{iLay}~{iPieNext}};
+ EndFor
+ EndFor
+
+ // Surfaces
+ For iPie In {0:Npie_DOM-1}
+ For iLay In {0:Nlay_DOM-1}
+ iPieNext = (iPie+1)%Npie_DOM;
+ ll = newll;
+ Line Loop(ll) = { l_straight~{iLay}~{iPie}, l_curve~{iLay+1}~{iPie},
+ -l_straight~{iLay}~{iPieNext}, -l_curve~{iLay }~{iPie} };
+ omega~{iLay}~{iPie} = news;
+ Plane Surface(omega~{iLay}~{iPie}) = {ll};
+ EndFor
+ EndFor
+
+EndIf
+
+// =================================================================================================
+// Generate MESH for each subdomain and reference domain
+// =================================================================================================
+
+// Mesh
+If(StrCmp(OnelabAction, "check")) // only mesh if not in onelab check mode
+ Mesh 2;
+EndIf
+
+For iPie In {0:Npie_DOM-1}
+For iLay In {0:Nlay_DOM-1}
+ iDom = iLay + Nlay_DOM*iPie;
+ iPieNext = (iPie+1)%Npie_DOM;
+
+ Delete Physicals;
+
+If(Npie_DOM == 1)
+ Physical Line(TAG_BND~{iDom}~{1}) = { l_curve~{iLay+1}~{0}, l_curve~{iLay+1}~{1} }; // Up
+ Physical Line(TAG_BND~{iDom}~{3}) = { l_curve~{iLay }~{0}, l_curve~{iLay }~{1} }; // Down
+Else
+ Physical Point(TAG_CRN~{iDom}~{0}) = { p~{iLay}~{iPie} };
+ Physical Point(TAG_CRN~{iDom}~{1}) = { p~{iLay+1}~{iPie} };
+ Physical Point(TAG_CRN~{iDom}~{2}) = { p~{iLay+1}~{iPieNext} };
+ Physical Point(TAG_CRN~{iDom}~{3}) = { p~{iLay}~{iPieNext} };
+ Physical Line(TAG_BND~{iDom}~{0}) = { l_straight~{iLay}~{iPie} }; // Right
+ Physical Line(TAG_BND~{iDom}~{1}) = { l_curve~{iLay+1}~{iPie} }; // Up
+ Physical Line(TAG_BND~{iDom}~{2}) = {-l_straight~{iLay}~{iPieNext} }; // Left
+ Physical Line(TAG_BND~{iDom}~{3}) = { l_curve~{iLay }~{iPie} }; // Down
+EndIf
+
+ Physical Surface(TAG_DOM~{iDom}) = omega~{iLay}~{iPie};
+
+ Printf("Saving subdomain %g...", iDom);
+ Save StrCat(MSH_NAME, Sprintf("_%g.msh", iDom));
+ Printf("Done.");
+
+EndFor
+EndFor
+
+Delete Physicals;
+
+For iPie In {0:Npie_DOM-1}
+For iLay In {0:Nlay_DOM-1}
+ iDom = iLay + Nlay_DOM*iPie;
+ iPieNext = (iPie+1)%Npie_DOM;
+
+If(Npie_DOM == 1)
+If(iLay == 0)
+ Physical Line(TAG_BND~{iDom}~{3}) = { l_curve~{iLay }~{0}, l_curve~{iLay }~{1} }; // Down
+EndIf
+If(iLay == Nlay_DOM-1)
+ Physical Line(TAG_BND~{iDom}~{1}) = { l_curve~{iLay+1}~{0}, l_curve~{iLay+1}~{1} }; // Up
+EndIf
+Else
+If(iLay == 0)
+ Physical Line(TAG_BND~{iDom}~{3}) = { l_curve~{iLay }~{iPie} }; // Down
+EndIf
+If(iLay == Nlay_DOM-1)
+ Physical Line(TAG_BND~{iDom}~{1}) = { l_curve~{iLay+1}~{iPie} }; // Up
+EndIf
+EndIf
+
+ Physical Surface(TAG_DOM~{iDom}) = omega~{iLay}~{iPie};
+
+EndFor
+EndFor
+
+Printf("Saving domain");
+Save StrCat(MSH_NAME, Sprintf(".msh"));
+Printf("Done.");
diff --git a/HelmholtzDDMwithCrosspoints/circularDom.pro b/HelmholtzDDMwithCrosspoints/circularDom.pro
new file mode 100644
index 0000000..c2c86cf
--- /dev/null
+++ b/HelmholtzDDMwithCrosspoints/circularDom.pro
@@ -0,0 +1,217 @@
+Include "circularDom.dat";
+
+// ====================================================================================================
+// FUNCTIONS
+// ====================================================================================================
+
+Function{
+ R[] = Sqrt[X[]*X[]+Y[]*Y[]];
+ f_inc[] = Complex[Cos[WAVENUMBER*X[]], Sin[WAVENUMBER*X[]]];
+ dfdx_inc[] = WAVENUMBER * Complex[-Sin[WAVENUMBER*X[]], Cos[WAVENUMBER*X[]]];
+
+ // Dirichlet
+If(BC_SCATT == BC_Dir)
+ f_ref[] = AcousticFieldSoftCylinder[XYZ[]]{WAVENUMBER, R_SCA};
+ f_dir[] = -f_inc[];
+EndIf
+
+ // Neumann
+If(BC_SCATT == BC_Neu)
+ f_ref[] = AcousticFieldHardCylinder[XYZ[]]{WAVENUMBER, R_SCA, 0, 0, 50};
+ f_neu[] = dfdx_inc[] * (X[]/R[]);
+EndIf
+}
+
+// ====================================================================================================
+// LISTS ABC/TBC
+// ====================================================================================================
+
+// Is there an ABC for main domain? (1=yes, 0=no)
+isEdgeABC~{0} = 1;
+isEdgeABC~{1} = 1;
+isEdgeABC~{2} = 1;
+isEdgeABC~{3} = 1;
+isEdgeRad~{0} = 1;
+isEdgeRad~{1} = 1;
+isEdgeRad~{2} = 1;
+isEdgeRad~{3} = 1;
+
+ListOfSubdom = {};
+For iPie In {0:Npie_DOM-1}
+For iLay In {0:Nlay_DOM-1}
+ iDom = iLay + Nlay_DOM*iPie;
+
+If (iDom % MPI_Size == MPI_Rank)
+ ListOfSubdom += iDom;
+EndIf
+
+ iPiePrev = (iPie+Npie_DOM-1)%Npie_DOM;
+ iPieNext = (iPie+1)%Npie_DOM;
+
+ iDomNeigh~{iDom}~{0} = iLay + Nlay_DOM*iPiePrev; // Right
+ iDomNeigh~{iDom}~{1} = (iLay+1) + Nlay_DOM*iPie; // Top
+ iDomNeigh~{iDom}~{2} = iLay + Nlay_DOM*iPieNext; // Left
+ iDomNeigh~{iDom}~{3} = (iLay-1) + Nlay_DOM*iPie; // Down
+ iEdgeNeigh~{iDom}~{0} = 2;
+ iEdgeNeigh~{iDom}~{1} = 3;
+ iEdgeNeigh~{iDom}~{2} = 0;
+ iEdgeNeigh~{iDom}~{3} = 1;
+ isEdgeRad~{iDom}~{0} = 0;
+ isEdgeRad~{iDom}~{1} = 1;
+ isEdgeRad~{iDom}~{2} = 0;
+ isEdgeRad~{iDom}~{3} = 1;
+
+ // Is there an ABC or TBC? (1=yes, 0=no)
+ For iEdge In {0:3}
+ isEdgeABC~{iDom}~{iEdge} = 0;
+ isEdgeTBC~{iDom}~{iEdge} = 1;
+ EndFor
+ If(iLay == 0)
+ isEdgeTBC~{iDom}~{3} = 0;
+ EndIf
+ If(iLay == Nlay_DOM-1)
+ isEdgeABC~{iDom}~{1} = 1;
+ isEdgeTBC~{iDom}~{1} = 0;
+ isEdgeRad~{iDom}~{1} = isEdgeRad~{1};
+ EndIf
+ If(Npie_DOM == 1)
+ isEdgeTBC~{iDom}~{0} = 0;
+ isEdgeTBC~{iDom}~{2} = 0;
+ EndIf
+
+ // List of Edges for Absorbing/Transmission Boundary Condition
+ ListOfEdgesWithABC~{iDom} = {};
+ ListOfEdgesWithTBC~{iDom} = {};
+ For iEdge In {0:3}
+ If(isEdgeABC~{iDom}~{iEdge} == 1)
+ ListOfEdgesWithABC~{iDom} += iEdge;
+ EndIf
+ If(isEdgeTBC~{iDom}~{iEdge} == 1)
+ ListOfEdgesWithTBC~{iDom} += iEdge;
+ EndIf
+ EndFor
+
+EndFor
+EndFor
+
+// ====================================================================================================
+// GROUPS
+// ====================================================================================================
+
+Group {
+
+// === REFERENCE CASE ===
+
+ Omega = Region[{}];
+ GammaD = Region[{}];
+ GammaD0 = Region[{}];
+ GammaN = Region[{}];
+ GammaN0 = Region[{}];
+ GammaPoint = Region[{}];
+ For iEdge In {0:3}
+ SigmaMain~{iEdge} = Region[{}];
+ SigmaMainSides~{iEdge} = Region[{}];
+ SigmaMainSide~{iEdge}~{0} = Region[{}];
+ SigmaMainSide~{iEdge}~{1} = Region[{}];
+ EndFor
+ For iCorner In {0:3}
+ CornerMain~{iCorner} = Region[{}];
+ EndFor
+
+For iPie In {0:Npie_DOM-1}
+For iLay In {0:Nlay_DOM-1}
+ iDom = iLay + Nlay_DOM*iPie;
+
+ // DOMAIN
+ Omega += Region[TAG_DOM~{iDom}];
+
+ // BOUNDARY (Dirichlet/Neumann BC)
+ If(iLay == 0)
+ If(BC_SCATT == BC_Dir)
+ GammaD += Region[TAG_BND~{iDom}~{3}];
+ EndIf
+ If(BC_SCATT == BC_Neu)
+ GammaN += Region[TAG_BND~{iDom}~{3}];
+ EndIf
+ EndIf
+
+ // BOUNDARY (Absorbing BC)
+ If(iLay == Nlay_DOM-1)
+ SigmaMain~{1} += Region[{TAG_BND~{iDom}~{1}}];
+ EndIf
+
+EndFor
+EndFor
+
+ SigmaMain = Region[{ SigmaMain~{0}, SigmaMain~{1}, SigmaMain~{2}, SigmaMain~{3} }];
+ CornerMain = Region[{ CornerMain~{0}, CornerMain~{1}, CornerMain~{2}, CornerMain~{3} }];
+
+// === DDM CASE ===
+
+For iPie In {0:Npie_DOM-1}
+For iLay In {0:Nlay_DOM-1}
+ iDom = iLay + Nlay_DOM*iPie;
+
+ // DOMAIN
+ Omega~{iDom} = Region[TAG_DOM~{iDom}];
+
+ // SOURCE
+ GammaPoint~{iDom} = Region[{}];
+
+ // BOUNDARY (Dirichlet/Neumann BC)
+ GammaD0~{iDom} = Region[{}];
+ GammaN0~{iDom} = Region[{}];
+ GammaD~{iDom} = Region[{}];
+ GammaN~{iDom} = Region[{}];
+ If(iLay == 0)
+ If(BC_SCATT == BC_Dir)
+ GammaD~{iDom} = Region[ TAG_BND~{iDom}~{3} ]; // Down
+ EndIf
+ If(BC_SCATT == BC_Neu)
+ GammaN~{iDom} = Region[ TAG_BND~{iDom}~{3} ]; // Down
+ EndIf
+ EndIf
+
+ // BOUNDARY (Absorbing BC + Transmission BC)
+ For iEdge In {0:3}
+ Sigma~{iDom}~{iEdge} = Region[{}];
+ SigmaSide~{iDom}~{iEdge}~{0} = Region[{}];
+ SigmaSide~{iDom}~{iEdge}~{1} = Region[{}];
+ GammaD~{iDom}~{iEdge} = Region[{}];
+ GammaD0~{iDom}~{iEdge} = Region[{}];
+ GammaN~{iDom}~{iEdge} = Region[{}];
+ GammaN0~{iDom}~{iEdge} = Region[{}];
+ If((isEdgeABC~{iDom}~{iEdge} == 1) || (isEdgeTBC~{iDom}~{iEdge} == 1))
+ iCornerSide~{0} = iEdge;
+ iCornerSide~{1} = (iEdge+1)%4;
+ iEdgeSide~{0} = (iEdge+3)%4;
+ iEdgeSide~{1} = (iEdge+1)%4;
+
+ Sigma~{iDom}~{iEdge} = Region[{TAG_BND~{iDom}~{iEdge}}];
+ SigmaSide~{iDom}~{iEdge}~{0} = Region[{TAG_CRN~{iDom}~{iCornerSide~{0}}}];
+ SigmaSide~{iDom}~{iEdge}~{1} = Region[{TAG_CRN~{iDom}~{iCornerSide~{1}}}];
+
+ For iSide In {0:1}
+ If((isEdgeABC~{iDom}~{iEdgeSide~{iSide}} == 0) && (isEdgeTBC~{iDom}~{iEdgeSide~{iSide}} == 0))
+ If(BC_SCATT == BC_Dir)
+ GammaD~{iDom}~{iEdge} = Region[{TAG_CRN~{iDom}~{iCornerSide~{iSide}}}];
+ EndIf
+ If(BC_SCATT == BC_Neu)
+ GammaN~{iDom}~{iEdge} = Region[{TAG_CRN~{iDom}~{iCornerSide~{iSide}}}];
+ EndIf
+ EndIf
+ EndFor
+
+ EndIf
+ EndFor
+ Sigma~{iDom} = Region[{ Sigma~{iDom}~{0}, Sigma~{iDom}~{1}, Sigma~{iDom}~{2}, Sigma~{iDom}~{3} }];
+
+ // CORNER (Absorbing BC + Transmission BC)
+ For iCorner In {0:3}
+ Corner~{iDom}~{iCorner} = Region[{TAG_CRN~{iDom}~{iCorner}}];
+ EndFor
+ Corner~{iDom} = Region[{ Corner~{iDom}~{0}, Corner~{iDom}~{1}, Corner~{iDom}~{2}, Corner~{iDom}~{3} }];
+EndFor
+EndFor
+
+}
diff --git a/HelmholtzDDMwithCrosspoints/ddmHelmholtzCrossPoints.pro b/HelmholtzDDMwithCrosspoints/ddmHelmholtzCrossPoints.pro
new file mode 100644
index 0000000..8584c91
--- /dev/null
+++ b/HelmholtzDDMwithCrosspoints/ddmHelmholtzCrossPoints.pro
@@ -0,0 +1,954 @@
+CROSSPOINT_NO = 0;
+CROSSPOINT_Full = 2;
+
+DefineConstant[
+ nPadeABC = {0, Choices {0, 1, 2, 3, 4, 5, 6}, Highlight "Yellow", // 6
+ Name "Input/3ABC and TBC/3Pade ABC: Number of fields"},
+ thetaPadeInputABC = {0, Min 0, Max 0.5, Step 0.05, // 0.3
+ Name "Input/3ABC and TBC/4Pade ABC: Rotation of branch cut"},
+ nPadeTBC = {3, Choices {0, 2, 4, 6}, Highlight "Yellow",// Loop 1,
+ Name "Input/3ABC and TBC/5Pade TBC: Number of fields"},
+ thetaPadeInputTBC = {0.3, Min 0.1, Max 0.5, Step 0.1,
+ Name "Input/3ABC and TBC/6Pade TBC: Rotation of branch cut"},
+ stretchPadeInputTBC = {1, Choices {0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50},
+ Name "Input/3ABC and TBC/7Pade ABC: Stretch of branch cut"},
+ CROSSPOINT_TREAT = {CROSSPOINT_Full, Highlight "Blue", //Loop 2,
+ Choices {CROSSPOINT_NO = "Nothing",
+ CROSSPOINT_Full = "Compatibility everywhere"},
+ Name "Input/3ABC and TBC/8Compatibility Cross-Points"}
+];
+
+// ====================================================================================================
+// FUNCTIONS
+// ====================================================================================================
+
+DefineConstant[ R_SCA, f_sou ];
+For iDom In {0:N_DOM-1}
+ DefineConstant[ f_sou~{iDom} ];
+EndFor
+
+Function{
+
+ DefineFunction[ f_dir, f_neu ];
+
+// === Imaginary unit and wavenumber
+
+ I[] = Complex[0, 1];
+If (FLAG_PBM == PBM_MARMOUSI)
+ k[] = 2*Pi*FREQ/cData[];
+Else
+ k[] = 2*Pi*FREQ;
+EndIf
+
+// === Functions for the Pade ABC and Pade TBC
+
+ mPadeABC = 2*nPadeABC+1;
+ mPadeTBC = 2*nPadeTBC+1;
+
+ For i In {1:nPadeABC}
+ cPadeABC~{i} = Tan[i*Pi/mPadeABC]^2;
+ EndFor
+ For i In {1:nPadeTBC}
+ cPadeTBC~{i} = Tan[i*Pi/mPadeTBC]^2;
+ EndFor
+
+ For iEdge In {0:3}
+ kEps~{iEdge}[] = k[];
+ If(isEdgeRad~{iEdge} == 1)
+ //alphaBT[] = 0.5/R_EXT - (1/R_EXT^2) / (8*(1/R_EXT - I[]*k));
+ //betaBT[] = 0.5/(1/R_EXT - I[]*k);
+
+ paramCurv1~{iEdge}[] = - 0.5 * (1/R[]) + (1/R[])^2 / (8*((1/R[]) - I[]*k[]));
+ paramCurv2~{iEdge}[] = - 0.5 / ((1/R[]) - I[]*k[]);
+ //paramCurv2~{iEdge}[] = - 0.5 / (R[]*k[]*k[]);
+ Else
+ paramCurv1~{iEdge}[] = 0;
+ paramCurv2~{iEdge}[] = 0;
+ EndIf
+ EndFor
+
+ // Gander/Magoules/Nataf OO0
+ kMin[] = Pi/7.5;
+ kMinus[] = k[] - kMin[];
+ kPlus[] = k[] + kMin[];
+ kMax[] = Pi/LC;
+ //alphaPadeTBC[] = Sqrt[Sqrt[(kMax[]*kMax[]-k[]*k[]) * (k[]*k[]-kMinus[]*kMinus[])]]/k[] * Complex[Cos[Pi/4],Sin[Pi/4]];
+
+ alphaPadeABC[] = Complex[Cos[thetaPadeInputABC*Pi/2.],Sin[thetaPadeInputABC*Pi/2.]];
+ alphaPadeTBC[] = Complex[stretchPadeInputTBC*Cos[thetaPadeInputTBC*Pi/2.],stretchPadeInputTBC*Sin[thetaPadeInputTBC*Pi/2.]];
+
+ For iDom In {0:N_DOM-1}
+ For iEdge In {0:3}
+ If((isEdgeABC~{iDom}~{iEdge} == 1) && (isEdgeRad~{iDom}~{iEdge} == 1))
+ paramCurv1~{iDom}~{iEdge}[] = - 0.5 * (1/R[]) + (1/R[])^2 / (8*((1/R[]) - I[]*k[]));
+ paramCurv2~{iDom}~{iEdge}[] = - 0.5 / ((1/R[]) - I[]*k[]);
+ //paramCurv2~{iDom}~{iEdge}[] = - 0.5/(R[]*k[]*k[]);
+ Else
+ paramCurv1~{iDom}~{iEdge}[] = 0;
+ paramCurv2~{iDom}~{iEdge}[] = 0;
+ EndIf
+ If((isEdgeABC~{iDom}~{iEdge} == 0) && (isEdgeRad~{iDom}~{iEdge} == 1))
+ kEps~{iDom}~{iEdge}[] = k[] + I[] * 0.4 * k[]^(1/3) * (1/R[])^(2/3); // or 0.6
+ //ElseIf((isEdgeABC~{iDom}~{iEdge} == 0) && (isEdgeRad~{iDom}~{iEdge} == 0))
+ // kEps~{iDom}~{iEdge}[] = k[] + I[] * k[]/4;
+ Else
+ kEps~{iDom}~{iEdge}[] = k[];
+ EndIf
+ If(isEdgeTBC~{iDom}~{iEdge} == 1)
+ nPade~{iDom}~{iEdge} = nPadeTBC;
+ mPade~{iDom}~{iEdge} = mPadeTBC;
+ For i In {1:nPadeTBC}
+ cPade~{i}~{iDom}~{iEdge} = cPadeTBC~{i};
+ EndFor
+ alphaPade~{iDom}~{iEdge}[] = alphaPadeTBC[];
+ Else
+ nPade~{iDom}~{iEdge} = nPadeABC;
+ mPade~{iDom}~{iEdge} = mPadeABC;
+ For i In {1:nPadeABC}
+ cPade~{i}~{iDom}~{iEdge} = cPadeABC~{i};
+ EndFor
+ alphaPade~{iDom}~{iEdge}[] = alphaPadeABC[];
+ EndIf
+ EndFor
+ EndFor
+
+// === Numerotation of fields
+
+ index = 1;
+ For iDom In {0:N_DOM-1}
+ SaveSOL~{iDom} = index; index = index+1;
+ For iEdge In {0:3}
+ FIELD~{iDom}~{iEdge} = index; index = index+1;
+
+ iEdgeSide~{0} = (iEdge+3)%4;
+ iEdgeSide~{1} = (iEdge+1)%4;
+ For iSide In {0:1}
+ For i In {1:nPade~{iDom}~{iEdgeSide~{iSide}}}
+ FIELD~{i}~{iDom}~{iEdge}~{iSide} = index; index = index+1;
+ EndFor
+ EndFor
+ EndFor
+ EndFor
+
+// === Connectivity of fields
+
+ ListOfFields = {}; // Tableau flottant contenant les fields
+ ListOfConnectedFields = {}; // fields connected to my fields
+
+ For i0 In {0:#ListOfSubdom()-1}
+ iDom = ListOfSubdom(i0);
+ For i1 In {0:#ListOfEdgesWithTBC~{iDom}()-1}
+ iEdge = ListOfEdgesWithTBC~{iDom}(i1);
+ iEdgeSide~{0} = (iEdge+3)%4;
+ iEdgeSide~{1} = (iEdge+1)%4;
+ iDomNeigh = iDomNeigh~{iDom}~{iEdge};
+ iEdgeNeigh = iEdgeNeigh~{iDom}~{iEdge};
+ iSideNeigh~{0} = 1;
+ iSideNeigh~{1} = 0;
+
+ g_in~{iDom}~{iEdge}[] = ComplexScalarField[XYZ[]]{ FIELD~{iDomNeigh}~{iEdgeNeigh}() };
+ ListOfFields += FIELD~{iDom}~{iEdge};
+ ListOfConnectedFields += { 1, FIELD~{iDomNeigh}~{iEdgeNeigh}() };
+
+ For iSide In {0:1}
+ If (CROSSPOINT_TREAT == CROSSPOINT_Full)
+ For j In {1:nPade~{iDom}~{iEdgeSide~{iSide}}}
+ g_in~{j}~{iDom}~{iEdge}~{iSide}[] = ComplexScalarField[XYZ[]]{ FIELD~{j}~{iDomNeigh}~{iEdgeNeigh}~{iSideNeigh~{iSide}}() };
+ ListOfFields += FIELD~{j}~{iDom}~{iEdge}~{iSide};
+ ListOfConnectedFields += { 1, FIELD~{j}~{iDomNeigh}~{iEdgeNeigh}~{iSideNeigh~{iSide}}() };
+ EndFor
+ EndIf
+ EndFor
+
+ EndFor
+ EndFor
+
+// === Reference solution
+
+ FIELD_REF = index+1; index = index+1;
+ If(FLAG_ERROR == ERROR_ANA)
+ f_refErr[] = f_ref[];
+ EndIf
+ If(FLAG_ERROR == ERROR_NUM)
+ f_refErr[] = ComplexScalarField[XYZ[]]{ FIELD_REF() };
+ EndIf
+
+}
+
+// ====================================================================================================
+// CONSTRAINTS
+// ====================================================================================================
+
+Constraint{
+ { Name Dirichlet_u;
+ Case {
+ { Region GammaD; Value f_dir[]; }
+ { Region GammaD0; Value 0; }
+ }
+ }
+For i0 In {0:#ListOfSubdom()-1}
+iDom = ListOfSubdom(i0);
+ { Name Dirichlet_u~{iDom};
+ Case {
+ { Region GammaD~{iDom}; Value $PhysicalSource ? f_dir[] : 0.; }
+ { Region GammaD0~{iDom}; Value 0.; }
+ }
+ }
+For iEdge In {0:3}
+For i In {1:nPade~{iDom}~{iEdge}}
+ { Name Dirichlet_u~{i}~{iDom}~{iEdge};
+ Case {
+ { Region GammaD~{iDom}~{iEdge}; Value $PhysicalSource ? f_dir[] : 0.; } // SigmaSide~{iDom}~{iEdge}~{0}, SigmaSide~{iDom}~{iEdge}~{1}
+ { Region GammaD0~{iDom}~{iEdge}; Value 0.; }
+ }
+ }
+EndFor
+EndFor
+EndFor
+}
+
+// ====================================================================================================
+// FUNCTION SPACE
+// ====================================================================================================
+
+FunctionSpace {
+
+ { Name Href; Type Form0;
+ BasisFunction {{ Name sn; NameOfCoef un; Function BF_Node; Support Region[ {Omega, SigmaMain, CornerMain, GammaPoint, GammaN} ]; Entity NodesOf[All]; }}
+ Constraint {{ NameOfCoef un; EntityType NodesOf; NameOfConstraint Dirichlet_u; }}
+ }
+For iEdge In {0:3}
+ { Name Href_du~{iEdge}; Type Form0;
+ BasisFunction {{ Name sn; NameOfCoef un; Function BF_Node; Support Region[ {SigmaMain~{iEdge}, SigmaMainSide~{iEdge}~{0}, SigmaMainSide~{iEdge}~{1}} ]; Entity NodesOf[All]; }}
+ }
+For i In {1:nPadeABC}
+ { Name Href~{i}~{iEdge}; Type Form0;
+ BasisFunction {{ Name sn; NameOfCoef un; Function BF_Node; Support Region[ {SigmaMain~{iEdge}, SigmaMainSide~{iEdge}~{0}, SigmaMainSide~{iEdge}~{1}} ]; Entity NodesOf[All]; }}
+ }
+For iSide In {0:1}
+ { Name Href_du~{i}~{iEdge}~{iSide}; Type Form0;
+ BasisFunction {{ Name sn; NameOfCoef un; Function BF_Node; Support Region[ {SigmaMainSide~{iEdge}~{iSide}} ]; Entity NodesOf[All]; }}
+ }
+EndFor
+EndFor
+EndFor
+For iCorner In {0:3}
+For i In {1:nPadeABC}
+For j In {1:nPadeABC}
+ { Name Href~{i}~{j}~{iCorner}; Type Form0;
+ BasisFunction {{ Name sn; NameOfCoef un; Function BF_Node; Support Region[ {CornerMain~{iCorner}} ]; Entity NodesOf[All]; }}
+ }
+EndFor
+EndFor
+EndFor
+
+For i0 In {0:#ListOfSubdom()-1}
+iDom = ListOfSubdom(i0);
+
+ { Name Hddm_u~{iDom}; Type Form0;
+ BasisFunction {{ Name sn; NameOfCoef un; Function BF_Node; Support Region[ {Omega~{iDom}, Sigma~{iDom}, Corner~{iDom}, GammaPoint~{iDom}, GammaN~{iDom}} ]; Entity NodesOf[All]; }}
+ Constraint {{ NameOfCoef un; EntityType NodesOf; NameOfConstraint Dirichlet_u~{iDom}; }}
+ }
+For iEdge In {0:3}
+ { Name Hddm_du~{iDom}~{iEdge}; Type Form0;
+ BasisFunction {{ Name sn; NameOfCoef un; Function BF_Node; Support Region[ {Sigma~{iDom}~{iEdge}, SigmaSide~{iDom}~{iEdge}~{0}, SigmaSide~{iDom}~{iEdge}~{1}} ]; Entity NodesOf[All]; }} // , Not {GammaD~{iDom}}
+ }
+For i In {1:nPade~{iDom}~{iEdge}}
+ { Name Hddm_u~{i}~{iDom}~{iEdge}; Type Form0;
+ BasisFunction {{ Name sn; NameOfCoef un; Function BF_Node; Support Region[ {Sigma~{iDom}~{iEdge}, SigmaSide~{iDom}~{iEdge}~{0}, SigmaSide~{iDom}~{iEdge}~{1}} ]; Entity NodesOf[All]; }}
+// Constraint {{ NameOfCoef un; EntityType NodesOf; NameOfConstraint Dirichlet_u~{i}~{iDom}~{iEdge}; }}
+ }
+For iSide In {0:1}
+ { Name Hddm_du~{i}~{iDom}~{iEdge}~{iSide}; Type Form0;
+ BasisFunction {{ Name sn; NameOfCoef un; Function BF_Node; Support Region[ {SigmaSide~{iDom}~{iEdge}~{iSide}} ]; Entity NodesOf[All]; }}
+ }
+EndFor
+EndFor
+EndFor
+For iCorner In {0:3}
+iEdgeSide~{0} = (iCorner+3)%4;
+iEdgeSide~{1} = iCorner;
+For i In {1:nPade~{iDom}~{iEdgeSide~{0}}}
+For j In {1:nPade~{iDom}~{iEdgeSide~{1}}}
+ { Name Hddm_u~{i}~{j}~{iDom}~{iCorner}; Type Form0;
+ BasisFunction {{ Name sn; NameOfCoef un; Function BF_Node; Support Region[ {Corner~{iDom}~{iCorner}} ]; Entity NodesOf[All]; }}
+ }
+EndFor
+EndFor
+EndFor
+
+For iEdge In {0:3}
+iEdgeSide~{0} = (iEdge+3)%4;
+iEdgeSide~{1} = (iEdge+1)%4;
+ { Name Hddm_g_out~{iDom}~{iEdge}; Type Form0;
+ BasisFunction {{ Name sn; NameOfCoef un; Function BF_Node; Support Region[ {Sigma~{iDom}~{iEdge}, SigmaSide~{iDom}~{iEdge}~{0}, SigmaSide~{iDom}~{iEdge}~{1}} ]; Entity NodesOf[All]; }} // , Not {GammaD~{iDom}}
+ }
+For iSide In {0:1}
+For i In {1:nPade~{iDom}~{iEdgeSide~{iSide}}}
+ { Name Hddm_g_out~{i}~{iDom}~{iEdge}~{iSide}; Type Form0;
+ BasisFunction {{ Name sn; NameOfCoef un; Function BF_Node; Support Region[ {SigmaSide~{iDom}~{iEdge}~{iSide}} ]; Entity NodesOf[All]; }}
+ }
+EndFor
+EndFor
+EndFor
+
+EndFor
+}
+
+
+// ====================================================================================================
+// FORMULATION
+// ====================================================================================================
+
+Formulation {
+
+// ====================================================================================================
+// Reference SOLVER without DDM
+// ====================================================================================================
+
+ { Name FormRef; Type FemEquation;
+ Quantity {
+ { Name uRef; Type Local; NameOfSpace Href; }
+ For iEdge In {0:3}
+ { Name duRef~{iEdge}; Type Local; NameOfSpace Href_du~{iEdge}; }
+ For i In {1:nPadeABC}
+ { Name uRef~{i}~{iEdge}; Type Local; NameOfSpace Href~{i}~{iEdge}; }
+ For iSide In {0:1}
+ { Name duRef~{i}~{iEdge}~{iSide}; Type Local; NameOfSpace Href_du~{i}~{iEdge}~{iSide}; }
+ EndFor
+ EndFor
+ EndFor
+ For iCorner In {0:3}
+ For i In {1:nPadeABC}
+ For j In {1:nPadeABC}
+ { Name uRef~{i}~{j}~{iCorner}; Type Local; NameOfSpace Href~{i}~{j}~{iCorner}; }
+ EndFor
+ EndFor
+ EndFor
+ }
+ Equation {
+
+// Field on SURFACE
+
+ Galerkin { [ Dof{d uRef} , {d uRef} ]; In Omega; Jacobian JSur; Integration I1; }
+ Galerkin { [ - k[]^2 * Dof{uRef} , {uRef} ]; In Omega; Jacobian JSur; Integration I1; }
+ Galerkin { [ - f_sou , {uRef} ]; In GammaPoint; Jacobian JSur; Integration I1; }
+ Galerkin { [ - f_neu[] , {uRef} ]; In GammaN; Jacobian JLin; Integration I1; }
+ For iEdge In {0:3}
+ Galerkin { [ - Dof{duRef~{iEdge}} , {uRef} ]; In SigmaMain~{iEdge}; Jacobian JLin; Integration I1; }
+ EndFor
+
+// DtN on EDGES
+
+ For iEdge In {0:3}
+ Galerkin { [ Dof{duRef~{iEdge}} , {duRef~{iEdge}} ]; In SigmaMain~{iEdge}; Jacobian JLin; Integration I1; }
+ Galerkin { [ - paramCurv1~{iEdge}[] * Dof{uRef} , {duRef~{iEdge}} ]; In SigmaMain~{iEdge}; Jacobian JLin; Integration I1; }
+ Galerkin { [ - paramCurv2~{iEdge}[] * Dof{d uRef} , {d duRef~{iEdge}} ]; In SigmaMain~{iEdge}; Jacobian JLin; Integration I1; }
+ Galerkin { [ - I[]*k[]*alphaPadeABC[] * Dof{uRef} , {duRef~{iEdge}} ]; In SigmaMain~{iEdge}; Jacobian JLin; Integration I1; }
+ For i In {1:nPadeABC}
+ Galerkin { [ - I[]*k[]*alphaPadeABC[] * 2./mPadeABC * cPadeABC~{i} * Dof{uRef} , {duRef~{iEdge}} ]; In SigmaMain~{iEdge}; Jacobian JLin; Integration I1; }
+ Galerkin { [ - I[]*k[]*alphaPadeABC[] * 2./mPadeABC * cPadeABC~{i} * Dof{uRef~{i}~{iEdge}} , {duRef~{iEdge}} ]; In SigmaMain~{iEdge}; Jacobian JLin; Integration I1; }
+ EndFor
+ EndFor
+
+// Fields on EDGES
+
+ For iEdge In {0:3}
+ iCornerSide~{0} = iEdge;
+ iCornerSide~{1} = (iEdge+1)%4;
+ For i In {1:nPadeABC}
+
+ Galerkin { [ Dof{d uRef~{i}~{iEdge}} , {d uRef~{i}~{iEdge}} ]; In SigmaMain~{iEdge}; Jacobian JLin; Integration I1; }
+ Galerkin { [ - kEps~{iEdge}[]^2*(alphaPadeABC[]^2*cPadeABC~{i}+1) * Dof{uRef~{i}~{iEdge}} , {uRef~{i}~{iEdge}} ]; In SigmaMain~{iEdge}; Jacobian JLin; Integration I1; }
+ Galerkin { [ - kEps~{iEdge}[]^2*alphaPadeABC[]^2*(cPadeABC~{i}+1) * Dof{uRef} , {uRef~{i}~{iEdge}} ]; In SigmaMain~{iEdge}; Jacobian JLin; Integration I1; }
+ For iSide In {0:1}
+ Galerkin { [ - Dof{duRef~{i}~{iEdge}~{iSide}} , {uRef~{i}~{iEdge}} ]; In CornerMain~{iCornerSide~{iSide}}; Jacobian JVol; Integration I1; }
+ EndFor
+
+ EndFor
+ EndFor
+
+// DtN on EDGES
+
+ For iEdge In {0:3}
+ iCornerSide~{0} = iEdge;
+ iCornerSide~{1} = (iEdge+1)%4;
+ For i In {1:nPadeABC}
+
+ For iSide In {0:1}
+ Galerkin { [ Dof{duRef~{i}~{iEdge}~{iSide}} , {duRef~{i}~{iEdge}~{iSide}} ]; In CornerMain~{iCornerSide~{iSide}}; Jacobian JVol; Integration I1; }
+ Galerkin { [ - I[]*k[]*alphaPadeABC[] * Dof{uRef~{i}~{iEdge}} , {duRef~{i}~{iEdge}~{iSide}} ]; In CornerMain~{iCornerSide~{iSide}}; Jacobian JVol; Integration I1; }
+ For j In {1:nPadeABC}
+ Galerkin { [ - I[]*k[]*alphaPadeABC[] * 2./mPadeABC * cPadeABC~{j} * Dof{uRef~{i}~{iEdge}} , {duRef~{i}~{iEdge}~{iSide}} ]; In CornerMain~{iCornerSide~{iSide}}; Jacobian JVol; Integration I1; }
+ If (iSide == 0)
+ Galerkin { [ - I[]*k[]*alphaPadeABC[] * 2./mPadeABC * cPadeABC~{j} * Dof{uRef~{j}~{i}~{iCornerSide~{iSide}}} , {duRef~{i}~{iEdge}~{iSide}} ]; In CornerMain~{iCornerSide~{iSide}}; Jacobian JVol; Integration I1; }
+ Else
+ Galerkin { [ - I[]*k[]*alphaPadeABC[] * 2./mPadeABC * cPadeABC~{j} * Dof{uRef~{i}~{j}~{iCornerSide~{iSide}}} , {duRef~{i}~{iEdge}~{iSide}} ]; In CornerMain~{iCornerSide~{iSide}}; Jacobian JVol; Integration I1; }
+ EndIf
+ EndFor
+ EndFor
+
+ EndFor
+ EndFor
+
+// Fields on CORNERS
+
+ For iCorner In {0:3}
+ iEdgeSide~{0} = (iCorner+3)%4;
+ iEdgeSide~{1} = iCorner;
+ For i In {1:nPadeABC}
+ For j In {1:nPadeABC}
+ Galerkin { [ Dof{uRef~{i}~{j}~{iCorner}} , {uRef~{i}~{j}~{iCorner}} ]; In CornerMain~{iCorner}; Jacobian JVol; Integration I1; }
+ Galerkin { [ alphaPadeABC[]^2*(cPadeABC~{j}+1) * Dof{uRef~{i}~{iEdgeSide~{0}}} / (alphaPadeABC[]^2*cPadeABC~{i} + alphaPadeABC[]^2*cPadeABC~{j} + 1) , {uRef~{i}~{j}~{iCorner}} ]; In CornerMain~{iCorner}; Jacobian JVol; Integration I1; }
+ Galerkin { [ alphaPadeABC[]^2*(cPadeABC~{i}+1) * Dof{uRef~{j}~{iEdgeSide~{1}}} / (alphaPadeABC[]^2*cPadeABC~{i} + alphaPadeABC[]^2*cPadeABC~{j} + 1) , {uRef~{i}~{j}~{iCorner}} ]; In CornerMain~{iCorner}; Jacobian JVol; Integration I1; }
+ EndFor
+ EndFor
+ EndFor
+
+ }
+ }
+
+// ====================================================================================================
+// SOLVER for subdomain 'iDom'
+// ====================================================================================================
+
+For i0 In {0:#ListOfSubdom()-1}
+iDom = ListOfSubdom(i0);
+
+ { Name FormVol~{iDom}; Type FemEquation;
+ Quantity {
+ { Name u~{iDom}; Type Local; NameOfSpace Hddm_u~{iDom}; }
+ For iEdge In {0:3}
+ { Name du~{iDom}~{iEdge}; Type Local; NameOfSpace Hddm_du~{iDom}~{iEdge}; }
+ For i In {1:nPade~{iDom}~{iEdge}}
+ { Name u~{i}~{iDom}~{iEdge}; Type Local; NameOfSpace Hddm_u~{i}~{iDom}~{iEdge}; }
+ For iSide In {0:1}
+ { Name du~{i}~{iDom}~{iEdge}~{iSide}; Type Local; NameOfSpace Hddm_du~{i}~{iDom}~{iEdge}~{iSide}; }
+ EndFor
+ EndFor
+ EndFor
+ For iCorner In {0:3}
+ iEdgeSide~{0} = (iCorner+3)%4;
+ iEdgeSide~{1} = iCorner;
+ For i In {1:nPade~{iDom}~{iEdgeSide~{0}}}
+ For j In {1:nPade~{iDom}~{iEdgeSide~{1}}}
+ { Name u~{i}~{j}~{iDom}~{iCorner}; Type Local; NameOfSpace Hddm_u~{i}~{j}~{iDom}~{iCorner}; }
+ EndFor
+ EndFor
+ EndFor
+ }
+ Equation {
+
+// Field on SURFACE
+
+ Galerkin { [ Dof{d u~{iDom}} , {d u~{iDom}} ]; In Omega~{iDom}; Jacobian JSur; Integration I1; }
+ Galerkin { [ - k[]^2 * Dof{u~{iDom}} , {u~{iDom}} ]; In Omega~{iDom}; Jacobian JSur; Integration I1; }
+ Galerkin { [ ($PhysicalSource ? -f_sou~{iDom} : 0) , {u~{iDom}} ]; In GammaPoint~{iDom}; Jacobian JSur; Integration I1; }
+ Galerkin { [ ($PhysicalSource ? -f_neu[] : 0) , {u~{iDom}} ]; In GammaN~{iDom}; Jacobian JLin; Integration I1; }
+ For iEdge In {0:3}
+ Galerkin { [ - Dof{du~{iDom}~{iEdge}} , {u~{iDom}} ]; In Sigma~{iDom}~{iEdge}; Jacobian JLin; Integration I1; }
+ If (isEdgeTBC~{iDom}~{iEdge})
+ Galerkin { [ ($ArtificialSource ? -g_in~{iDom}~{iEdge}[] : 0) , {u~{iDom}} ]; In Sigma~{iDom}~{iEdge}; Jacobian JLin; Integration I1; }
+ EndIf
+ EndFor
+
+// DtN on EDGES
+
+ For iEdge In {0:3}
+ Galerkin { [ Dof{du~{iDom}~{iEdge}} , {du~{iDom}~{iEdge}} ]; In Sigma~{iDom}~{iEdge}; Jacobian JLin; Integration I1; }
+ Galerkin { [ - paramCurv1~{iDom}~{iEdge}[] * Dof{u~{iDom}} , {du~{iDom}~{iEdge}} ]; In Sigma~{iDom}~{iEdge}; Jacobian JLin; Integration I1; }
+ Galerkin { [ - paramCurv2~{iDom}~{iEdge}[] * Dof{d u~{iDom}} , {d du~{iDom}~{iEdge}} ]; In Sigma~{iDom}~{iEdge}; Jacobian JLin; Integration I1; }
+ Galerkin { [ - I[]*k[]*alphaPade~{iDom}~{iEdge}[] * Dof{u~{iDom}} , {du~{iDom}~{iEdge}} ]; In Sigma~{iDom}~{iEdge}; Jacobian JLin; Integration I1; }
+ For i In {1:nPade~{iDom}~{iEdge}}
+ Galerkin { [ - I[]*k[]*alphaPade~{iDom}~{iEdge}[] * 2./mPade~{iDom}~{iEdge} * cPade~{i}~{iDom}~{iEdge} * Dof{u~{iDom}} , {du~{iDom}~{iEdge}} ]; In Sigma~{iDom}~{iEdge}; Jacobian JLin; Integration I1; }
+ Galerkin { [ - I[]*k[]*alphaPade~{iDom}~{iEdge}[] * 2./mPade~{iDom}~{iEdge} * cPade~{i}~{iDom}~{iEdge} * Dof{u~{i}~{iDom}~{iEdge}} , {du~{iDom}~{iEdge}} ]; In Sigma~{iDom}~{iEdge}; Jacobian JLin; Integration I1; }
+ EndFor
+ EndFor
+
+// Fields on EDGES
+
+ For iEdge In {0:3}
+ iEdgeSide~{0} = (iEdge+3)%4;
+ iEdgeSide~{1} = (iEdge+1)%4;
+ iCornerSide~{0} = iEdge;
+ iCornerSide~{1} = (iEdge+1)%4;
+ iSideSide~{0} = 1;
+ iSideSide~{1} = 0;
+ For i In {1:nPade~{iDom}~{iEdge}}
+
+ Galerkin { [ Dof{d u~{i}~{iDom}~{iEdge}} , {d u~{i}~{iDom}~{iEdge}} ]; In Sigma~{iDom}~{iEdge}; Jacobian JLin; Integration I1; }
+ Galerkin { [ - kEps~{iDom}~{iEdge}[]^2*(alphaPade~{iDom}~{iEdge}[]^2*cPade~{i}~{iDom}~{iEdge}+1) * Dof{u~{i}~{iDom}~{iEdge}} , {u~{i}~{iDom}~{iEdge}} ]; In Sigma~{iDom}~{iEdge}; Jacobian JLin; Integration I1; }
+ Galerkin { [ - kEps~{iDom}~{iEdge}[]^2*alphaPade~{iDom}~{iEdge}[]^2*(cPade~{i}~{iDom}~{iEdge}+1) * Dof{u~{iDom}} , {u~{i}~{iDom}~{iEdge}} ]; In Sigma~{iDom}~{iEdge}; Jacobian JLin; Integration I1; }
+ For iSide In {0:1}
+ If ((CROSSPOINT_TREAT == CROSSPOINT_Full) || (isEdgeABC~{iDom}~{iEdge} && isEdgeABC~{iDom}~{iEdgeSide~{iSide}}))
+ Galerkin { [ - Dof{du~{i}~{iDom}~{iEdge}~{iSide}} , {u~{i}~{iDom}~{iEdge}} ]; In Corner~{iDom}~{iCornerSide~{iSide}}; Jacobian JVol; Integration I1; }
+ If (isEdgeTBC~{iDom}~{iEdgeSide~{iSide}})
+ Galerkin { [ ($ArtificialSource ? -g_in~{i}~{iDom}~{iEdgeSide~{iSide}}~{iSideSide~{iSide}}[] : 0) , {u~{i}~{iDom}~{iEdge}} ]; In Corner~{iDom}~{iCornerSide~{iSide}}; Jacobian JVol; Integration I1; }
+ EndIf
+ EndIf
+ EndFor
+ EndFor
+ EndFor
+
+// DtN at CORNERS
+
+ For iEdge In {0:3}
+ iEdgeSide~{0} = (iEdge+3)%4;
+ iEdgeSide~{1} = (iEdge+1)%4;
+ iCornerSide~{0} = iEdge;
+ iCornerSide~{1} = (iEdge+1)%4;
+ For i In {1:nPade~{iDom}~{iEdge}}
+
+ For iSide In {0:1}
+ Galerkin { [ Dof{du~{i}~{iDom}~{iEdge}~{iSide}} , {du~{i}~{iDom}~{iEdge}~{iSide}} ]; In Corner~{iDom}~{iCornerSide~{iSide}}; Jacobian JVol; Integration I1; }
+ Galerkin { [ - I[]*k[]*alphaPade~{iDom}~{iEdgeSide~{iSide}}[] * Dof{u~{i}~{iDom}~{iEdge}} , {du~{i}~{iDom}~{iEdge}~{iSide}} ]; In Corner~{iDom}~{iCornerSide~{iSide}}; Jacobian JVol; Integration I1; }
+ For j In {1:nPade~{iDom}~{iEdgeSide~{iSide}}}
+ Galerkin { [ - I[]*k[]*alphaPade~{iDom}~{iEdgeSide~{iSide}}[] * 2./mPade~{iDom}~{iEdgeSide~{iSide}} * cPade~{j}~{iDom}~{iEdgeSide~{iSide}} * Dof{u~{i}~{iDom}~{iEdge}} , {du~{i}~{iDom}~{iEdge}~{iSide}} ]; In Corner~{iDom}~{iCornerSide~{iSide}}; Jacobian JVol; Integration I1; }
+ If (iSide == 0)
+ Galerkin { [ - I[]*k[]*alphaPade~{iDom}~{iEdgeSide~{iSide}}[] * 2./mPade~{iDom}~{iEdgeSide~{iSide}} * cPade~{j}~{iDom}~{iEdgeSide~{iSide}} * Dof{u~{j}~{i}~{iDom}~{iCornerSide~{iSide}}} , {du~{i}~{iDom}~{iEdge}~{iSide}} ]; In Corner~{iDom}~{iCornerSide~{iSide}}; Jacobian JVol; Integration I1; }
+ Else
+ Galerkin { [ - I[]*k[]*alphaPade~{iDom}~{iEdgeSide~{iSide}}[] * 2./mPade~{iDom}~{iEdgeSide~{iSide}} * cPade~{j}~{iDom}~{iEdgeSide~{iSide}} * Dof{u~{i}~{j}~{iDom}~{iCornerSide~{iSide}}} , {du~{i}~{iDom}~{iEdge}~{iSide}} ]; In Corner~{iDom}~{iCornerSide~{iSide}}; Jacobian JVol; Integration I1; }
+ EndIf
+ EndFor
+ EndFor
+
+ EndFor
+ EndFor
+
+// Fields at CORNERS
+
+ For iCorner In {0:3}
+ iEdge0 = (iCorner+3)%4;
+ iEdge1 = iCorner;
+ For i In {1:nPade~{iDom}~{iEdge0}}
+ For j In {1:nPade~{iDom}~{iEdge1}}
+ Galerkin { [ Dof{u~{i}~{j}~{iDom}~{iCorner}} , {u~{i}~{j}~{iDom}~{iCorner}} ]; In Corner~{iDom}~{iCorner}; Jacobian JVol; Integration I1; }
+ Galerkin { [ alphaPade~{iDom}~{iEdge1}[]^2*(cPade~{j}~{iDom}~{iEdge1}+1) * Dof{u~{i}~{iDom}~{iEdge0}} / (alphaPade~{iDom}~{iEdge0}[]^2*cPade~{i}~{iDom}~{iEdge0} + alphaPade~{iDom}~{iEdge1}[]^2*cPade~{j}~{iDom}~{iEdge1} + 1) , {u~{i}~{j}~{iDom}~{iCorner}} ]; In Corner~{iDom}~{iCorner}; Jacobian JVol; Integration I1; }
+ Galerkin { [ alphaPade~{iDom}~{iEdge0}[]^2*(cPade~{i}~{iDom}~{iEdge0}+1) * Dof{u~{j}~{iDom}~{iEdge1}} / (alphaPade~{iDom}~{iEdge0}[]^2*cPade~{i}~{iDom}~{iEdge0} + alphaPade~{iDom}~{iEdge1}[]^2*cPade~{j}~{iDom}~{iEdge1} + 1) , {u~{i}~{j}~{iDom}~{iCorner}} ]; In Corner~{iDom}~{iCorner}; Jacobian JVol; Integration I1; }
+ EndFor
+ EndFor
+ EndFor
+
+ }
+ }
+
+EndFor // loop on iDom
+
+// ====================================================================================================
+// SOLVER for outgoing data for side 'iEdge' of 'iDom'
+// ====================================================================================================
+
+For i0 In {0:#ListOfSubdom()-1}
+iDom = ListOfSubdom(i0);
+For i1 In {0:#ListOfEdgesWithTBC~{iDom}()-1}
+iEdge = ListOfEdgesWithTBC~{iDom}(i1);
+iEdgeSide~{0} = (iEdge+3)%4;
+iEdgeSide~{1} = (iEdge+1)%4;
+iCornerSide~{0} = iEdge;
+iCornerSide~{1} = (iEdge+1)%4;
+iSideSide~{0} = 1;
+iSideSide~{1} = 0;
+
+ { Name FormSur~{iDom}~{iEdge}; Type FemEquation;
+ Quantity {
+ { Name du~{iDom}~{iEdge}; Type Local; NameOfSpace Hddm_du~{iDom}~{iEdge}; }
+ { Name g_out~{iDom}~{iEdge}; Type Local; NameOfSpace Hddm_g_out~{iDom}~{iEdge}; }
+ For iSide In {0:1}
+ For i In {1:nPade~{iDom}~{iEdgeSide~{iSide}}}
+ { Name du~{i}~{iDom}~{iEdgeSide~{iSide}}~{iSideSide~{iSide}}; Type Local; NameOfSpace Hddm_du~{i}~{iDom}~{iEdgeSide~{iSide}}~{iSideSide~{iSide}}; }
+ { Name g_out~{i}~{iDom}~{iEdge}~{iSide}; Type Local; NameOfSpace Hddm_g_out~{i}~{iDom}~{iEdge}~{iSide}; }
+ EndFor
+ EndFor
+ }
+ Equation {
+
+ Galerkin { [ Dof{g_out~{iDom}~{iEdge}} , {g_out~{iDom}~{iEdge}} ]; In Sigma~{iDom}~{iEdge}; Jacobian JSur; Integration I1; }
+ Galerkin { [ $ArtificialSource ? g_in~{iDom}~{iEdge}[] : 0 , {g_out~{iDom}~{iEdge}} ]; In Sigma~{iDom}~{iEdge}; Jacobian JSur; Integration I1; }
+ Galerkin { [ 2 * {du~{iDom}~{iEdge}} , {g_out~{iDom}~{iEdge}} ]; In Sigma~{iDom}~{iEdge}; Jacobian JSur; Integration I1; }
+
+ For iSide In {0:1}
+ If (CROSSPOINT_TREAT == CROSSPOINT_Full)
+ For i In {1:nPade~{iDom}~{iEdgeSide~{iSide}}}
+ Galerkin { [ Dof{g_out~{i}~{iDom}~{iEdge}~{iSide}} , {g_out~{i}~{iDom}~{iEdge}~{iSide}} ]; In Corner~{iDom}~{iCornerSide~{iSide}}; Jacobian JLin; Integration I1; }
+ Galerkin { [ $ArtificialSource ? g_in~{i}~{iDom}~{iEdge}~{iSide}[] : 0 , {g_out~{i}~{iDom}~{iEdge}~{iSide}} ]; In Corner~{iDom}~{iCornerSide~{iSide}}; Jacobian JLin; Integration I1; }
+ Galerkin { [ 2 * {du~{i}~{iDom}~{iEdgeSide~{iSide}}~{iSideSide~{iSide}}} , {g_out~{i}~{iDom}~{iEdge}~{iSide}} ]; In Corner~{iDom}~{iCornerSide~{iSide}}; Jacobian JLin; Integration I1; }
+ EndFor
+ EndIf
+ EndFor
+
+ }
+ }
+
+EndFor // loop on iEdge
+EndFor // loop on iDom
+
+}
+
+// ====================================================================================================
+// RESOLUTION
+// ====================================================================================================
+
+Resolution {
+ { Name ResoRef;
+ System {
+ { Name SysRef; NameOfFormulation FormRef; Type Complex; NameOfMesh Sprintf[StrCat[MSH_NAME, ".msh"]]; }
+ }
+ Operation {
+ Generate[SysRef]; Solve[SysRef]; PostOperation[PostOpRef];
+ }
+ }
+
+ { Name ResoDDM;
+ System {
+ If(FLAG_ERROR == ERROR_NUM)
+ { Name SysRef; NameOfFormulation FormRef; Type Complex; NameOfMesh Sprintf[StrCat[MSH_NAME, ".msh"]]; }
+ EndIf
+ For i0 In {0:#ListOfSubdom()-1}
+ iDom = ListOfSubdom(i0);
+ { Name SysVol~{iDom}; NameOfFormulation FormVol~{iDom}; Type Complex; NameOfMesh Sprintf[StrCat[MSH_NAME, "_%g.msh"], iDom]; }
+ For i1 In {0:#ListOfEdgesWithTBC~{iDom}()-1}
+ iEdge = ListOfEdgesWithTBC~{iDom}(i1);
+ { Name SysSur~{iDom}~{iEdge}; NameOfFormulation FormSur~{iDom}~{iEdge}; Type Complex; NameOfMesh Sprintf[StrCat[MSH_NAME, "_%g.msh"], iDom]; }
+ EndFor
+ EndFor
+ }
+ Operation {
+
+ If(FLAG_ERROR == ERROR_NUM)
+ Generate[SysRef]; Solve[SysRef]; PostOperation[PostOpRef];
+ EndIf
+
+// For MAXITeff In {1:50}
+
+ // =========================================================
+ // BUILD local part of distributed rhs b for Krylov solver using physical sources only, and update surface data
+ // =========================================================
+
+ SetCommSelf;
+
+ // SolveVolumePDE (without artificial/with physical sources)
+ Evaluate[$ArtificialSource = 0];
+ Evaluate[$PhysicalSource = 1];
+ For i0 In {0:#ListOfSubdom()-1}
+ iDom = ListOfSubdom(i0);
+ UpdateConstraint[SysVol~{iDom}, GammaD~{iDom}, Assign];
+ Generate[SysVol~{iDom}];
+ Solve[SysVol~{iDom}];
+ EndFor
+
+ If(#ListOfSubdom() > 1)
+
+ // SolveSurfacePDE
+ For i0 In {0:#ListOfSubdom()-1}
+ iDom = ListOfSubdom(i0);
+ For i1 In {0:#ListOfEdgesWithTBC~{iDom}()-1}
+ iEdge = ListOfEdgesWithTBC~{iDom}(i1);
+ Generate[SysSur~{iDom}~{iEdge}];
+ Solve[SysSur~{iDom}~{iEdge}];
+ EndFor
+ EndFor
+
+ // UpdateSurfaceFields
+ For i0 In {0:#ListOfSubdom()-1}
+ iDom = ListOfSubdom(i0);
+ For i1 In {0:#ListOfEdgesWithTBC~{iDom}()-1}
+ iEdge = ListOfEdgesWithTBC~{iDom}(i1);
+ PostOperation[PostOpSur~{iDom}~{iEdge}];
+ EndFor
+ EndFor
+
+ // =========================================================
+ // Krylov solver using artificial sources only. IterativeLinearSolver solves (I-A) g = b
+ // ListOfFields() initially stores the local part of b; then stores each local part of iterate g^n.
+ // =========================================================
+
+ // UpdateConstraint (with artificial/without physical sources)
+ Evaluate[$ArtificialSource = 1];
+ Evaluate[$PhysicalSource = 0];
+ For i0 In {0:#ListOfSubdom()-1}
+ iDom = ListOfSubdom(i0);
+ UpdateConstraint[SysVol~{iDom}, GammaD~{iDom}, Assign];
+ EndFor
+
+ SetCommWorld;
+
+ IterativeLinearSolver["I-A", SOLVER, TOL, MAXIT, RESTART, {ListOfFields()}, {ListOfConnectedFields()}, {}]
+// IterativeLinearSolver["I-A", SOLVER, TOL, MAXITeff, RESTART, {ListOfFields()}, {ListOfConnectedFields()}, {}]
+ {
+
+ SetCommSelf;
+
+ // SolveVolumePDE
+ For i0 In {0:#ListOfSubdom()-1}
+ iDom = ListOfSubdom(i0);
+ GenerateRHSGroup[SysVol~{iDom}, Region[{GammaD~{iDom}, Sigma~{iDom}, Corner~{iDom}}] ];
+ SolveAgain[SysVol~{iDom}];
+ EndFor
+
+ // SolveSurfacePDE
+ For i0 In {0:#ListOfSubdom()-1}
+ iDom = ListOfSubdom(i0);
+ For i1 In {0:#ListOfEdgesWithTBC~{iDom}()-1}
+ iEdge = ListOfEdgesWithTBC~{iDom}(i1);
+ GenerateRHSGroup[SysSur~{iDom}~{iEdge}, Region[{Sigma~{iDom}~{iEdge}, SigmaSide~{iDom}~{iEdge}~{0}, SigmaSide~{iDom}~{iEdge}~{1}}]];
+ SolveAgain[SysSur~{iDom}~{iEdge}];
+ EndFor
+ EndFor
+
+ // UpdateSurfaceFields
+ For i0 In {0:#ListOfSubdom()-1}
+ iDom = ListOfSubdom(i0);
+ For i1 In {0:#ListOfEdgesWithTBC~{iDom}()-1}
+ iEdge = ListOfEdgesWithTBC~{iDom}(i1);
+ PostOperation[PostOpSur~{iDom}~{iEdge}];
+ EndFor
+ EndFor
+
+ SetCommWorld;
+
+ Barrier;
+ Test[ $KSPIteration == 0 ]{
+ Print[ {$KSPResidual}, Format "%12.5e", File Sprintf("out/STAT_residualInit_%g_%g_%g_%g_%g_%g.dat", FLAG_PBM, N_DOM, nPadeABC, thetaPadeInputABC, nPadeTBC, CROSSPOINT_TREAT) ];
+ //Print[ {$KSPResidual}, Format "%12.5e", File Sprintf("out/STAT_residualInit_%g_%g_%g_%g_%g_%g_%g.dat", FLAG_PBM, N_DOM, nPadeABC, thetaPadeInputABC, nPadeTBC, thetaPadeInputTBC, CROSSPOINT_TREAT) ];
+ }
+ //Print[ {$KSPResidual}, Format "%12.5e", File Sprintf("out/STAT_solverRes_%g_%g_%g_%g_%g_%g_%g_%g_%g_%g.dat", FLAG_PBM, N_DOM, nPadeABC, thetaPadeInputABC, nPadeTBC, thetaPadeInputTBC, CROSSPOINT_TREAT, WAVENUMBER, N_LAMBDAtextsf) ];
+ }
+
+ //Print[ {FLAG_PBM, N_DOM, nPadeABC, thetaPadeInputABC, nPadeTBC, thetaPadeInputTBC, CROSSPOINT_TREAT, WAVENUMBER, N_LAMBDA, $KSPIts}, Format "%g %g %g %g %g %g %g %g %g %g", File Sprintf("out/STAT_solverNumIter.dat") ];
+ Evaluate[$NumIter = $KSPIts];
+ Evaluate[$ResidualFinal = $KSPResidual];
+
+ //Print[ {$KSPResidual}, Format "%12.5e", File Sprintf("out/STAT_solverRes_%g_%g_%g_%g_%g_%g_%g_%g_%g.dat", FLAG_PBM, N_DOM, nPadeABC, thetaPadeInputABC, nPadeTBC, thetaPadeInputTBC, CROSSPOINT_TREAT, WAVENUMBER, N_LAMBDA) ];
+
+ EndIf
+
+ SetCommSelf;
+
+ // Compute final solution
+ Evaluate[$ArtificialSource = 1];
+ Evaluate[$PhysicalSource = 1];
+ For i0 In {0:#ListOfSubdom()-1}
+ iDom = ListOfSubdom(i0);
+ UpdateConstraint[SysVol~{iDom}, GammaD~{iDom}, Assign];
+ Generate[SysVol~{iDom}];
+ Solve[SysVol~{iDom}];
+ EndFor
+
+ // Save final solution
+ For i0 In {0:#ListOfSubdom()-1}
+ iDom = ListOfSubdom(i0);
+ PostOperation[PostOpVol~{iDom}];
+ EndFor
+
+ SetCommWorld;
+
+ // Compute error
+ If(FLAG_ERROR != ERROR_NO)
+ Evaluate[$error2Var = 0];
+ Evaluate[$energy2Var = 0];
+ For i0 In {0:#ListOfSubdom()-1}
+ iDom = ListOfSubdom(i0);
+ PostOperation[PostOpStat~{iDom}];
+ Evaluate[$error2Var = $error2Var + $error2Var~{iDom}];
+ Evaluate[$energy2Var = $energy2Var + $energy2Var~{iDom}];
+ EndFor
+ EndIf
+ PostOperation[PostOpStat];
+
+// EndFor
+
+ }
+ }
+}
+
+
+// ====================================================================================================
+// POST-PROCESSING
+// ====================================================================================================
+
+PostProcessing {
+
+// REFERENCE SOLVER
+
+ { Name PostProRef; NameOfFormulation FormRef;
+ PostQuantity {
+// { Name cNumREF; Value { Local { [ cData[] ]; In Omega; Jacobian JVol; }}}
+ { Name uNumREF; Value { Local { [ {uRef} ]; In Omega; Jacobian JVol; }}}
+ If((FLAG_PBM == PBM_SCATT_CIRC) || (FLAG_PBM == PBM_SCATT_RECT))
+ { Name uRefREF; Value { Local { [ f_ref[] ]; In Omega; Jacobian JVol; }}}
+ { Name uErrREF; Value { Local { [ Norm[f_ref[]-{uRef}] ]; In Omega; Jacobian JVol; }}}
+ EndIf
+ }
+ }
+
+// SUBDOMAIN SOLVER
+
+For i0 In {0:#ListOfSubdom()-1}
+iDom = ListOfSubdom(i0);
+ { Name PostProVol~{iDom}; NameOfFormulation FormVol~{iDom};
+ PostQuantity {
+ { Name uNum~{iDom}; Value { Local { [ {u~{iDom}} ]; In Omega~{iDom}; Jacobian JVol; }}}
+ If(FLAG_ERROR != ERROR_NO)
+ { Name uRef~{iDom}; Value { Local { [ f_refErr[] ]; In Omega~{iDom}; Jacobian JVol; }}}
+ { Name uErr~{iDom}; Value { Local { [ Norm[f_refErr[]-{u~{iDom}}]^2 ]; In Omega~{iDom}; Jacobian JVol; }}}
+ EndIf
+ }
+ }
+EndFor
+
+// INTERFACE CONDITION
+
+For i0 In {0:#ListOfSubdom()-1}
+iDom = ListOfSubdom(i0);
+For i1 In {0:#ListOfEdgesWithTBC~{iDom}()-1}
+iEdge = ListOfEdgesWithTBC~{iDom}(i1);
+iEdgeSide~{0} = (iEdge+3)%4;
+iEdgeSide~{1} = (iEdge+1)%4;
+ { Name PostProSur~{iDom}~{iEdge}; NameOfFormulation FormSur~{iDom}~{iEdge};
+ PostQuantity {
+ { Name g_out~{iDom}~{iEdge}; Value { Local { [ {g_out~{iDom}~{iEdge}} ]; In Sigma~{iDom}~{iEdge}; Jacobian JSur; }}}
+ For iSide In {0:1}
+ If (CROSSPOINT_TREAT == CROSSPOINT_Full)
+ For i In {1:nPade~{iDom}~{iEdgeSide~{iSide}}}
+ { Name g_out~{i}~{iDom}~{iEdge}~{iSide}; Value { Local { [ {g_out~{i}~{iDom}~{iEdge}~{iSide}} ]; In SigmaSide~{iDom}~{iEdge}~{iSide}; Jacobian JLin; }}}
+ EndFor
+ EndIf
+ EndFor
+ }
+ }
+EndFor
+EndFor
+
+// STATS (subdomain)
+
+For i0 In {0:#ListOfSubdom()-1}
+iDom = ListOfSubdom(i0);
+ { Name PostProStat~{iDom}; NameOfFormulation FormVol~{iDom};
+ PostQuantity {
+ If(FLAG_ERROR != ERROR_NO)
+ { Name energy2~{iDom}; Value { Integral { [ Norm[f_refErr[]]^2 ]; In Omega~{iDom}; Jacobian JVol; Integration I1; }}}
+ { Name error2~{iDom}; Value { Integral { [ Norm[f_refErr[]-{u~{iDom}}]^2 ]; In Omega~{iDom}; Jacobian JVol; Integration I1; }}}
+ EndIf
+ }
+ }
+EndFor
+
+// STATS (global)
+
+If (MPI_Rank == 0)
+ { Name PostProStat; NameOfFormulation FormVol~{0};
+ PostQuantity {
+ If(FLAG_ERROR != ERROR_NO)
+ { Name energAbs; Value { Term { Type Global; [Sqrt[$energy2Var]] ; In Omega~{0}; Jacobian JVol; }}}
+ { Name errorAbs; Value { Term { Type Global; [Sqrt[$error2Var]] ; In Omega~{0}; Jacobian JVol; }}}
+ { Name errorRel; Value { Term { Type Global; [Sqrt[$error2Var/$energy2Var]] ; In Omega~{0}; Jacobian JVol; }}}
+ EndIf
+ { Name numIter; Value { Term { Type Global; [$NumIter]; In Omega~{0}; Jacobian JVol; }}}
+ { Name residual; Value { Term { Type Global; [$ResidualFinal]; In Omega~{0}; Jacobian JVol; }}}
+ }
+ }
+EndIf
+}
+
+// ====================================================================================================
+// POST-OPERATIONS
+// ====================================================================================================
+
+PostOperation {
+
+// REFERENCE SOLVER
+
+ { Name PostOpRef; NameOfPostProcessing PostProRef;
+ Operation {
+// Print [uNumREF, OnElementsOf Omega, StoreInField (FIELD_REF), AtGaussPoints NumGaussPointsTRI ];
+ Print [uNumREF, OnElementsOf Omega, StoreInField (FIELD_REF)];
+// Print [uNumREF, OnElementsOf Omega, File StrCat(DIR, "uNumREF.pos") ];
+// Print [cNumREF, OnElementsOf Omega, File StrCat(DIR, "cNumREF.pos") ];
+// If((FLAG_PBM == PBM_SCATT_CIRC) || (FLAG_PBM == PBM_SCATT_RECT))
+// Print [uRefREF, OnElementsOf Omega, File StrCat(DIR, "uRef.pos") ];
+// Print [uErrREF, OnElementsOf Omega, File StrCat(DIR, "uErr.pos") ];
+// EndIf
+ }
+ }
+
+// SUB-DOMAIN SOLVER
+
+For i0 In {0:#ListOfSubdom()-1}
+iDom = ListOfSubdom(i0);
+ { Name PostOpVol~{iDom}; NameOfPostProcessing PostProVol~{iDom};
+ Operation {
+ Print [uNum~{iDom}, OnElementsOf Omega~{iDom}, File StrCat(DIR, Sprintf("uNum_%g.pos", iDom))];
+ If(FLAG_ERROR != ERROR_NO)
+ Print [uRef~{iDom}, OnElementsOf Omega~{iDom}, File StrCat(DIR, Sprintf("uRef_%g.pos", iDom))];
+ Print [uErr~{iDom}, OnElementsOf Omega~{iDom}, File StrCat(DIR, Sprintf("uErr_%g.pos", iDom))];
+ EndIf
+ }
+ }
+EndFor
+
+// INTERFACE CONDITION
+
+For i0 In {0:#ListOfSubdom()-1}
+iDom = ListOfSubdom(i0);
+For i1 In {0:#ListOfEdgesWithTBC~{iDom}()-1}
+iEdge = ListOfEdgesWithTBC~{iDom}(i1);
+iEdgeSide~{0} = (iEdge+3)%4;
+iEdgeSide~{1} = (iEdge+1)%4;
+ { Name PostOpSur~{iDom}~{iEdge}; NameOfPostProcessing PostProSur~{iDom}~{iEdge};
+ Operation {
+ Print [ g_out~{iDom}~{iEdge}, OnElementsOf Sigma~{iDom}~{iEdge}, StoreInField (FIELD~{iDom}~{iEdge}), AtGaussPoints NumGaussPointsLIN ];
+ For iSide In {0:1}
+ If (CROSSPOINT_TREAT == CROSSPOINT_Full)
+ For i In {1:nPade~{iDom}~{iEdgeSide~{iSide}}}
+ Print [ g_out~{i}~{iDom}~{iEdge}~{iSide}, OnElementsOf SigmaSide~{iDom}~{iEdge}~{iSide}, StoreInField (FIELD~{i}~{iDom}~{iEdge}~{iSide}), AtGaussPoints NumGaussPointsPNT ];
+ EndFor
+ EndIf
+ EndFor
+ }
+ }
+EndFor
+EndFor
+
+// STATS (subdomain)
+
+For i0 In {0:#ListOfSubdom()-1}
+iDom = ListOfSubdom(i0);
+ { Name PostOpStat~{iDom}; NameOfPostProcessing PostProStat~{iDom};
+ Operation {
+ If(FLAG_ERROR != ERROR_NO)
+ Print [energy2~{iDom}[Omega~{iDom}], OnRegion Omega~{iDom}, Format Table, StoreInVariable $energy2Var~{iDom}];
+ Print [error2~{iDom}[Omega~{iDom}], OnRegion Omega~{iDom}, Format Table, StoreInVariable $error2Var~{iDom}];
+ EndIf
+ }
+ }
+EndFor
+
+// STATS (global)
+
+If (MPI_Rank == 0)
+ { Name PostOpStat; NameOfPostProcessing PostProStat;
+ Operation {
+ tmp0 = Sprintf("out/STAT_energAbs_%g_%g_%g_%g_%g_%g.dat", FLAG_PBM, N_DOM, nPadeABC, thetaPadeInputABC, nPadeTBC, CROSSPOINT_TREAT);
+ tmp1 = Sprintf("out/STAT_errorAbs_%g_%g_%g_%g_%g_%g.dat", FLAG_PBM, N_DOM, nPadeABC, thetaPadeInputABC, nPadeTBC, CROSSPOINT_TREAT);
+ tmp2 = Sprintf("out/STAT_errorRel_%g_%g_%g_%g_%g_%g.dat", FLAG_PBM, N_DOM, nPadeABC, thetaPadeInputABC, nPadeTBC, CROSSPOINT_TREAT);
+ tmp3 = Sprintf("out/STAT_numIter_%g_%g_%g_%g_%g_%g.dat", FLAG_PBM, N_DOM, nPadeABC, thetaPadeInputABC, nPadeTBC, CROSSPOINT_TREAT);
+ tmp4 = Sprintf("out/STAT_residualFinal_%g_%g_%g_%g_%g_%g.dat", FLAG_PBM, N_DOM, nPadeABC, thetaPadeInputABC, nPadeTBC, CROSSPOINT_TREAT);
+ If(FLAG_ERROR != ERROR_NO)
+ Print [energAbs, OnRegion Omega~{0}, SendToServer "Output/1energAbs", Format Table, File > tmp0];
+ Print [errorAbs, OnRegion Omega~{0}, SendToServer "Output/2errorAbs", Format Table, File > tmp1];
+ Print [errorRel, OnRegion Omega~{0}, SendToServer "Output/3errorRel", Format Table, File > tmp2];
+ EndIf
+ Print [numIter, OnRegion Omega~{0}, SendToServer "Output/4Num iterations", Format Table, File > tmp3];
+ Print [residual, OnRegion Omega~{0}, SendToServer "Output/5Residual", Format Table, File > tmp4];
+ }
+ }
+EndIf
+}
+
+// ====================================================================================================
+
+DefineConstant[
+ R_ = {"ResoDDM", Choices {"ResoRef", "ResoDDM"}, Name "GetDP/1ResolutionChoices", Visible 1},
+ C_ = {"-solve -v 3 -bin -v2 -ksp_monitor", Name "GetDP/9ComputeCommand", Visible 0}
+ P_ = {"", Name "GetDP/2PostOperationChoices", Visible 1}
+];
diff --git a/HelmholtzDDMwithCrosspoints/main.dat b/HelmholtzDDMwithCrosspoints/main.dat
new file mode 100644
index 0000000..9fad56e
--- /dev/null
+++ b/HelmholtzDDMwithCrosspoints/main.dat
@@ -0,0 +1,45 @@
+DefineConstant[
+ MSH_BASE_NAME = "mesh",
+ DIR = "out/"
+];
+MSH_NAME = StrCat(DIR, MSH_BASE_NAME);
+
+// =================================================================================================
+// SPECIFIC PROBLEM
+// =================================================================================================
+
+PBM_SCATT_CIRC = 1;
+PBM_SCATT_RECT = 2;
+PBM_MARMOUSI = 3;
+
+DefineConstant[
+ FLAG_PBM = {PBM_SCATT_RECT, Name "Input/01Benchmark", Highlight "Blue",
+ GmshOption "Reset", Autocheck 0,
+ Choices {PBM_SCATT_CIRC = "Scattering in circular domain",
+ PBM_SCATT_RECT = "Scattering in rectangular domain",
+ PBM_MARMOUSI = "Benchmark Marmousi"} }
+];
+
+If (FLAG_PBM == PBM_SCATT_CIRC)
+ LinkGeo = "circularDom.geo";
+ LinkPro = "circularDom.pro";
+EndIf
+If ((FLAG_PBM == PBM_SCATT_RECT) || (FLAG_PBM == PBM_MARMOUSI))
+ LinkGeo = "rectangularDom.geo";
+ LinkPro = "rectangularDom.pro";
+EndIf
+LinkDDM = "ddmHelmholtzCrossPoints.pro";
+
+ERROR_NO = 0;
+ERROR_ANA = 1;
+ERROR_NUM = 2;
+
+DefineConstant[
+ FLAG_ERROR = {ERROR_NUM, Name "Input/02Error", Autocheck 1,
+ Choices {ERROR_NO = "No",
+ ERROR_ANA = "... vs analytic reference",
+ ERROR_NUM = "... vs numerical reference"} },
+ ORDER = {1,
+ Name "Input/05Polynomial order",
+ Choices {1 = "First-order", 2 = "Second-order"}}
+];
diff --git a/HelmholtzDDMwithCrosspoints/main.geo b/HelmholtzDDMwithCrosspoints/main.geo
new file mode 100644
index 0000000..51284d0
--- /dev/null
+++ b/HelmholtzDDMwithCrosspoints/main.geo
@@ -0,0 +1,11 @@
+Include "main.dat" ;
+
+CreateDir Str(DIR);
+
+Solver.AutoMesh = -1;
+
+SetOrder ORDER;
+Mesh.ElementOrder = ORDER;
+Mesh.SecondOrderLinear = 0;
+
+Include Str[LinkGeo];
diff --git a/HelmholtzDDMwithCrosspoints/main.pro b/HelmholtzDDMwithCrosspoints/main.pro
new file mode 100644
index 0000000..cdba1db
--- /dev/null
+++ b/HelmholtzDDMwithCrosspoints/main.pro
@@ -0,0 +1,68 @@
+Include "main.dat" ;
+
+// =================================================================================================
+// GENERAL OPTIONS
+// =================================================================================================
+
+DefineConstant[
+ SOLVER = {"gmres", Choices {"gmres", "fgmres", "bcgs", "print", "jacobi"},
+ Name "Iterative Solver/0Solver"},
+ TOLlog10 = {-6, Max -1, Min -16, Step -1,
+ Name "Iterative Solver/1Tolerance (log10)"},
+ TOL = 10^(TOLlog10),
+ MAXIT = {500, Min 1, Step 1, Max 100000,
+ Name "Iterative Solver/2Max. iterations"},
+ RESTART_MAXIT = {0, Choices {0,1}, Visible 0,
+ Name "Iterative Solver/31Force Restart = Max. iterations"},
+ RESTART = {RESTART_MAXIT ? MAXIT : MAXIT, Min 0, Max 100000, Step 1, Visible 0,
+ Name "Iterative Solver/30Restart", ReadOnly RESTART_MAXIT }
+];
+
+If(RESTART > MAXIT || RESTART == 0)
+ RESTART = MAXIT;
+EndIf
+
+// =================================================================================================
+// JACOBIAN & INTEGRATION
+// =================================================================================================
+
+Jacobian {
+ { Name JVol; Case {{ Region All; Jacobian Vol; }}}
+ { Name JSur; Case {{ Region All; Jacobian Sur; }}}
+ { Name JLin; Case {{ Region All; Jacobian Lin; }}}
+}
+
+If (ORDER==1)
+ NumGaussPointsPNT = 1;
+ NumGaussPointsLIN = 4; // NumberOfPoints
+ NumGaussPointsTRI = 6; // NumberOfPoints
+EndIf
+If (ORDER==2)
+ NumGaussPointsPNT = 1;
+ NumGaussPointsLIN = 6; // NumberOfPoints
+ NumGaussPointsTRI = 12; // NumberOfPoints
+EndIf
+
+Integration {
+ { Name I1;
+ Case {
+ { Type Gauss;
+ Case {
+ { GeoElement Point; NumberOfPoints NumGaussPointsPNT; }
+ { GeoElement Line; NumberOfPoints NumGaussPointsLIN; }
+ { GeoElement Line2; NumberOfPoints NumGaussPointsLIN; }
+ { GeoElement Triangle; NumberOfPoints NumGaussPointsTRI; }
+ { GeoElement Triangle2; NumberOfPoints NumGaussPointsTRI; } // 1 3 4 6 7 12 13 16
+ { GeoElement Quadrangle; NumberOfPoints 7; }
+ }
+ }
+ }
+ }
+}
+
+// =================================================================================================
+// SPECIFIC
+// =================================================================================================
+
+Include Str[LinkPro];
+Include Str[LinkDDM];
diff --git a/HelmholtzDDMwithCrosspoints/rectangularDom.dat b/HelmholtzDDMwithCrosspoints/rectangularDom.dat
new file mode 100644
index 0000000..096e812
--- /dev/null
+++ b/HelmholtzDDMwithCrosspoints/rectangularDom.dat
@@ -0,0 +1,97 @@
+// =================================================================================================
+
+// Geometry: Scattering case
+If(FLAG_PBM == PBM_SCATT_RECT)
+
+// Subdomains
+DefineConstant[
+ Lx = {7.5, Min 0.01, Max 20, Step 0.01, Name "Input/1Model/40Domain length (Lx)"},
+ Ly = {7.5, Min 0.01, Max 20, Step 0.01, Name "Input/1Model/41Domain length (Ly)"},
+ X_SCA = { 1.25, Min -10, Max 10, Step 0.01, Name "Input/1Model/42Scatterer position (x)"},
+ Y_SCA = { 1.25, Min -10, Max 10, Step 0.01, Name "Input/1Model/43Scatterer position (y)"},
+ R_SCA = { 1., Min 0.01, Max 20, Step 0.01, Name "Input/1Model/44Scatterer radius"},
+ Nx_DOM = {3, Min 1, Max 10, Step 1, Name "Input/1Model/50Nx subdomains"},
+ Ny_DOM = {3, Min 1, Max 10, Step 1, Name "Input/1Model/51Ny subdomains"},
+ TWIST = {0, Min 0, Max 1.5, Step 0.5, Name "Input/1Model/52 TWIST"}
+];
+
+ X0_DOM = -X_SCA;
+ Y0_DOM = -Y_SCA;
+// X0_DOM = -Lx/Nx_DOM/2.;
+// Y0_DOM = -Ly/Ny_DOM/2.;
+
+DefineConstant[
+// LAMBDA = {0.5, Min 0.1, Max 30, Step 0.1, Name "Input/03Wavelength"},
+ WAVENUMBER = {4*Pi, Min 1, Max 24, Step 1, Name "Input/03Wavenumber"},
+ N_LAMBDA = {10, Min 5, Max 30, Step 1, Name "Input/04Points per wavelength"}
+];
+
+ //WAVENUMBER = (2*Pi)/LAMBDA;
+ LAMBDA = (2*Pi)/WAVENUMBER;
+ FREQ = WAVENUMBER/(2*Pi);
+ LC = LAMBDA/N_LAMBDA;
+EndIf
+
+// =================================================================================================
+
+// Geometry: Marmousi case
+If(FLAG_PBM == PBM_MARMOUSI)
+
+// Subdomains
+DefineConstant[
+ Nx_DOM = {15, Min 1, Max 10, Step 1, Name "Input/1Model/50Nx subdomains"},
+ Ny_DOM = {4, Min 1, Max 10, Step 1, Name "Input/1Model/51Ny subdomains"}
+];
+ TWIST = 0;
+
+ Lx = 9192.;
+ Ly = 2904.;
+ X0_DOM = 0.;
+ Y0_DOM = -Ly;
+ R_SCA = 1000;
+
+ X_SOU = 4585.;
+ Y_SOU = -10.;
+ Lx_SDOM = Lx/Nx_DOM;
+ Ly_SDOM = Ly/Ny_DOM;
+ I_SOU = Ceil[(X_SOU-X0_DOM)/Lx_SDOM]-1;
+ J_SOU = Ceil[(Y_SOU-Y0_DOM)/Ly_SDOM]-1;
+ Idom_SOU = J_SOU*Nx_DOM + I_SOU;
+ //Printf("I_SOU: %g",I_SOU);
+ //Printf("J_SOU: %g",J_SOU);
+ //Printf("Idom_SOU: %g",Idom_SOU);
+
+DefineConstant[
+ FREQ = {10, Min 0.1, Max 30, Step 0.1, Name "Input/03Frequency"}, //10
+ N_LAMBDA = {5, Name "Input/04Points per wavelength"} //10
+];
+
+ // meshing for shortest wavelength
+ cMin = 1500.;
+ WAVENUMBER = 2*Pi*FREQ/cMin;
+ LAMBDA = 2*Pi/WAVENUMBER ;
+ LC = LAMBDA/N_LAMBDA;
+EndIf
+
+// =================================================================================================
+
+N_DOM = Nx_DOM*Ny_DOM;
+
+// =================================================================================================
+
+If(FLAG_PBM == PBM_SCATT_RECT)
+ TAG_SCA = 1000;
+EndIf
+If(FLAG_PBM == PBM_MARMOUSI)
+ TAG_SOU = 1000;
+EndIf
+
+For iDom In {0:N_DOM-1}
+ TAG_DOM~{iDom} = 2000 + iDom;
+For iEdge In {0:3}
+ TAG_BND~{iDom}~{iEdge} = 3000 + 4*iDom + iEdge;
+EndFor
+For iCorner In {0:3}
+ TAG_CRN~{iDom}~{iCorner} = 4000 + 4*iDom + iCorner;
+EndFor
+EndFor
diff --git a/HelmholtzDDMwithCrosspoints/rectangularDom.geo b/HelmholtzDDMwithCrosspoints/rectangularDom.geo
new file mode 100644
index 0000000..75c65bf
--- /dev/null
+++ b/HelmholtzDDMwithCrosspoints/rectangularDom.geo
@@ -0,0 +1,161 @@
+Include "rectangularDom.dat";
+
+Mesh.CharacteristicLengthMin = LC;
+Mesh.CharacteristicLengthMax = LC;
+
+// =================================================================================================
+// Build SCATTERER or SOURCE
+// =================================================================================================
+
+If(FLAG_PBM == PBM_SCATT_RECT)
+ p0 = newp; Point(p0) = { 0, 0, 0};
+ p1 = newp; Point(p1) = { R_SCA, 0, 0};
+ p2 = newp; Point(p2) = { 0, R_SCA, 0};
+ p3 = newp; Point(p3) = {-R_SCA, 0, 0};
+ p4 = newp; Point(p4) = { 0,-R_SCA, 0};
+ c1 = newl; Circle(c1) = {p1, p0, p2};
+ c2 = newl; Circle(c2) = {p2, p0, p3};
+ c3 = newl; Circle(c3) = {p3, p0, p4};
+ c4 = newl; Circle(c4) = {p4, p0, p1};
+ llSca = newll; Line loop(llSca) = {-c1, -c2, -c3, -c4};
+EndIf
+
+If(FLAG_PBM == PBM_MARMOUSI)
+ p0 = newp; Point(p0) = {X_SOU, Y_SOU, 0};
+ Physical Point(TAG_SOU) = p0;
+EndIf
+
+// =================================================================================================
+// Build POINTS, STRAIGHT LINES, RECTANGLES
+// =================================================================================================
+
+For i In {0:Nx_DOM}
+For j In {0:Ny_DOM}
+ p~{i}~{j} = newp;
+ If((i == 1) && (j == 1))
+ xAdd = TWIST;
+ yAdd = 0;
+ ElseIf((i == 1) && (j == 2))
+ xAdd = 0;
+ yAdd = TWIST;
+ ElseIf((i == 2) && (j == 2))
+ xAdd = -TWIST;
+ yAdd = 0;
+ ElseIf((i == 2) && (j == 1))
+ xAdd = 0;
+ yAdd = -TWIST;
+ Else
+ xAdd = 0;
+ yAdd = 0;
+ EndIf
+ Point(p~{i}~{j}) = {X0_DOM + Lx*i/Nx_DOM + xAdd, Y0_DOM + Ly*j/Ny_DOM + yAdd, 0};
+EndFor
+EndFor
+
+For i In {0:Nx_DOM}
+For j In {0:Ny_DOM}
+ If (i < Nx_DOM)
+ lx~{i}~{j} = newl;
+ Line(lx~{i}~{j}) = {p~{i}~{j}, p~{i+1}~{j}};
+ EndIf
+ If (j < Ny_DOM)
+ ly~{i}~{j} = newl;
+ Line(ly~{i}~{j}) = {p~{i}~{j}, p~{i}~{j+1}};
+ EndIf
+EndFor
+EndFor
+
+For i In {0:Nx_DOM-1}
+For j In {0:Ny_DOM-1}
+ ll~{i}~{j} = newll;
+ Line loop(ll~{i}~{j}) = {lx~{i}~{j}, ly~{i+1}~{j}, -lx~{i}~{j+1}, -ly~{i}~{j}};
+ s~{i}~{j} = news;
+ If ((i == 0) && (j == 0) && (FLAG_PBM == PBM_SCATT_RECT))
+ Plane Surface(s~{i}~{j}) = {ll~{i}~{j}, llSca};
+ Else
+ Plane Surface(s~{i}~{j}) = {ll~{i}~{j}};
+ EndIf
+ If (FLAG_PBM == PBM_MARMOUSI)
+ If ((i == I_SOU) && (j == J_SOU))
+ Point {p0} In Surface {s~{i}~{j}};
+ EndIf
+ EndIf
+EndFor
+EndFor
+
+// =================================================================================================
+// Generate MESH for each subdomain and reference domain
+// =================================================================================================
+
+If(StrCmp(OnelabAction, "check"))
+ Mesh 2;
+EndIf
+
+For i In {0:Nx_DOM-1}
+For j In {0:Ny_DOM-1}
+ idom = j*Nx_DOM + i;
+ Delete Physicals;
+
+ Physical Point(TAG_CRN~{idom}~{0}) = p~{i}~{j};
+ Physical Point(TAG_CRN~{idom}~{1}) = p~{i+1}~{j};
+ Physical Point(TAG_CRN~{idom}~{2}) = p~{i+1}~{j+1};
+ Physical Point(TAG_CRN~{idom}~{3}) = p~{i}~{j+1};
+ Physical Line(TAG_BND~{idom}~{0}) = lx~{i}~{j};
+ Physical Line(TAG_BND~{idom}~{1}) = ly~{i+1}~{j};
+ Physical Line(TAG_BND~{idom}~{2}) = lx~{i}~{j+1};
+ Physical Line(TAG_BND~{idom}~{3}) = ly~{i}~{j};
+ Physical Surface(TAG_DOM~{idom}) = s~{i}~{j};
+
+ If((i == 0) && (j == 0) && (FLAG_PBM == PBM_SCATT_RECT))
+ Physical Line(TAG_SCA) = {-c1, -c2, -c3, -c4};
+ EndIf
+ If(FLAG_PBM == PBM_MARMOUSI)
+ If((i == I_SOU) && (j == J_SOU))
+ Physical Point(TAG_SOU) = p0;
+ EndIf
+ EndIf
+
+ Printf("Saving subdomain %g...", idom);
+ Save StrCat(MSH_NAME, Sprintf("_%g.msh", idom));
+ Printf("Done.");
+EndFor
+EndFor
+
+Delete Physicals;
+
+If(FLAG_PBM == PBM_SCATT_RECT)
+ Physical Line(TAG_SCA) = {-c1, -c2, -c3, -c4};
+EndIf
+If(FLAG_PBM == PBM_MARMOUSI)
+ Physical Point(TAG_SOU) = p0;
+EndIf
+
+For i In {0:Nx_DOM-1}
+For j In {0:Ny_DOM-1}
+ idom = j*Nx_DOM + i;
+ Physical Surface(TAG_DOM~{idom}) = s~{i}~{j};
+
+ If(j == 0)
+ Physical Line(TAG_BND~{idom}~{0}) = lx~{i}~{j};
+ EndIf
+ If(i == Nx_DOM-1)
+ Physical Line(TAG_BND~{idom}~{1}) = ly~{i+1}~{j};
+ EndIf
+ If(j == Ny_DOM-1)
+ Physical Line(TAG_BND~{idom}~{2}) = lx~{i}~{j+1};
+ EndIf
+ If(i == 0)
+ Physical Line(TAG_BND~{idom}~{3}) = ly~{i}~{j};
+ EndIf
+
+EndFor
+EndFor
+
+Physical Point(TAG_CRN~{ 0*Nx_DOM + 0 }~{0}) = p~{0 }~{0 };
+Physical Point(TAG_CRN~{ 0*Nx_DOM + (Nx_DOM-1) }~{1}) = p~{Nx_DOM}~{0 };
+Physical Point(TAG_CRN~{ (Ny_DOM-1)*Nx_DOM + (Nx_DOM-1) }~{2}) = p~{Nx_DOM}~{Ny_DOM};
+Physical Point(TAG_CRN~{ (Ny_DOM-1)*Nx_DOM + 0 }~{3}) = p~{0 }~{Ny_DOM};
+
+Printf("Saving domain ...");
+Save StrCat(MSH_NAME, Sprintf(".msh"));
+Printf("Done.");
diff --git a/HelmholtzDDMwithCrosspoints/rectangularDom.pro b/HelmholtzDDMwithCrosspoints/rectangularDom.pro
new file mode 100644
index 0000000..872f10c
--- /dev/null
+++ b/HelmholtzDDMwithCrosspoints/rectangularDom.pro
@@ -0,0 +1,222 @@
+Include "rectangularDom.dat";
+
+// =================================================================================================
+// FUNCTIONS
+// =================================================================================================
+
+Function{
+ If (FLAG_PBM == PBM_SCATT_RECT)
+ f_inc[] = Complex[Cos[WAVENUMBER*X[]], Sin[WAVENUMBER*X[]]];
+ f_ref[] = AcousticFieldSoftCylinder[XYZ[]]{WAVENUMBER, R_SCA};
+ f_dir[] = -f_inc[];
+ EndIf
+ If (FLAG_PBM == PBM_MARMOUSI)
+ f_inc[] = 0;
+ f_ref[] = 0;
+ velocityField[] = InterpolationBilinear[ $1, $2 ]{ ListFromFile["rectangularDomMarmousi.dat"] };
+ cData[] = velocityField[ X[], Y[] ];
+ f_dir[] = -f_inc[];
+ f_sou = 1;
+ For iDom In {0:N_DOM-1}
+ f_sou~{iDom} = 1;
+ EndFor
+ EndIf
+}
+
+// =================================================================================================
+// LISTS ABC/TBC
+// =================================================================================================
+
+// Is there an ABC for main domain? (1=yes, 0=no)
+isEdgeABC~{0} = 1;
+isEdgeABC~{1} = 1;
+isEdgeABC~{2} = 1;
+isEdgeABC~{3} = 1;
+isEdgeRad~{0} = 0;
+isEdgeRad~{1} = 0;
+isEdgeRad~{2} = 0;
+isEdgeRad~{3} = 0;
+
+ListOfSubdom = {};
+For xdom In {0:Nx_DOM-1}
+For ydom In {0:Ny_DOM-1}
+ iDom = ydom*Nx_DOM + xdom;
+
+If (iDom % MPI_Size == MPI_Rank)
+ ListOfSubdom += iDom;
+EndIf
+
+ iDomNeigh~{iDom}~{0} = (ydom-1)*Nx_DOM + xdom; // Down
+ iDomNeigh~{iDom}~{1} = ydom*Nx_DOM + (xdom+1); // Right
+ iDomNeigh~{iDom}~{2} = (ydom+1)*Nx_DOM + xdom; // Top
+ iDomNeigh~{iDom}~{3} = ydom*Nx_DOM + (xdom-1); // Left
+ iEdgeNeigh~{iDom}~{0} = 2;
+ iEdgeNeigh~{iDom}~{1} = 3;
+ iEdgeNeigh~{iDom}~{2} = 0;
+ iEdgeNeigh~{iDom}~{3} = 1;
+
+ // Is there an ABC or TBC? (1=yes, 0=no)
+ For iEdge In {0:3}
+ isEdgeABC~{iDom}~{iEdge} = 0;
+ isEdgeTBC~{iDom}~{iEdge} = 1;
+ isEdgeRad~{iDom}~{iEdge} = 0;
+ EndFor
+ If(ydom == 0)
+ isEdgeABC~{iDom}~{0} = 1;
+ isEdgeTBC~{iDom}~{0} = 0;
+ EndIf
+ If(xdom == Nx_DOM-1)
+ isEdgeABC~{iDom}~{1} = 1;
+ isEdgeTBC~{iDom}~{1} = 0;
+ EndIf
+ If(ydom == Ny_DOM-1)
+ isEdgeABC~{iDom}~{2} = 1;
+ isEdgeTBC~{iDom}~{2} = 0;
+ EndIf
+ If(xdom == 0)
+ isEdgeABC~{iDom}~{3} = 1;
+ isEdgeTBC~{iDom}~{3} = 0;
+ EndIf
+
+ // List of Edges for Absorbing/Transmission Boundary Condition
+ ListOfEdgesWithABC~{iDom} = {};
+ ListOfEdgesWithTBC~{iDom} = {};
+ For iEdge In {0:3}
+ If(isEdgeABC~{iDom}~{iEdge} == 1)
+ ListOfEdgesWithABC~{iDom} += iEdge;
+ EndIf
+ If(isEdgeTBC~{iDom}~{iEdge} == 1)
+ ListOfEdgesWithTBC~{iDom} += iEdge;
+ EndIf
+ EndFor
+
+EndFor
+EndFor
+
+// =================================================================================================
+// GROUPS
+// =================================================================================================
+
+Group {
+
+// === REFERENCE CASE ===
+
+ // DOMAIN
+ Omega = Region[{}];
+
+ // SOURCE
+ GammaPoint = Region[{}];
+
+ // BOUNDARY (Dirichlet BC)
+ GammaD0 = Region[{}];
+ GammaN0 = Region[{}];
+ GammaD = Region[{}];
+ GammaN = Region[{}];
+
+ // BOUNDARY (Absorbing BC)
+ For iEdge In {0:3}
+ SigmaMain~{iEdge} = Region[{}];
+ SigmaMainSide~{iEdge}~{0} = Region[{}];
+ SigmaMainSide~{iEdge}~{1} = Region[{}];
+ EndFor
+ SigmaMain = Region[{}];
+
+ // CORNER (Absorbing BC)
+ CornerMain~{0} = Region[{TAG_CRN~{ 0*Nx_DOM + 0 }~{0}}];
+ CornerMain~{1} = Region[{TAG_CRN~{ 0*Nx_DOM + (Nx_DOM-1) }~{1}}];
+ CornerMain~{2} = Region[{TAG_CRN~{ (Ny_DOM-1)*Nx_DOM + (Nx_DOM-1) }~{2}}];
+ CornerMain~{3} = Region[{TAG_CRN~{ (Ny_DOM-1)*Nx_DOM + 0 }~{3}}];
+ CornerMain = Region[{ CornerMain~{0}, CornerMain~{1}, CornerMain~{2}, CornerMain~{3}}];
+
+ If(FLAG_PBM == PBM_SCATT_RECT)
+ GammaD += Region[{TAG_SCA}];
+ EndIf
+
+ If(FLAG_PBM == PBM_MARMOUSI)
+ GammaPoint += Region[{TAG_SOU}];
+ EndIf
+
+For xdom In {0:Nx_DOM-1}
+For ydom In {0:Ny_DOM-1}
+ iDom = ydom*Nx_DOM + xdom;
+
+ // DOMAIN
+ Omega += Region[TAG_DOM~{iDom}];
+
+ // BOUNDARY (Absorbing BC)
+ For iEdge In {0:3}
+ If(ydom == 0)
+ SigmaMain~{0} += Region[{TAG_BND~{iDom}~{0}}];
+ SigmaMain += Region[{TAG_BND~{iDom}~{0}}];
+ EndIf
+ If(xdom == Nx_DOM-1)
+ SigmaMain~{1} += Region[{TAG_BND~{iDom}~{1}}];
+ SigmaMain += Region[{TAG_BND~{iDom}~{1}}];
+ EndIf
+ If(ydom == Ny_DOM-1)
+ SigmaMain~{2} += Region[{TAG_BND~{iDom}~{2}}];
+ SigmaMain += Region[{TAG_BND~{iDom}~{2}}];
+ EndIf
+ If(xdom == 0)
+ SigmaMain~{3} += Region[{TAG_BND~{iDom}~{3}}];
+ SigmaMain += Region[{TAG_BND~{iDom}~{3}}];
+ EndIf
+ EndFor
+EndFor
+EndFor
+
+ For iEdge In {0:3}
+ iCornerSide1 = iEdge;
+ iCornerSide2 = (iEdge+1)%4;
+ SigmaMainSide~{iEdge}~{0} = Region[{CornerMain~{iCornerSide1}}];
+ SigmaMainSide~{iEdge}~{1} = Region[{CornerMain~{iCornerSide2}}];
+ EndFor
+
+// === DDM CASE ===
+
+For i0 In {0:#ListOfSubdom()-1}
+iDom = ListOfSubdom(i0);
+
+ // DOMAIN
+ Omega~{iDom} = Region[TAG_DOM~{iDom}];
+
+ // SOURCE
+ GammaPoint~{iDom} = Region[{}];
+ If(FLAG_PBM == PBM_MARMOUSI)
+ If(iDom == Idom_SOU)
+ GammaPoint~{iDom} += Region[{TAG_SOU}];
+ EndIf
+ EndIf
+
+ // BOUNDARY (Dirichlet/Neumann BC)
+ GammaD0~{iDom} = Region[{}];
+ GammaN0~{iDom} = Region[{}];
+ GammaD~{iDom} = Region[{}];
+ GammaN~{iDom} = Region[{}];
+ If((FLAG_PBM == PBM_SCATT_RECT) && (iDom == 0))
+ GammaD~{iDom} = Region[{TAG_SCA}];
+ EndIf
+ TrOmegaGammaD~{iDom} = ElementsOf[ Omega~{iDom}, OnOneSideOf GammaD~{iDom} ];
+
+ // BOUNDARY (Absorbing BC + Transmission BC)
+ For iEdge In {0:3}
+ iCornerSide1 = iEdge;
+ iCornerSide2 = (iEdge+1)%4;
+ Sigma~{iDom}~{iEdge} = Region[{TAG_BND~{iDom}~{iEdge}}];
+ SigmaSide~{iDom}~{iEdge}~{0} = Region[{TAG_CRN~{iDom}~{iCornerSide1}}];
+ SigmaSide~{iDom}~{iEdge}~{1} = Region[{TAG_CRN~{iDom}~{iCornerSide2}}];
+ GammaD~{iDom}~{iEdge} = Region[{}];
+ GammaD0~{iDom}~{iEdge} = Region[{}];
+ GammaN~{iDom}~{iEdge} = Region[{}];
+ GammaN0~{iDom}~{iEdge} = Region[{}];
+ EndFor
+ Sigma~{iDom} = Region[{ Sigma~{iDom}~{0}, Sigma~{iDom}~{1}, Sigma~{iDom}~{2}, Sigma~{iDom}~{3} }];
+
+ // CORNER (Absorbing BC + Transmission BC)
+ For iCorner In {0:3}
+ Corner~{iDom}~{iCorner} = Region[{TAG_CRN~{iDom}~{iCorner}}];
+ EndFor
+ Corner~{iDom} = Region[{ Corner~{iDom}~{0}, Corner~{iDom}~{1}, Corner~{iDom}~{2}, Corner~{iDom}~{3} }];
+
+EndFor
+}
diff --git a/HelmholtzDDMwithCrosspoints/rectangularDomMarmousi.dat b/HelmholtzDDMwithCrosspoints/rectangularDomMarmousi.dat
new file mode 100644
index 0000000..1a104c8
--- /dev/null
+++ b/HelmholtzDDMwithCrosspoints/rectangularDomMarmousi.dat
@@ -0,0 +1,125 @@
+384 122
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diff --git a/HelmholtzDDMwithCrosspoints/rectangularDomMarmousiGmsh.dat b/HelmholtzDDMwithCrosspoints/rectangularDomMarmousiGmsh.dat
new file mode 100644
index 0000000..cd14c96
--- /dev/null
+++ b/HelmholtzDDMwithCrosspoints/rectangularDomMarmousiGmsh.dat
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--
GitLab