diff --git a/AcousticScattering/.gitignore b/AcousticScattering/.gitignore
new file mode 100644
index 0000000000000000000000000000000000000000..547656a59b8d2e8b9c682a94e237906e5f0cd737
--- /dev/null
+++ b/AcousticScattering/.gitignore
@@ -0,0 +1,4 @@
+*.pos
+*.msh
+*.pre
+*.db
diff --git a/DDM-Corner-Helmholtz-2D/.gitignore b/DDM-Corner-Helmholtz-2D/.gitignore
new file mode 100644
index 0000000000000000000000000000000000000000..f32b9714f07d0b0b900e6304842f231485b3596f
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/.gitignore
@@ -0,0 +1,6 @@
+*.pos
+*.msh
+*.pre
+*.db
+out_ABC/**
+out_TC/**
\ No newline at end of file
diff --git a/DDM-Corner-Helmholtz-2D/ABC_norm.py b/DDM-Corner-Helmholtz-2D/ABC_norm.py
new file mode 100644
index 0000000000000000000000000000000000000000..cbcd96260fb3dbe1b1c8d7b0d35bccf65eb7aad6
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/ABC_norm.py
@@ -0,0 +1,48 @@
+import sys
+import os, os.path
+import numpy as np
+import subprocess
+import matplotlib.pyplot as plt
+
+def sumNorm(foldername, rootname):
+ # Find number of files
+ nfile = 0
+ for name in os.listdir(foldername):
+ if os.path.isfile(os.path.join(foldername, name)):
+ if rootname in name:
+ nfile += 1
+ print("Number of files : " + str(nfile))
+
+ normL2 =[]
+ for n in range(nfile):
+ norm = 0.
+ f = open(os.path.join(foldername, rootname +str(n)), "r")
+ for line in f:
+ if(len(line) != 1):
+ values = line.split()
+ norm += float(values[1])
+ f.close()
+ normL2.append(np.sqrt(norm))
+
+ print(normL2)
+ return(normL2)
+
+foldername = "out_ABC/"
+rootname = "ABC_DDM_normg.pos"
+NDom = 6
+MaxIt = 100
+
+subprocess.run(["rm", "-rf", foldername])
+subprocess.run(["gmsh", "ABC_main.geo", "-2"])
+subprocess.run(["getdp", "main.pro", "-solve", "DDM_1",
+ "-v", "3",
+ "-setstring", "PROBLEM", "Absorbing BC",
+ "-setstring", "SOLVER", "jacobi",
+ "-setstring", "ABC_DIRREL", foldername,
+ "-setnumber", "MAXIT", str(MaxIt),
+ "-setnumber", "Ndom", str(NDom)])
+
+errorL2 = sumNorm(foldername, rootname)
+
+plt.plot(errorL2)
+plt.show()
\ No newline at end of file
diff --git a/DDM-Corner-Helmholtz-2D/COPYING b/DDM-Corner-Helmholtz-2D/COPYING
new file mode 100644
index 0000000000000000000000000000000000000000..f288702d2fa16d3cdf0035b15a9fcbc552cd88e7
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/COPYING
@@ -0,0 +1,674 @@
+ GNU GENERAL PUBLIC LICENSE
+ Version 3, 29 June 2007
+
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+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
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+ 13. Use with the GNU Affero General Public License.
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+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+ To do so, attach the following notices to the program. It is safest
+to attach them to the start of each source file to most effectively
+state the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
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+ <one line to give the program's name and a brief idea of what it does.>
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+ (at your option) any later version.
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+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with this program. If not, see <https://www.gnu.org/licenses/>.
+
+Also add information on how to contact you by electronic and paper mail.
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+if any, to sign a "copyright disclaimer" for the program, if necessary.
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+
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+may consider it more useful to permit linking proprietary applications with
+the library. If this is what you want to do, use the GNU Lesser General
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+<https://www.gnu.org/licenses/why-not-lgpl.html>.
diff --git a/DDM-Corner-Helmholtz-2D/README.md b/DDM-Corner-Helmholtz-2D/README.md
new file mode 100644
index 0000000000000000000000000000000000000000..bb8f851773d688226ece49044574ba43da2087a1
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/README.md
@@ -0,0 +1,96 @@
+# ABC and Transmission CondtionCorner
+
+## Requierement
+
+Two open-source software are requiered to be installed:
+
+- [GMSH](https://gmsh.info), *latest automatic Gmsh snapshot* (Version > 4.5.6 (Not the 4.5.6))
+- [GetDP](http://getdp.info/) : Version >= 3.3.0
+
+GMSH is a mesh generator with post-processing facilities while GetDP is a finite element solver.
+
+## How to use
+
+Launch the script `main.pro` with GMSH, either through the GUI (Graphical User Interface) or from CLI (Command Line Interface):
+```bash
+gmsh main.pro
+```
+
+On the left-sided menu, choose the `Problem` ("Absorbing BC" or "Transmission Condition"), set the `Resolution` and the different parameters in the `Input` sub-menu and finally click on `Run`. A consol log can be show by clicking on the bottom line of the windows on the left part.
+
+> See the wiki for an animated summary!
+
+## Parameters and Options
+
+### ABC
+
+The script produces three functions:
+- `u`: Scattered field (not the total field!)
+- `uNorm`: Absolute value of the scattered field
+- `err`: Error (difference) between `u` and an analytic solution computed thanks to Mie Serie decomposition
+
+
+
+
+Here are the main options that can be tuned by the user:
+
+- `ABC`: Order of the condition (0 or 2) and the type of corner condition (Homogeneous Neumann or with our "corner correction")
+- `DDM`: Number of subdomain: 2,3 or 6 (if launched with a DD-Algorithm). The monodomain problem can be launched independently of the geometry (see section `GetDP`). The `beta` parameter cannot be changed.
+- `Geometry`: the radii of the ABC and obstacle and the position of the obstacle.
+- `GetDP`: The `Resolution` value:
+ - `MonoDomain`: Direct solver / Mono domain problem (every sub-domains are merged)
+ - `DDM-1`: First algorithm presented in the paper: auxiliary function `phi` is global
+ - `DDM-2`: Second algorithm where `phi` is local to each subdomain
+- `GMSH`: nothing
+- `Input` : `Incident angle` of the plane wave and `Wavenumber`
+- `IterativeSolver`
+ - `Solver`: `Jacobi` ("Parallel Schwarz") or `gmres`. The `print` is only for debugging purpose and might not work on your configuration.
+ - `Tolerance`, `Max it` and `Restart` (for GMRES) are classical parameter
+- `Mesh`: `NLambda` is the number of discretization points per wavelength
+- `Output`: `Output Directory` of the results
+
+## Transmission Condition
+
+The script returns the total field `u` in the waveguide.
+
+
+
+Here are the available options:
+
+- `GetDP`: The `Resolution` value:
+ - `MonoDomain`: Direct solver / Mono domain problem (every sub-domains are merged)
+ - `DDM`: Domain Decomposition Algorithm
+- `GMSH`: nothing
+- `DDM`:
+ - `Order 2` (continuous auxiliary function), `Homog. Neumann` or (our) `Corner Correction`
+ - `Corner Condition`: `Dirichlet` (continuous auxiliary function), `Homog. Neumann` or (our) `Corner Correction`
+- `Geometry`:
+ - `X-width` and `Y-width`: resp. X-length and Y-length of the waveguide
+ - `Type of border line`: `Broken Line` or `Straight Line`
+ - `X-coord of the pick point`: Move the middle (peak) point on the x-line
+ - `Y-coord of bottom point`: Move the bottom point on the y-line. The top point is moved symmetrically
+- `Boundary Conditions`:
+ - `Incoming (left)`: the boundary condition of the left side of the square, where the incoming wave is sent. It can be either `Fourier` (dn u + iwu) or `Dirichlet`.
+ - `Outgoing (right, =0)`: either `Fourier` (dn u + iwu), `Neumann` or `Dirichlet`. The condition is homogeneous (=0) and set on the right side of the square.
+ - `Top (=0)`: either `Neumann` or `Dirichlet`, homogeneous in both case (=0), for the top side of the square.
+ - `Bottom (=0)`: either `Neumann` or `Dirichlet`, homogeneous in both case (=0), for the bottom side of the square.
+- `Input`:
+ - `wavenumber`
+ - `Type of incident wave`: `Plane wave` (exp^{i*k*(alpha*x)}, alpha = `Incident angle`) or Fourier mode (with m = `Mode number`)
+- `IterativeSolver`
+ - `Solver`: `Jacobi` ("Parallel Schwarz") or `gmres`. The `print` is only for debugging purpose and might not work on your configuration.
+ - `Tolerance`, `Max it` and `Restart` (GMRES only) are classical parameter
+- `Mesh`: `NLambda` is the number of discretization points per wavelength. The quantity `h` is the diameter of an element.
+- `Output`:
+ - `Prefix for filename`: prefix applied to every saved file
+ - `Output Directory` of the results
+ - `Print every phi`: print on disk every auxiliary functions
+
+# Authors
+
+Bruno Després, Anouk Nicolopoulos, Bertrand Thierry
+# License
+
+GNU General Public License v3.0 or later
+
+See COPYING to see the full text.
\ No newline at end of file
diff --git a/DDM-Corner-Helmholtz-2D/img/ABC.png b/DDM-Corner-Helmholtz-2D/img/ABC.png
new file mode 100644
index 0000000000000000000000000000000000000000..15ff9890436f06216ea6fbc2607f21c3df11113d
Binary files /dev/null and b/DDM-Corner-Helmholtz-2D/img/ABC.png differ
diff --git a/DDM-Corner-Helmholtz-2D/img/TC.png b/DDM-Corner-Helmholtz-2D/img/TC.png
new file mode 100644
index 0000000000000000000000000000000000000000..a0ffefa93a998f4be59b3dd6e41e533c6f19247f
Binary files /dev/null and b/DDM-Corner-Helmholtz-2D/img/TC.png differ
diff --git a/DDM-Corner-Helmholtz-2D/main.data b/DDM-Corner-Helmholtz-2D/main.data
new file mode 100644
index 0000000000000000000000000000000000000000..9be4111049a56c5eb68b8f0e85732ac65fc85622
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/main.data
@@ -0,0 +1,12 @@
+DefineConstant[
+ PROBLEM = {"Absorbing BC", Choices {"Absorbing BC", "Transmission Condition"}, Visible 1, Name "GetDP/0Problem", GmshOption "Reset", Highlight "Blue"}
+];
+
+
+// GetDP
+DefineConstant[
+ // default getdp parameters for onelab
+ R_ = {"MonoDomain", Name "GetDP/1ResolutionChoices", Visible 1, Highlight "Blue"},
+ C_ = {"-solve -v 3 -bin -ksp_monitor", Name "GetDP/9ComputeCommand", Visible 0},
+ P_ = {"", Name "GetDP/2PostOperationChoices", Visible 0}
+];
\ No newline at end of file
diff --git a/DDM-Corner-Helmholtz-2D/main.geo b/DDM-Corner-Helmholtz-2D/main.geo
new file mode 100644
index 0000000000000000000000000000000000000000..cf39f62a63c1b5aed11b3aab5d4ec0f4b4f04509
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/main.geo
@@ -0,0 +1,10 @@
+WorkingDir = CurrentDir;
+Include "main.data";
+
+If(!StrCmp(PROBLEM, "Absorbing BC"))
+ Include "src/ABC_main.data";
+ Include "src/ABC_main.geo";
+Else
+ Include "src/TC_main.data";
+ Include "src/TC_main.geo";
+EndIf
diff --git a/DDM-Corner-Helmholtz-2D/main.pro b/DDM-Corner-Helmholtz-2D/main.pro
new file mode 100644
index 0000000000000000000000000000000000000000..7e8f6c39a9dc72296e63ed10fa5fa5e05ec7ee05
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/main.pro
@@ -0,0 +1,14 @@
+WorkingDir = CurrentDir;
+Include "main.data";
+
+Include "src/Common.pro";
+
+If(!StrCmp(PROBLEM,"Absorbing BC"))
+ Include "src/ABC_main.data";
+ Include "src/ABC_main.pro";
+Else
+ Include "src/TC_main.data";
+ Include "src/TC_main.pro";
+EndIf
+
+
diff --git a/DDM-Corner-Helmholtz-2D/notes.md b/DDM-Corner-Helmholtz-2D/notes.md
new file mode 100644
index 0000000000000000000000000000000000000000..64a89769b8ea70d1f3d7838e6f3ca1370acd5ca7
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/notes.md
@@ -0,0 +1,51 @@
+# Notations
+
+## GetDP Group (`hexa.pro`)
+
+Les indices `i` et `j` sont réservés aux sous domaines tandis que `k` et `l` le sont pour les segments du bord extérieur.
+
+### Numbers
+
+| Nom| Fonction|
+| ----- | ----- |
+|`NGammaExt` |Number of segments of exterior boundary $\Gamma$ |
+|`NGammaExt~{i}` |Number of segments of $\Gamma\cap\partial\Omega_i$ |
+|`NDom` | Number of subdomains|
+
+### Indices
+
+| Nom| Fonction|
+| ----- | ----- |
+|`Omega~{i}` | Domaine $\Omega_i$|
+|`GammaExt` | Bord $\Gamma$ en entier|
+|`GammaExt~{k}` | Segment $\Gamma_k$|
+| `GammaExt~{i}~{k}`| Segment $\Gamma_k^i$|
+|`GammaInt` | Bord intérieur (obstacle) en entier|
+|`GammaInt~{i}` | `GammaInt`$\cap\partial\Omega_i$|
+| `Apt~{i}~{j}~{k}~{l}` | Point $A_{k\ell}^{ij}$ |
+| `dGammaExt~{i}~{k}~{0}` | Same as one of the `Apt~{i}~{j}~{k}~{l}` but listed differently |
+| `Cset~{i}~{k}` | End-points of $\Gamma_k^i$|
+| `dGammaExt~{i}~{k}` | = `Cset~{i}~{k}`|
+| `dOmegaInt~{i}` | $=$`GammaInt~{i}`$=\partial\Omega_i \cap$`GammaInt`|
+| `dOmegaExt~{i}` | $=\partial\Omega_i \cap$`GammaExt`$=\cup_k\Gamma_k^i$|
+| `Sigma~{i}~{j}` | $=\Sigma_{ij} = \partial\Omega_i\cap\partial\Omega_j$|
+| `Sigma~{i}` | $=\cap_j$ `Sigma~{i}~{j}`|
+| `dSigmaExt~{i}~{j}~{n}` <br> with `n = 0,1,2...` | $n^{th}$ (End-) Point of $\Sigma_{ij}$ such that it also belons to $\Gamma$ (could be more than 1 end-point !)|
+| `dSigmaInt~{i}~{j}~{n}` <br> with `n = 0,1,2...` | Same but switch the role of `GammaExt`($=\Gamma$) with `GammaInt`|
+| `dSigmaExt~{i}~{j}` | $=\partial\Sigma_{ij}\cap\Gamma= \cup_n$`dSigmaExt~{i}~{j}~{n}`|
+| `dSigmaInt~{i}~{j}` | $=\partial\Sigma_{ij}\cap\Gamma^{int}= \cup_n$`dSigmaInt~{i}~{j}~{n}`|
+| `dSigma~{i}~{j}` | $=\partial\Sigma_{ij}=$`dSigmaExt~{i}~{j}`$\cup$`dSigmaInt~{i}~{j}`|
+
+### Lists
+
+> A list in GetDP is always monodimensional. When a list is said to be of dimension 2, explanation are provided to explain how to access the data.
+
+| Nom| Dim | Fonction|
+| ----- | ----- |----- |
+|`D()` | 1 |Indices $i$ of subdomains $\Omega_{\texttt{D(index)}}$ with `index=0,1,2...,Ndom-1`. The index `i` of the subdomain is obtained through: `i= D(index)`. When subdomains are numbered from 0 to `Ndom`-1, then `D()` is simply equal to `[0,1,2,...Ndom-1]`.|
+|`myD()` | 1 |Indices `index=0,1,2,...` in `D()` such that $\Omega_{\texttt{D(index)}}$ is a subdmain the current MPI process has to treat (sequential case: `myD() = 0,1,2,...,Ndom-1`)|
+| `D~{i}`| 1 |Indices $j$ of neighbor : *i.e.* such that $\partial\Omega_j\cap\partial\Omega_i\neq\emptyset$. Note that `i` and `j` are the "real" subdomain numbers |
+| `ListGammaExt~{i}()` | 1 |Indices $k$ (global) of $\Gamma_k^i$ ($\neq \emptyset$ by definition) |
+| `ListdGammaExt~{i}~{k}()` | 2 | Couple of indices $(j, \ell)$ of the $n^{th}$ end-point of $\Gamma_k^i$ (*i.e.* the $j$ and $\ell$ of $A_{k\ell}^{ij}$. Store contiguously : `[j,l, j,l, j,l,...]` |
+| `ListdSigmaExt~{i}~{j}()` | 2 | Couple of indices $(k, \ell)$ of the $n^{th}$ end-point of $\Sigma_{ij}$ such that it also belongs to $\Gamma$ (*i.e.* the $k$ and $\ell$ of $A_{k\ell}^{ij}$. Store contiguously : `[j,l, j,l, j,l,...]` (same role as `ListdGammaExt~{i}~{k}()`) |
+
diff --git a/DDM-Corner-Helmholtz-2D/src/ABC_DDM.pro b/DDM-Corner-Helmholtz-2D/src/ABC_DDM.pro
new file mode 100644
index 0000000000000000000000000000000000000000..fe07e3b7c77ee64c6cecaf44c83251b5d21bc004
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/src/ABC_DDM.pro
@@ -0,0 +1,131 @@
+// DDM-algorithms
+// Common quantities and operations are defined here
+// DDM algorithm are included below
+
+// Numbering of the unknowns of the DD algorithms
+Include "ABC_Decomposition.pro";
+
+Group {
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ TrdOmegaInt~{i} = ElementsOf[Omega~{i}, OnOneSideOf dOmegaInt~{i}];
+ EndFor
+}
+
+Constraint {
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ {Name Dirichlet~{i}; Type Assign; Case{{Region dOmegaInt~{i}; Value $PhysicalSource?-uInc[]:0.; } } }
+ EndFor
+}
+
+FunctionSpace{
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ {Name H_grad~{i}; Type Form0;
+ BasisFunction{
+ {Name u~{i}; NameOfCoef ui; Function BF_Node;
+ Support Region[{Omega~{i}, dOmegaExt~{i}, dOmegaInt~{i}, Sigma~{i}}]; Entity NodesOf[All];}
+ }
+ Constraint{
+ {NameOfCoef ui; EntityType NodesOf; NameOfConstraint Dirichlet~{i};}
+ }
+ }
+
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ {Name H_g~{i}~{j}; Type Form0;
+ BasisFunction{
+ {Name g~{i}~{j}; NameOfCoef gj; Function BF_Node;
+ Support Region[{Sigma~{i}~{j}}];Entity NodesOf[Sigma~{i}~{j}];}
+ }
+ }
+ EndFor
+ EndFor
+}
+
+// ============ DDM Algorithms
+Include "ABC_DDM_1.pro";
+Include "ABC_DDM_2.pro";
+// ===============
+
+// Common Post-Processings to every DDM algorithms
+// ===============================================
+PostProcessing{
+ // Transmitted Data
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ {Name G~{j}~{i}; NameOfFormulation G~{j}~{i};
+ Quantity {
+ {Name g~{j}~{i}; Value {Local { [{g~{j}~{i}}] ; In Sigma~{i}~{j}; Jacobian JSur; }}}
+ }
+ }
+ {Name NormL2G~{j}~{i}; NameOfFormulation G~{j}~{i};
+ Quantity {
+ {Name normL2g~{j}~{i}; Value { Integral { [ Abs[g~{j}~{i}[] - {g~{j}~{i}} - b~{j}~{i}[]]^2 ]; In Sigma~{i}~{j}; Jacobian JSur; Integration I1; }}}
+ }
+ }
+ EndFor
+ EndFor
+ // Local solutions (whatever the algorithm)
+ {Name DDM; NameOfFormulation DDM_1;
+ Quantity {
+ {Name u_ddm; Value {
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ Local { [{u~{i}}] ; In Omega~{i}; Jacobian JVol; }
+ EndFor
+ }
+ }
+ {Name u_ddm_abs; Value {
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ Local { [Norm[{u~{i}}]] ; In Omega~{i}; Jacobian JVol; }
+ EndFor
+ }
+ }
+ //Error between solution and exact solution (exact in free space!)
+ {Name uerr_ddm; Value {
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ Local { [Norm[{u~{i}} - uex[]]] ; In Omega~{i}; Jacobian JVol; }
+ EndFor
+ }
+ }
+ }
+ }
+}
+
+// Common Post-Operations to every DDM-algorithms
+// ===============================================
+PostOperation{
+ // Compute the transmitted data + Store it in memory
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ {Name G~{j}~{i}; NameOfPostProcessing G~{j}~{i};
+ Operation { Print [g~{j}~{i}, OnElementsOf Sigma~{i}~{j}, StoreInField tag_g~{j}~{i}];}
+ }
+ //Store RHS to compute L2 error (Jacobi)
+ {Name B~{j}~{i}; NameOfPostProcessing G~{j}~{i};
+ Operation { Print [g~{j}~{i}, OnElementsOf Sigma~{i}~{j}, StoreInField tag_b~{j}~{i}];}
+ }
+ {Name NormL2G~{j}~{i}; NameOfPostProcessing NormL2G~{j}~{i};
+ Operation{
+ Print [normL2g~{j}~{i}[Sigma~{i}~{j}], OnRegion Sigma~{i}~{j}, Format Table, AppendExpressionToFileName $ItCount, File >> StrCat[ABC_DIR,"ABC_DDM_normg.pos"]];
+ }
+ }
+ EndFor
+ EndFor
+ // Print the solution on HDD + error wrt exact solution
+ {Name DDM; NameOfPostProcessing DDM;
+ Operation {
+ Print [u_ddm, OnElementsOf Omega, File StrCat[ABC_DIR, StrCat[ABC_PREFIX, "DDM_Scattered_Field.pos"]]];
+ Print [u_ddm_abs, OnElementsOf Omega, File StrCat[ABC_DIR, StrCat[ABC_PREFIX, "DDM_Scattered_Field_(abs._value).pos"]]];
+ Print [uerr_ddm, OnElementsOf Omega, File StrCat[ABC_DIR, StrCat[ABC_PREFIX, "DDM_Error_numeric_vs_analytic.pos"]]];
+ }
+ }
+}
diff --git a/DDM-Corner-Helmholtz-2D/src/ABC_DDM_1.pro b/DDM-Corner-Helmholtz-2D/src/ABC_DDM_1.pro
new file mode 100644
index 0000000000000000000000000000000000000000..fff9eb8fb78c086d8814752b8c60763c05e571c5
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/src/ABC_DDM_1.pro
@@ -0,0 +1,172 @@
+// First algorithm
+
+Formulation {
+ { Name DDM_1; Type FemEquation;
+ Quantity{
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ { Name u~{i} ; Type Local; NameOfSpace H_grad~{i};}
+ EndFor
+ For k In {0:#ListGammaExt()-1}
+ { Name phi~{k} ; Type Local; NameOfSpace H_phi~{k};}
+ EndFor
+ }
+ Equation{
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ // PDE on u_i
+ //Helmholtz equation
+ Galerkin{[Dof{Grad u~{i}}, {Grad u~{i}}];
+ In Omega~{i}; Jacobian JVol; Integration I1;}
+ Galerkin{[-kap^2*Dof{u~{i}}, {u~{i}}];
+ In Omega~{i}; Jacobian JVol; Integration I1;}
+ // dni ui -i*kap ui = gij on Sigma ij
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ Galerkin{[-I[]*kap*Dof{u~{i}}, {u~{i}}];
+ In Sigma~{i}~{j}; Jacobian JSur; Integration I1;}
+ Galerkin{[$TCSource?-g~{i}~{j}[]:0., {u~{i}}];
+ In Sigma~{i}~{j}; Jacobian JSur; Integration I1;}
+ EndFor
+ If(ABC_ORDER==0)
+ Galerkin{[-I[]*kap*Dof{u~{i}}, {u~{i}}];
+ In dOmegaExt~{i}; Jacobian JSur; Integration I1;}
+ Else
+ // dn u_i = i*omega*phi_k on Gamma_i^k
+ For kk In {0:#ListGammaExt~{i}()-1}
+ k=ListGammaExt~{i}(kk);
+ Galerkin{[-I[]*kap*Dof{phi~{k}}, {u~{i}}];
+ In GammaExt~{i}~{k}; Jacobian JSur; Integration I1;}
+ EndFor
+ EndIf
+ EndFor
+
+ // Operator T
+ If(ABC_ORDER == 2)
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For kk In {0:#ListGammaExt~{i}()-1}
+ k = ListGammaExt~{i}(kk);
+ Galerkin{[-Dof{u~{i}}, {phi~{k}}];
+ In GammaExt~{i}~{k}; Jacobian JSur; Integration I1;}
+ EndFor
+ EndFor
+ For kk In {0:#ListGammaExt()-1}
+ k = ListGammaExt(kk);
+ Galerkin{[Dof{phi~{k}}, {phi~{k}}];
+ In GammaExt~{k}; Jacobian JSur; Integration I1;}
+ Galerkin{[1/(2*kap^2)*Dof{d phi~{k}}, {d phi~{k}}];
+ In GammaExt~{k}; Jacobian JSur; Integration I1;}
+ // Corner correction
+ If(CORNER_CONDITION == 2)
+ For index In {0:#ListdGammaExt~{k}()-1}
+ // Loop on end-point
+ l=ListdGammaExt~{k}(index); // Index of ajacent segment
+ Galerkin{[-I[]/(4*kap)*(Cos[theta]/Cos[theta/2]+Cos[theta/2])*Dof{phi~{k}}, {phi~{k}}];
+ In Apt~{k}~{l}; Jacobian JLin; Integration I1;}
+ Galerkin{[-I[]/(4*kap)*(-Cos[theta]/Cos[theta/2]+Cos[theta/2])*Dof{phi~{l}}, {phi~{k}}];
+ In Apt~{k}~{l}; Jacobian JLin; Integration I1;}
+ EndFor
+ EndIf
+ EndFor
+ EndIf
+ }
+ }
+
+ // Equation to compute the transmitted data g_{ji} that is sent to Omega_j
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ { Name G~{j}~{i}; Type FemEquation;
+ Quantity{
+ { Name u~{i} ; Type Local; NameOfSpace H_grad~{i};}
+ { Name g~{j}~{i} ; Type Local; NameOfSpace H_g~{j}~{i};}
+ }
+ Equation{
+ Galerkin{[Dof{g~{j}~{i}},{g~{j}~{i}}];
+ In Sigma~{j}~{i}; Jacobian JSur; Integration I1;}
+ Galerkin{[$TCSource?+g~{i}~{j}[]:0.,{g~{j}~{i}}];
+ In Sigma~{j}~{i}; Jacobian JSur; Integration I1;}
+ Galerkin{[2*I[]*kap*{u~{i}},{g~{j}~{i}}];
+ In Sigma~{j}~{i}; Jacobian JSur; Integration I1;}
+ }
+ }
+ EndFor
+ EndFor
+}
+
+Resolution{
+ {Name DDM_1;
+ System{
+ {Name DDM_1; NameOfFormulation DDM_1; Type Complex; }
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ {Name G~{j}~{i}; NameOfFormulation G~{j}~{i}; Type Complex; }
+ EndFor
+ EndFor
+ }
+ Operation{
+ CreateDir[ABC_DIR];
+ // Initialisation
+ Evaluate[$PhysicalSource = 1];
+ Evaluate[$TCSource = 0];
+ UpdateConstraint[DDM_1, dOmegaInt, Assign];
+ Generate[DDM_1];
+ Solve[DDM_1];
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ Generate[G~{j}~{i}];
+ Solve[G~{j}~{i}];
+ PostOperation[G~{j}~{i}];
+ //Save RHS if jacobi
+ If(StrCmp(SOLVER, "jacobi") == 0)
+ PostOperation[B~{j}~{i}];
+ EndIf
+ EndFor
+ EndFor
+ Evaluate[$PhysicalSource = 0];
+ Evaluate[$TCSource = 1];
+ UpdateConstraint[DDM_1, dOmegaInt, Assign];
+ Evaluate[$ItCount = 0];
+ IterativeLinearSolver["I-A",SOLVER, TOL, MAXIT, RESTART, {ListOfFields_g()}, {}, {}]
+ {
+ // Compute local solutions
+ GenerateRHSGroup[DDM_1, Region[{Sigma, TrdOmegaInt, GammaExt, dGammaExt}]];
+ SolveAgain[DDM_1];
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ GenerateRHSGroup[G~{j}~{i}, Region[{Sigma~{i}}]];
+ SolveAgain[G~{j}~{i}];
+ EndFor
+ EndFor
+ // Update data to be exchanged
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ If(StrCmp(SOLVER, "jacobi") == 0)
+ PostOperation[NormL2G~{j}~{i}]; // Compute difference between new and old g_ji
+ EndIf
+ PostOperation[G~{j}~{i}];
+ EndFor
+ EndFor
+
+ Evaluate[$ItCount = $ItCount+1];
+ }
+ //Compute global solution
+ Evaluate[$PhysicalSource = 1];
+ Evaluate[$TCSource = 1];
+ UpdateConstraint[DDM_1, dOmegaInt, Assign];
+ GenerateRHSGroup[DDM_1, Region[{Sigma, TrdOmegaInt, GammaExt, dGammaExt}]];
+ SolveAgain[DDM_1];
+ PostOperation[DDM];
+ }
+ }
+}
diff --git a/DDM-Corner-Helmholtz-2D/src/ABC_DDM_2.pro b/DDM-Corner-Helmholtz-2D/src/ABC_DDM_2.pro
new file mode 100644
index 0000000000000000000000000000000000000000..3d3ab404539f28802cd906b028b8cd1499f4a92c
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/src/ABC_DDM_2.pro
@@ -0,0 +1,283 @@
+// Algorithm DDM-2
+Function{
+ coef_sigma[] = -(1 + I[]*beta/kap*Cos[theta/2]/Cos[theta]);
+ coef_gamma[] = beta + I[]*kap*Cos[theta/2];
+ If(ABC_ORDER==0)
+ ListOfFields_ddm2() = {ListOfFields_g()};
+ Else
+ ListOfFields_ddm2() = {ListOfFields_g(),ListOfFields_h()};
+ EndIf
+}
+
+FunctionSpace{
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For kk In {0:#ListGammaExt~{i}()-1}
+ k=ListGammaExt~{i}(kk);
+ {Name H_phi~{i}~{k}; Type Form0;
+ BasisFunction{
+ {Name phi~{i}~{k}; NameOfCoef phiik; Function BF_Node;
+ Support Region[{GammaExt~{i}~{k}, dGammaExt~{i}~{k}}];
+ Entity NodesOf[All];}
+ }
+ }
+ // Quantities transfered at each Apt~{i}~{j}~{k}~{l}
+ For index In {0:#ListdGammaExt~{i}~{k}()-1:2}
+ j=ListdGammaExt~{i}~{k}(index);
+ l=ListdGammaExt~{i}~{k}(index+1);
+ {Name H_h~{i}~{j}~{k}~{l}; Type Form0;
+ BasisFunction{
+ {Name h~{i}~{j}~{k}~{l}; NameOfCoef hj; Function BF_Node;
+ Support Region[{Apt~{i}~{j}~{k}~{l}}]; Entity NodesOf[All];}
+ }
+ }
+ EndFor
+ EndFor
+ EndFor
+}
+
+Formulation{
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ { Name DDM_2~{i}; Type FemEquation;
+ Quantity{
+ {Name u~{i} ; Type Local; NameOfSpace H_grad~{i};}
+ For kk In {0:#ListGammaExt~{i}()-1}
+ k=ListGammaExt~{i}(kk);
+ { Name phi~{i}~{k} ; Type Local; NameOfSpace H_phi~{i}~{k};}
+ EndFor
+ }
+ Equation{
+ // PDE on u_i
+ //Helmholtz equation
+ Galerkin{[Dof{Grad u~{i}}, {Grad u~{i}}];
+ In Omega~{i}; Jacobian JVol; Integration I1;}
+ Galerkin{[-kap^2*Dof{u~{i}}, {u~{i}}];
+ In Omega~{i}; Jacobian JVol; Integration I1;}
+ // dni ui -i*kap ui = gij on Sigma ij
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ Galerkin{[-I[]*kap*Dof{u~{i}}, {u~{i}}];
+ In Sigma~{i}~{j}; Jacobian JSur; Integration I1;}
+ Galerkin{[$TCSource?-g~{i}~{j}[]:0., {u~{i}}];
+ In Sigma~{i}~{j}; Jacobian JSur; Integration I1;}
+ EndFor
+ If(ABC_ORDER==0)
+ Galerkin{[-I[]*kap*Dof{u~{i}}, {u~{i}}];
+ In dOmegaExt~{i}; Jacobian JSur; Integration I1;}
+ Else
+ // dn u_i = i*omega*phi_k on Gamma_i^k
+ For kk In {0:#ListGammaExt~{i}()-1}
+ k=ListGammaExt~{i}(kk);
+ Galerkin{[-I[]*kap*Dof{phi~{i}~{k}}, {u~{i}}];
+ In GammaExt~{i}~{k}; Jacobian JSur; Integration I1;}
+ EndFor
+ // Operator T (Mandatory : Order = 2 + Corner Correction)
+ For kk In {0:#ListGammaExt~{i}()-1}
+ k=ListGammaExt~{i}(kk);
+ Galerkin{[Dof{phi~{i}~{k}}, {phi~{i}~{k}}];
+ In GammaExt~{i}~{k}; Jacobian JSur; Integration I1;}
+ Galerkin{[-Dof{u~{i}}, {phi~{i}~{k}}];
+ In GammaExt~{i}~{k}; Jacobian JSur; Integration I1;}
+ Galerkin{[1/(2*kap^2)*Dof{d phi~{i}~{k}}, {d phi~{i}~{k}}];
+ In GammaExt~{i}~{k}; Jacobian JSur; Integration I1;}
+ If(CORNER_CONDITION == 2)
+ For index In {0:#ListdGammaExt~{i}~{k}()-1:2}
+ j=ListdGammaExt~{i}~{k}(index);
+ l=ListdGammaExt~{i}~{k}(index+1);
+ If (k!=l) // corner point
+ Galerkin{[-Conj[coef_gamma[]]/2/kap/kap/coef_sigma[]*Dof{phi~{i}~{k}}, {phi~{i}~{k}}];
+ In Region[{Apt~{i}~{j}~{k}~{l}}]; Jacobian JLin; Integration I1;}
+ Galerkin{[$TCSource?-h~{i}~{j}~{k}~{l}[]/2/kap/kap:0., {phi~{i}~{k}}];
+ In Region[{Apt~{i}~{j}~{k}~{l}}]; Jacobian JLin; Integration I1;}
+ //TODO: Flatpoint
+ //Else
+ EndIf
+ EndFor
+ EndIf
+ EndFor
+ EndIf
+ }
+ }
+ EndFor
+
+ //Resolution h
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For kk In {0:#ListGammaExt~{i}()-1}
+ k=ListGammaExt~{i}(kk);
+ For index In {0:#ListdGammaExt~{i}~{k}()-1:2}
+ j=ListdGammaExt~{i}~{k}(index);
+ l=ListdGammaExt~{i}~{k}(index+1);
+ { Name H~{j}~{i}~{l}~{k}; Type FemEquation;
+ Quantity{
+ { Name phi~{i}~{k} ; Type Local; NameOfSpace H_phi~{i}~{k};}
+ { Name h~{j}~{i}~{l}~{k} ; Type Local; NameOfSpace H_h~{j}~{i}~{l}~{k};}
+ }
+ Equation{
+ Galerkin{[Dof{h~{j}~{i}~{l}~{k}},{h~{j}~{i}~{l}~{k}}];
+ In Apt~{i}~{j}~{k}~{l}; Jacobian JLin; Integration I1;}
+ Galerkin{[$TCSource?Conj[coef_sigma[]]/coef_sigma[]*h~{i}~{j}~{k}~{l}[]:0.,{h~{j}~{i}~{l}~{k}}];
+ In Apt~{i}~{j}~{k}~{l}; Jacobian JLin; Integration I1;}
+ Galerkin{[(Conj[coef_sigma[]*coef_gamma[]]/coef_sigma[]/coef_sigma[] + coef_gamma[]/coef_sigma[]) *{phi~{i}~{k}}, {h~{j}~{i}~{l}~{k}}];
+ In Apt~{i}~{j}~{k}~{l}; Jacobian JLin; Integration I1;}
+ }
+ }
+ EndFor
+ EndFor
+ EndFor
+}
+
+Resolution{
+ {Name DDM_2;
+ System{
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ {Name DDM_2~{i}; NameOfFormulation DDM_2~{i}; Type Complex; }
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ {Name G~{j}~{i}; NameOfFormulation G~{j}~{i}; Type Complex; }
+ EndFor
+ If(ABC_ORDER != 0)
+ For kk In {0:#ListGammaExt~{i}()-1}
+ k=ListGammaExt~{i}(kk);
+ For index In {0:#ListdGammaExt~{i}~{k}()-1:2}
+ j=ListdGammaExt~{i}~{k}(index);
+ l=ListdGammaExt~{i}~{k}(index+1);
+ {Name H~{j}~{i}~{l}~{k}; NameOfFormulation H~{j}~{i}~{l}~{k}; Type Complex; }
+ EndFor
+ EndFor
+ EndIf
+ EndFor
+ }
+ Operation{
+ // Initialisation
+ Evaluate[$PhysicalSource = 1];
+ Evaluate[$TCSource = 0];
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ UpdateConstraint[DDM_2~{i}, dOmegaInt~{i}, Assign];
+ Generate[DDM_2~{i}];
+ Solve[DDM_2~{i}];
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ Generate[G~{j}~{i}];
+ Solve[G~{j}~{i}];
+ PostOperation[G~{j}~{i}];
+ EndFor
+ If(ABC_ORDER != 0)
+ For kk In {0:#ListGammaExt~{i}()-1}
+ k=ListGammaExt~{i}(kk);
+ For index In {0:#ListdGammaExt~{i}~{k}()-1:2}
+ j=ListdGammaExt~{i}~{k}(index);
+ l=ListdGammaExt~{i}~{k}(index+1);
+ Generate[H~{j}~{i}~{l}~{k}];
+ Solve[H~{j}~{i}~{l}~{k}];
+ PostOperation[H~{j}~{i}~{l}~{k}];
+ EndFor
+ EndFor
+ EndIf
+ EndFor
+ // Set uinc=0 and unlock quantity on Sigma
+ Evaluate[$PhysicalSource = 0];
+ Evaluate[$TCSource = 1];
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ UpdateConstraint[DDM_2~{i}, dOmegaInt~{i}, Assign];
+ EndFor
+
+ IterativeLinearSolver["I-A",SOLVER, TOL, MAXIT, RESTART, ListOfFields_ddm2(), {}, {}]
+ {
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ GenerateRHSGroup[DDM_2~{i}, Region[{Sigma~{i}, TrdOmegaInt~{i}, dOmegaExt~{i}, dGammaExt}]];
+ SolveAgain[DDM_2~{i}];
+ EndFor
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ GenerateRHSGroup[G~{j}~{i},Region[{Sigma~{i}~{j}}]];
+ SolveAgain[G~{j}~{i}];
+ EndFor
+ If(ABC_ORDER != 0)
+ For kk In {0:#ListGammaExt~{i}()-1}
+ k=ListGammaExt~{i}(kk);
+ For index In {0:#ListdGammaExt~{i}~{k}()-1:2}
+ j=ListdGammaExt~{i}~{k}(index);
+ l=ListdGammaExt~{i}~{k}(index+1);
+ GenerateRHSGroup[H~{j}~{i}~{l}~{k}, Region[{Apt~{j}~{i}~{l}~{k}}]];
+ SolveAgain[H~{j}~{i}~{l}~{k}];
+ EndFor
+ EndFor
+ EndIf
+ EndFor
+
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ PostOperation[G~{j}~{i}];
+ EndFor
+ If(ABC_ORDER != 0)
+ For kk In {0:#ListGammaExt~{i}()-1}
+ k=ListGammaExt~{i}(kk);
+ For index In {0:#ListdGammaExt~{i}~{k}()-1:2}
+ j=ListdGammaExt~{i}~{k}(index);
+ l=ListdGammaExt~{i}~{k}(index+1);
+ PostOperation[H~{j}~{i}~{l}~{k}];
+ EndFor
+ EndFor
+ EndIf
+ EndFor
+ }
+ // Compute solution
+ Evaluate[$PhysicalSource = 1];
+ Evaluate[$TCSource = 1];
+
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ UpdateConstraint[DDM_2~{i}, dOmegaInt~{i}, Assign];
+ GenerateRHSGroup[DDM_2~{i}, Region[{Sigma~{i}, TrdOmegaInt~{i}, dOmegaExt~{i}, dGammaExt}]];
+ SolveAgain[DDM_2~{i}];
+ EndFor
+ PostOperation[DDM];
+ }
+ }
+}
+
+// Post Processing and Post Operation specific to DDM-2 algorithm
+// ================
+PostProcessing{
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For kk In {0:#ListGammaExt~{i}()-1}
+ k=ListGammaExt~{i}(kk);
+ For index In {0:#ListdGammaExt~{i}~{k}()-1:2}
+ j=ListdGammaExt~{i}~{k}(index);
+ l=ListdGammaExt~{i}~{k}(index+1);
+ {Name H~{j}~{i}~{l}~{k}; NameOfFormulation H~{j}~{i}~{l}~{k};
+ Quantity {
+ {Name h~{j}~{i}~{l}~{k}; Value {Local { [{h~{j}~{i}~{l}~{k}}] ; In Apt~{j}~{i}~{l}~{k}; Jacobian JLin; }}}
+ }
+ }
+ EndFor
+ EndFor
+ EndFor
+}
+
+PostOperation{
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For kk In {0:#ListGammaExt~{i}()-1}
+ k=ListGammaExt~{i}(kk);
+ For index In {0:#ListdGammaExt~{i}~{k}()-1:2}
+ j=ListdGammaExt~{i}~{k}(index);
+ l=ListdGammaExt~{i}~{k}(index+1);
+ {Name H~{j}~{i}~{l}~{k}; NameOfPostProcessing H~{j}~{i}~{l}~{k};
+ Operation {Print [h~{j}~{i}~{l}~{k}, OnElementsOf Apt~{j}~{i}~{l}~{k}, StoreInField tag_h~{j}~{i}~{l}~{k}];}
+ }
+ EndFor
+ EndFor
+ EndFor
+}
diff --git a/DDM-Corner-Helmholtz-2D/src/ABC_Decomposition.pro b/DDM-Corner-Helmholtz-2D/src/ABC_Decomposition.pro
new file mode 100644
index 0000000000000000000000000000000000000000..9cca9eb92930377208bf32f8494f742b59523687
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/src/ABC_Decomposition.pro
@@ -0,0 +1,57 @@
+// Dispatch subdomain to (MPI) processes (list myD())
+// Provide a unique tag to every transmitted data (e.g.: g_{i,j})
+Function{
+ myD = {} ; // the domains current process will treat (if MPI_NUM_PROC = 1 then myD()= {0,1,2,..., NDOM-1}
+ For i In {0:(NDom-1)}
+ myD~{i} = {};
+ If (i % MPI_Size == MPI_Rank)
+ myD() += D(i);
+ myD~{i} += D~{i}();
+ EndIf
+ EndFor
+ // Field managed by current MPI Process
+ // If sequential then every field
+ ListOfFields_g = {};
+ ListOfConnectedFields_g = {};
+ ListOfFields_h = {};
+ ListOfConnectedFields_h = {};
+
+ // Loop on subdomains
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ //Neighbors
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+
+ // Quantities coming from "the other side"
+ tag_g~{i}~{j} = 10000 + i*50 + j;
+ ListOfFields_g() += tag_g~{i}~{j};
+ g~{i}~{j}[ Sigma~{i}~{j} ] = ComplexScalarField[XYZ[]]{ tag_g~{i}~{j} };
+ // Quantities to be transmitted to domain j
+ tag_g~{j}~{i} = 10000 + j*50 + i;
+ ListOfConnectedFields_g() += 1;
+ ListOfConnectedFields_g() += tag_g~{j}~{i};
+
+ // RHS (for jacobi)
+ tag_b~{i}~{j} = 11000 + i*50 + j;
+ tag_b~{j}~{i} = 11000 + j*50 + i;
+ b~{i}~{j}[ Sigma~{i}~{j} ] = ComplexScalarField[XYZ[]]{ tag_b~{i}~{j} };
+ EndFor
+ // For DDM-2
+ For kk In {0:#ListGammaExt~{i}()-1}
+ k=ListGammaExt~{i}(kk);
+ For index In {0:#ListdGammaExt~{i}~{k}()-1:2}
+ j=ListdGammaExt~{i}~{k}(index);
+ l=ListdGammaExt~{i}~{k}(index+1);
+ // Quantities coming from "the other side" of Aijkl
+ tag_h~{i}~{j}~{k}~{l} = 100000 + i*1000 + j*100 + 10*k + l;
+ ListOfFields_h() += tag_h~{i}~{j}~{k}~{l};
+ h~{i}~{j}~{k}~{l}[ Apt~{i}~{j}~{k}~{l} ] = ComplexScalarField[XYZ[]]{ tag_h~{i}~{j}~{k}~{l} };
+ // Quantities to be transmitted to domain j
+ tag_h~{j}~{i}~{l}~{k} = 100000 + j*1000 + i*100 + 10*l + k;
+ ListOfConnectedFields_h() += 1;
+ ListOfConnectedFields_h() += tag_h~{j}~{i}~{l}~{k};
+ EndFor
+ EndFor
+ EndFor
+}
diff --git a/DDM-Corner-Helmholtz-2D/src/ABC_MonoDomain.pro b/DDM-Corner-Helmholtz-2D/src/ABC_MonoDomain.pro
new file mode 100644
index 0000000000000000000000000000000000000000..463a0b35286f5a395d23bebb9afb802318c7ccfb
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/src/ABC_MonoDomain.pro
@@ -0,0 +1,102 @@
+// Mono domain problem
+
+Constraint {
+ {Name Dirichlet; Type Assign; Case{{Region dOmegaInt; Value -uInc[]; } } }
+}
+
+FunctionSpace{
+ {Name H_grad; Type Form0;
+ BasisFunction{
+ {Name u; NameOfCoef ui; Function BF_Node;
+ Support Region[{Omega, dOmegaExt, dOmegaInt}]; Entity NodesOf[All];}
+ }
+ Constraint{
+ {NameOfCoef ui; EntityType NodesOf; NameOfConstraint Dirichlet;}
+ }
+ }
+ For k In {0:(#ListGammaExt()-1)}
+ {Name H_phi~{k}; Type Form0;
+ BasisFunction{
+ {Name phi~{k}; NameOfCoef phik; Function BF_Node;
+ Support Region[{GammaExt~{k}, dGammaExt~{k}}]; Entity NodesOf[All];}
+ }
+ }
+ EndFor
+}
+
+Formulation {
+ // Formulation for a Dirichlet boundary condition
+ { Name MonoDomain; Type FemEquation;
+ Quantity{
+ { Name u ; Type Local; NameOfSpace H_grad;}
+ For k In {0:(#ListGammaExt()-1)}
+ { Name phi~{k} ; Type Local; NameOfSpace H_phi~{k};}
+ EndFor
+ }
+ Equation{
+ //MonoDomain equation
+ Galerkin{[Dof{Grad u}, {Grad u}];
+ In Omega; Jacobian JVol; Integration I1;}
+ Galerkin{[-kap^2*Dof{u}, {u}];
+ In Omega; Jacobian JVol; Integration I1;}
+ // ABC
+ If(ABC_ORDER == 0)
+ Galerkin{[-I[]*kap*Dof{u}, {u}];
+ In dOmegaExt; Jacobian JSur; Integration I1;}
+ ElseIf(ABC_ORDER == 2)
+ For k In {0:(#ListGammaExt()-1)}
+ Galerkin{[-I[]*kap*Dof{phi~{k}}, {u}];
+ In GammaExt~{k}; Jacobian JSur; Integration I1;}
+ Galerkin{[Dof{phi~{k}}, {phi~{k}}];
+ In GammaExt~{k}; Jacobian JSur; Integration I1;}
+ Galerkin{[-Dof{u}, {phi~{k}}];
+ In GammaExt~{k}; Jacobian JSur; Integration I1;}
+ Galerkin{[1/(2*kap^2)*Dof{d phi~{k}}, {d phi~{k}}];
+ In GammaExt~{k}; Jacobian JSur; Integration I1;}
+ If(CORNER_CONDITION == 2)
+ For index In {0:#ListdGammaExt~{k}()-1}
+ // Loop on end-point
+ l=ListdGammaExt~{k}(index); // Index of ajacent segment
+ Galerkin{[-I[]/(4*kap)*(Cos[theta]/Cos[theta/2]+Cos[theta/2])*Dof{phi~{k}}, {phi~{k}}];
+ In Apt~{k}~{l}; Jacobian JLin; Integration I1;}
+ Galerkin{[-I[]/(4*kap)*(-Cos[theta]/Cos[theta/2]+Cos[theta/2])*Dof{phi~{l}}, {phi~{k}}];
+ In Apt~{k}~{l}; Jacobian JLin; Integration I1;}
+ EndFor
+ EndIf
+ EndFor
+ EndIf
+ }
+ }
+}
+
+Resolution{
+ {Name MonoDomain;
+ System{ {Name A; NameOfFormulation MonoDomain; Type Complex; } }
+ Operation{
+ CreateDir[ABC_DIR];
+ Generate[A];
+ Solve[A];
+ PostOperation[MonoDomain];
+ }
+ }
+}
+
+PostProcessing{
+ {Name MonoDomain; NameOfFormulation MonoDomain;
+ Quantity {
+ {Name u; Value {Local { [{u}] ; In Omega; Jacobian JVol; }}}
+ {Name uNorm; Value {Local { [Norm[{u}]] ; In Omega; Jacobian JVol; }}}
+ {Name err; Value {Local { [Norm[{u}-uex[]]] ; In Omega; Jacobian JVol; }}}
+ }
+ }
+}
+
+PostOperation{
+ {Name MonoDomain; NameOfPostProcessing MonoDomain;
+ Operation {
+ Print [u, OnElementsOf Omega, Name "Scattered_Field", File StrCat[ABC_DIR, StrCat[ABC_PREFIX, "u_mono.pos"]]];
+ Print [uNorm, OnElementsOf Omega, Name "Scattered_Field_(abs._value)", File StrCat[ABC_DIR,StrCat[ABC_PREFIX, "u_mono_abs.pos"]]];
+ Print [err, OnElementsOf Omega, Name "Error_numeric_vs_analytic", File StrCat[ABC_DIR,StrCat[ABC_PREFIX, "u_mono_err.pos"]]];
+ }
+ }
+}
diff --git a/DDM-Corner-Helmholtz-2D/src/ABC_main.data b/DDM-Corner-Helmholtz-2D/src/ABC_main.data
new file mode 100644
index 0000000000000000000000000000000000000000..83ac5a1d98ff04277a6816b11378960f538a60cf
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/src/ABC_main.data
@@ -0,0 +1,17 @@
+DefineConstant[
+ //Geometry
+ theta = {-2*Pi/3, ReadOnly 1, Name "Input/Geometry/0Theta"},
+ NGammaExt = {6, Visible 0, Name "Input/Geometry/1Nb. segments"},
+ r = {5, Min 0, Max 100, Step 0.1, Name "Input/Geometry/2Radius of the ABC"},
+ rs = {1, Min 1, Max 10, Step 0.1, Name "Input/Geometry/4Radius of the obstacle"},
+ xs = {0, Min -1, Max 1, Step 0.1, Name "Input/Geometry/6X-location of the obstacle"},
+ ys = {0, Min -1, Max 1, Step 0.1, Name "Input/Geometry/8Y-location of the obstacle"},
+ //Input
+ kap = {2*Pi, Min 1, Max 30, Step 0.1, Name "Input/Input/0Wavenumber"},
+ // Mesh
+ NLambda = {15, Min 10, Max 100, Step 1, Name "Input/Mesh/NLambda"},
+ h = {2*Pi/NLambda/kap, ReadOnly 1, Name "Input/Mesh/h"},
+ // DDM
+ NDom = {3, Choices {2="2", 3="3", 6="6"}, Name "Input/DDM/6Nb. sub-domains"}
+];
+
diff --git a/DDM-Corner-Helmholtz-2D/src/ABC_main.geo b/DDM-Corner-Helmholtz-2D/src/ABC_main.geo
new file mode 100644
index 0000000000000000000000000000000000000000..f0c7746fcf13891be7da5794886e0e45463f1198
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/src/ABC_main.geo
@@ -0,0 +1,90 @@
+//Hexagone regulier et point source/obstacle disque
+Mesh.CharacteristicLengthMin = h;
+Mesh.CharacteristicLengthMax = h;
+
+Point(10) = {xs,ys,0,h}; //Center of the disk and hexagone
+For i In {0:5}
+ Point(i+1) = {r*Cos[i*Pi/3],r*Sin[i*Pi/3],0,h}; //6 points hexagone
+ Point(10+i+1) = {xs+rs*Cos[i*Pi/3],ys+rs*Sin[i*Pi/3],0,h}; //6 points disk (obstacle)
+EndFor
+For i In {1:6}
+ Line(i) = {i,(i%6)+1}; //segments of the hexagone
+ Circle(10+i) = {10+i,10,10+(i%6)+1}; //circle arc of the disk
+EndFor
+
+// Segments of the hexagone (numbering does not depend on the decomposition)
+For k In {0:(NGammaExt-1)}
+ Physical Curve(30+k) = {k+1}; //segments Gamma k ext
+ Physical Point(40+k) = {k+1}; //noeud k-1,k
+ Physical Point(50+k) = {10+k+1}; //Noeuds Gamma Int
+EndFor
+
+// Numbering depends on the number of subdomains
+If (NDom==1)
+ Curve Loop(1) = {1:6}; //hexagone
+ Curve Loop(2) = {11:16}; // disk
+ Plane Surface(1) = {1,2}; // Hexagone minus disk (=propagation domain)
+
+ Physical Surface(0) = {1}; //Propagation domaine
+ Physical Curve(10) = {11:16}; // Boundary of disk (Gamma Int)
+EndIf
+
+// With 2 subdomaines, Omega_0 and Omega_1 share two boundaries in common
+If (NDom==2)
+ Line(21) = {1,11};
+ Line(22) = {4,14};
+ Curve Loop(1) = {1,2,3,22,-13,-12,-11,-21}; //Boundary of Omega 0
+ Plane Surface(1) = {1}; // Omega 0
+ Curve Loop(2) = {21,-16,-15,-14,-22,4,5,6}; //Boundary of Omega 1
+ Plane Surface(2) = {2}; //Omega 1
+
+ Physical Surface(0) = {1}; //Omega 0
+ Physical Surface(1) = {2}; //Omega 1
+
+ Physical Curve(10) = {11,12,13}; //Gamma Int 0
+ Physical Curve(11) = {14,15,16}; //Gamma Int 1
+
+ Physical Curve(20) = {21,22}; //Sigma_{0,1}
+EndIf
+
+If (NDom==3)
+ For i In {0:(NDom-1)}
+ Line(21+i) = {1+i*(NGammaExt/NDom),11+i*(NGammaExt/NDom)};
+ EndFor
+
+ Curve Loop(1) = {1,2,22,-12,-11,-21}; // Boundary of Omega 0
+ Plane Surface(1) = {1}; //Omega 0
+
+ Curve Loop(2) = {3,4,23,-14,-13,-22};
+ Plane Surface(2) = {2};
+
+ Curve Loop(3) = {21,-16,-15,-23,5,6};
+ Plane Surface(3) = {3};
+
+ For i In {0:(NDom-1)}
+ Physical Surface(i) = {i+1}; //Omega_i
+ Physical Curve(20+i) = {20+i+1}; //Sigma_{i, (i-1)}
+ Physical Curve(10+i) = {11 + 2*i, 12 + 2*i}; //Gamma Int of Omega_i
+ EndFor
+EndIf
+
+If (NDom==6)
+ For j In {1:NDom}
+ Line(20+j) = {j,10+j}; // Sigma
+ EndFor
+
+ For i In {1:(NDom-1)}
+ Curve Loop(i) = {i,20+i+1,-10-i,-20-i}; //Boundary Omega_i
+ Plane Surface(i) = {i}; //Omega_i
+ EndFor
+ Curve Loop(6) = {6,21,-16,-26}; //Boundary Omega_5
+ Plane Surface(6) = {6}; //Omega_5
+
+ For i In {0:(NDom-1)}
+ Physical Surface(i) = {i+1}; //Omega_i
+ Physical Curve(10+i) = {10+i+1}; //Gamma Interior of Omega_i
+ Physical Curve(20+i) = {20+i+1}; //Sigma_{i-1, i}
+ EndFor
+EndIf
+
+Solver.AutoMesh = 2; // auto mesh
diff --git a/DDM-Corner-Helmholtz-2D/src/ABC_main.pro b/DDM-Corner-Helmholtz-2D/src/ABC_main.pro
new file mode 100644
index 0000000000000000000000000000000000000000..7c743609aaca897873f0f87a595ea6354aa5eed0
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/src/ABC_main.pro
@@ -0,0 +1,325 @@
+DefineConstant[
+ //Input
+ alpha = {0, Min 0, Max 2*Pi, Step 0.1, Name "Input/Input/5Incident angle"},
+ // ABC
+ ABC_ORDER = {2, Choices {0="Order 0", 2="Order 2"}, Name "Input/ABC/0ABC order condition"},
+ CORNER_CONDITION = {2, Choices {1 ="Homog. Neumann", 2="Corner Correction"}, Name "Input/ABC/3Corner Condition", ReadOnly (ABC_ORDER == 0)},
+ // DDM
+ beta = {-kap*Cos[theta], ReadOnly 1, Name "Input/DDM/8beta parameter"},
+ // Solver
+ SOLVER = {"jacobi", Choices {"jacobi", "gmres", "print"}, Name "Input/IterativeSolver/0Solver"},
+ TOLlog10 = {-6, Max -1, Min -16, Step -1, Name "Input/IterativeSolver/1Tolerance (log10)"},
+ TOL = 10^(TOLlog10),
+ MAXIT = {10, Min 10, Max 10000, Step 1, Name "Input/IterativeSolver/2Max it"},
+ RESTART = {0, Min 0, Max 1000, Step 1, Name "Input/IterativeSolver/3Restart"},
+ //Output
+ ABC_DIRREL = {"out_ABC/", Name "Input/Output/01Output Directory"},
+ ABC_DIR = {StrCat[WorkingDir, ABC_DIRREL], ReadOnly 1, Visible 0, Name "Input/Output/Output Directory (Absolute)"}
+ ABC_PREFIX = {"", Name "Input/Output/05Prefix for filename"}
+];
+
+Function {
+ I[] = Complex[0.,1.]; // Pure imaginary "i"
+ alpha_vect[] = Vector[Cos[alpha],Sin[alpha],0]; // incidence vector
+ uInc[] = Complex[Cos[kap*(XYZ[]*alpha_vect[])],Sin[kap*(XYZ[]*alpha_vect[])]]; // Incident plane wave
+ //Exact solution for a cylindrical obstacle located at (0,0,0) of radius = rs and incident angle = alpha
+ uex[] = AcousticFieldSoftCylinder[XYZ[]]{kap, rs, alpha};
+}
+
+// Mono domain case
+Group{
+ Omega = Region[{(0:(NDom-1))}];
+ GammaExt = Region[{30:35}];
+ Sigma = Region[{20:25}];
+ dOmegaInt = Region[{10:15}];
+ dOmegaExt = Region[{GammaExt}];
+ ListGammaExt() = {}; // indices k of the segments
+ // Fourier or Neumann condition
+ For k In {0:NGammaExt-1}
+ ListGammaExt() +=k;
+ GammaExt~{k} = Region[(30+k)];
+ // End-points
+ l_left = (k-1+NGammaExt)%NGammaExt;
+ l_right = (k+1)%NGammaExt;
+ ListdGammaExt~{k}() = {l_left,l_right};
+ Apt~{k}~{l_left} = Region[(40 + k)];
+ Apt~{k}~{l_right} = Region[(40 + (k+1)%6)];
+ // Every end-points of Gamma_k
+ dGammaExt~{k} = Region[{Apt~{k}~{l_left},Apt~{k}~{l_right}}];
+ EndFor
+ dGammaExt = Region[{40:45}]; //every end-points
+ TrdOmegaInt = ElementsOf[Omega, OnOneSideOf dOmegaInt];
+}
+
+//DDM Case
+If (NDom == 2)
+ Group {
+ D() = {};
+ For i In {0:(NDom-1)}
+ Omega~{i} = Region[{i}];
+ D() += i;
+ // left = right = {1, 0}
+ j = (i+1)%NDom; // The other subdomain
+ D~{i} = {j};
+
+ GammaInt~{i} = Region[{(10+i)}];
+ NGammaExt~{i} = (NGammaExt/NDom); // Number of segments Gamma^i_k = dOmega_i cap Gamma
+ ListGammaExt~{i}() = {}; //Set of indices k such that Gamma^i_k is not empty
+ // Every subdomain has 3 Gamma^i_k :
+ // if i == 0 then k = {0,1,2}
+ // else i == 1 then k = {3,4,5}
+ For kk In {0:(NGammaExt~{i}-1)} // kk = 0,1,2
+ k = kk + 3*i; // k = 0,1,2 or 3,4,5
+ ListGammaExt~{i}() += k;
+ ListdGammaExt~{i}~{k}() = {}; // set of indices (j,l) of every end-points of Gamma^i_k
+ GammaExt~{i}~{k} = Region[{(30+k)}]; //Gamma^i_k
+ // Subdomain number of neightbor segment
+ If(kk == 0)
+ j_left = j;
+ Else
+ j_left = i;
+ EndIf
+ If(kk == 2)
+ j_right = j;
+ Else
+ j_right = i;
+ EndIf
+ // Indice of the previous/next segment (independant of subdomain number)
+ l_left = (k-1+NGammaExt)%NGammaExt;
+ l_right = (k+1)%NGammaExt;
+
+ // first end-point A^ij_kl of Gamma^i_k
+ Apt~{i}~{j_left}~{k}~{l_left} = Region[{(40+k)}];
+ dGammaExt~{i}~{j_left}~{k}~{l_left} = Region[{(40+k)}];
+ ListdGammaExt~{i}~{k}() += j_left; // j
+ ListdGammaExt~{i}~{k}() += l_left; // l
+
+ //second end-point A^ij_kl of Gamma^i_k
+ Apt~{i}~{j_right}~{k}~{l_right} = Region[{(40+(k+1)%NGammaExt)}];
+ dGammaExt~{i}~{j_right}~{k}~{l_right} = Region[{(40+(k+1)%NGammaExt)}];
+ ListdGammaExt~{i}~{k}() += j_right; // j
+ ListdGammaExt~{i}~{k}() += l_right; // l
+
+ //Set C^i_k of every end-points of Gamma^i_k
+ Cset~{i}~{k} = Region[{(40+k),(40+(k+1)%NGammaExt)}];
+ dGammaExt~{i}~{k} = Region[{(40+k),(40+(k+1)%NGammaExt)}];
+ EndFor
+
+ dOmegaInt~{i}= Region[{GammaInt~{i}}];
+ dOmegaExt~{i}= Region[{GammaExt~{i}~{3*i}, GammaExt~{i}~{1 + 3*i}, GammaExt~{i}~{2 + 3*i}}];
+ //Sigma_{i,j} = dOmega_i cap dOmega_j
+ Sigma~{i}~{j} = Region[{20}];
+
+ //2 end points on Sigma cap GammaExt
+ ListdSigmaExt~{i}~{j}() = {};
+ //First
+ k = 0 + 3*i;
+ l_left = (k - 1 + NGammaExt)%NGammaExt;
+ dSigmaExt~{i}~{j}~{0} = Region[{Apt~{i}~{j}~{k}~{l_left}}];
+ ListdSigmaExt~{i}~{j}() += j;
+ ListdSigmaExt~{i}~{j}() += l_left;
+ //Second
+ k = 2 + 3*i;
+ l_right = (k +1 )%NGammaExt;
+ dSigmaExt~{i}~{j}~{1} = Region[{Apt~{i}~{j}~{k}~{l_right}}];
+ ListdSigmaExt~{i}~{j}() += j;
+ ListdSigmaExt~{i}~{j}() += l_right;
+ // union
+ dSigmaExt~{i}~{j} = Region[{dSigmaExt~{i}~{j}~{0}, dSigmaExt~{i}~{j}~{1}}];
+
+ //2 end points on GammaInt
+ l = j;
+ ListdSigmaInt~{i}~{j}() = {};
+ dSigmaInt~{i}~{j}~{0} = Region[{(50)}];
+ ListdSigmaInt~{i}~{j}() += i; // k == i (6 sub dom)
+ ListdSigmaInt~{i}~{j}() += l; // l == j (6 sub dom)
+ dSigmaInt~{i}~{j}~{1} = Region[{(53)}];
+ ListdSigmaInt~{i}~{j}() += i; // k == i (6 sub dom)
+ ListdSigmaInt~{i}~{j}() += l; // l == j (6 sub dom)
+ dSigmaInt~{i}~{j} = Region[{dSigmaInt~{i}~{j}~{0}, dSigmaInt~{i}~{j}~{1}}];
+
+ dSigma~{i}~{j} = Region[{dSigmaExt~{i}~{j},dSigmaInt~{i}~{j}}];
+
+ Sigma~{i} = Region[{Sigma~{i}~{j}}];
+ EndFor
+ }
+EndIf
+
+If (NDom==3)
+ Group {
+ D() = {};
+ For i In {0:(NDom-1)}
+ Omega~{i} = Region[{i}];
+ D() += i;
+ left = (i-1+NDom)%NDom; //previous subdomain (counter-clowise orientation)
+ right = (i+1)%NDom; //next subdomain (counter-clowise orientation)
+ D~{i} = {left, right}; // neighbors subdomains
+
+ dOmegaInt~{i} = Region[{(10+i)}];
+ NGammaExt~{i} = (NGammaExt/NDom); // Number of Gamma^i_k (= 2)
+ ListGammaExt~{i}() = {}; //Indices k of these Gamma^i_k
+
+ For kk In {0:(NGammaExt~{i}-1)} // kk = 0,1
+ k = kk + 2*i; // k = [0,1] or [2,3] or [4,5]
+ ListGammaExt~{i}() += k;
+ ListdGammaExt~{i}~{k}() = {}; // indices (j,l) of the neightbor Gamma^i_k
+ GammaExt~{i}~{k} = Region[{(30+k)}]; //Gamma^i_k
+ // Subdomain number of neightbor segment
+ If(kk == 0)
+ j_left = left;
+ j_right = i;
+ EndIf
+ If(kk == 1)
+ j_left = i;
+ j_right = right;
+ EndIf
+ l_left = (k-1+NGammaExt)%NGammaExt;
+ l_right = (k+1)%NGammaExt;
+
+ //first end-point A^ij_kl of Gamma^i_k
+ Apt~{i}~{j_left}~{k}~{l_left} = Region[{(40+k)}];
+ ListdGammaExt~{i}~{k}() += j_left; // j
+ ListdGammaExt~{i}~{k}() += l_left; // l
+
+ //second noeud A^ij_kl de Gamma^i_k
+ Apt~{i}~{j_right}~{k}~{l_right} = Region[{(40+(k+1)%NGammaExt)}];
+ ListdGammaExt~{i}~{k}() += j_right; // j
+ ListdGammaExt~{i}~{k}() += l_right; // l
+
+ //ensemble C^i_k = noeuds bord Gamma^i_k
+ Cset~{i}~{k} = Region[{(40+k),(40+(k+1)%NGammaExt)}];
+ dGammaExt~{i}~{k} = Region[{(40+k),(40+(k+1)%NGammaExt)}];
+ EndFor
+ // Union
+ dOmegaExt~{i} = Region[{GammaExt~{i}~{2*i}, GammaExt~{i}~{1 + 2*i}}];
+
+ // Transmission boundaries
+ Sigma~{i}~{left} = Region[{(20 + i)}];
+ Sigma~{i}~{right} = Region[{(20 + right)}];
+ Sigma~{i} = Region[{Sigma~{i}~{left}, Sigma~{i}~{right}}];
+ // Unique End-point of Sigma_{ij} that also belons to Gamma
+ ListdSigmaExt~{i}~{left}() = {};
+ ListdSigmaExt~{i}~{right}() = {};
+ k_left = 2*i;
+ l_left = (k_left - 1 +NGammaExt )%NGammaExt;
+ k_right = 2*i +1 ;
+ l_right = (k_right + 1 )%NGammaExt;
+ dSigmaExt~{i}~{left}~{0} = Region[{Apt~{i}~{left}~{k_left}~{l_left}}];
+ ListdSigmaExt~{i}~{left}() += k_left;
+ ListdSigmaExt~{i}~{left}() += l_left;
+ dSigmaExt~{i}~{left} = Region[{dSigmaExt~{i}~{left}~{0}}];
+
+ dSigmaExt~{i}~{right}~{0} = Region[{Apt~{i}~{right}~{k_right}~{l_right}}];
+ ListdSigmaExt~{i}~{right}() += k_right;
+ ListdSigmaExt~{i}~{right}() += l_right;
+ dSigmaExt~{i}~{right} = Region[{dSigmaExt~{i}~{right}~{0}}];
+
+ ListdSigmaInt~{i}~{left}() = {};
+ dSigmaInt~{i}~{left}~{0} = Region[{(50 + 2*i)}];
+ ListdSigmaInt~{i}~{left}() += i; // Useless ?
+ ListdSigmaInt~{i}~{left}() += left; // Useless ?
+ dSigmaInt~{i}~{left} = Region[{dSigmaInt~{i}~{left}~{0}}];
+
+ ListdSigmaInt~{i}~{right}() = {};
+ dSigmaInt~{i}~{right}~{0} = Region[{(50 + 2*i + 1)}];
+ ListdSigmaInt~{i}~{right}() += i; // Useless ?
+ ListdSigmaInt~{i}~{right}() += right; // Useless ?
+ dSigmaInt~{i}~{right} = Region[{dSigmaInt~{i}~{right}~{0}}];
+
+ dSigma~{i}~{left} = Region[{dSigmaExt~{i}~{left},dSigmaInt~{i}~{left}}];
+ dSigma~{i}~{right} = Region[{dSigmaExt~{i}~{right},dSigmaInt~{i}~{right}}];
+
+ //Sigma i = Sigma i i-1 U Sigma i i+1
+ Sigma~{i} = Region[{Sigma~{i}~{left},Sigma~{i}~{right}}];
+ dSigmaExt~{i} = Region[{dSigmaExt~{i}~{left},dSigmaExt~{i}~{right}}];
+ dSigmaInt~{i} = Region[{dSigmaInt~{i}~{left},dSigmaInt~{i}~{right}}];
+ dSigma~{i} = Region[{dSigmaExt~{i},dSigmaInt~{i}}];
+ EndFor
+ }
+EndIf
+
+If (NDom==6)
+ Group {
+ D() = {};
+ For i In {0:(NDom-1)}
+ Omega~{i} = Region[{i}]; //Omega_i
+ D() += i;
+ left = (i-1+NDom)%NDom; // previous subdomain (counter-clockwise orientation)
+ right = (i+1)%NDom; //next subdomain (counter-clockwise orientation)
+ D~{i} = {left,right};
+
+ NGammaExt~{i} = (NGammaExt/NDom); // Number of segments Gamma^i_k (=1)
+ dOmegaInt~{i} = Region[{(10+i)}]; //Gamma i int
+ ListGammaExt~{i}() = {}; // index k of this Gamma^i_k and in this case k=i
+ k = i;
+ ListGammaExt~{i}() += k;
+ GammaExt~{i}~{k} = Region[{(30+k)}]; //Gamma i k ext
+ ListdGammaExt~{i}~{k}() = {}; // list of indices (j,l) for end-points A^{ij}_{kl} of Gamma^i_k
+ j_left = left;
+ l_left = left; // l = j
+ j_right = right;
+ l_right = right; //l =j
+ // first end-point A^ij_kl of Gamma^i_k
+ Apt~{i}~{j_left}~{k}~{l_left} = Region[{(40+k)}];
+ dGammaExt~{i}~{j_left}~{k}~{l_left} = Region[{(40+k)}];
+ ListdGammaExt~{i}~{k}() += j_left; // j
+ ListdGammaExt~{i}~{k}() += l_left; // l
+ //second end-point A^ij_kl of Gamma^i_k
+ Apt~{i}~{j_right}~{k}~{l_right} = Region[{(40+(k+1)%NGammaExt)}];
+ dGammaExt~{i}~{j_right}~{k}~{l_right} = Region[{(40+(k+1)%NGammaExt)}];
+ ListdGammaExt~{i}~{k}() += j_right; // j
+ ListdGammaExt~{i}~{k}() += l_right; // l
+ //Set C^i_k = end-points of Gamma^i_k
+ Cset~{i}~{k} = Region[{(40+k),(40+(k+1)%NGammaExt)}];
+ dGammaExt~{i}~{k} = Region[{(40+k),(40+(k+1)%NGammaExt)}];
+ // Union (here =) of gamma^i_k
+ dOmegaExt~{i}= Region[{GammaExt~{i}~{k}}];
+
+ //Sigma_{ij} = dOmega_i cap dOmega_j
+ // For the left subdomain
+ Sigma~{i}~{left} = Region[{(20+i)}];
+ ListdSigmaExt~{i}~{left}() = {}; // get k and l for provided i and j
+ dSigmaExt~{i}~{left}~{0} = Region[{Apt~{i}~{left}~{i}~{left}}];
+ ListdSigmaExt~{i}~{left}() += k; // k == i (6 sub dom)
+ ListdSigmaExt~{i}~{left}() += l_left; // l == left (6 sub dom)
+ dSigmaExt~{i}~{left} = Region[{dSigmaExt~{i}~{left}~{0}}];
+
+ ListdSigmaInt~{i}~{left}() = {}; // get k and l for provided i and j
+ dSigmaInt~{i}~{left}~{0} = Region[{(50+i)}];
+ ListdSigmaInt~{i}~{left}() += i; // k == i (6 sub dom)
+ ListdSigmaInt~{i}~{left}() += left; // l == left (6 sub dom)
+ dSigmaInt~{i}~{left} = Region[{dSigmaInt~{i}~{left}~{0}}];
+
+ dSigma~{i}~{left} = Region[{dSigmaExt~{i}~{left},dSigmaInt~{i}~{left}}];
+
+ // For the right subdomain
+ Sigma~{i}~{right} = Region[{(20+right)}];
+
+ ListdSigmaExt~{i}~{right}() = {}; // get k and l for provided i and j
+ dSigmaExt~{i}~{right}~{0} = Region[{Apt~{i}~{right}~{i}~{right}}];
+ ListdSigmaExt~{i}~{right}() += i; // k == i (6 sub dom)
+ ListdSigmaExt~{i}~{right}() += right; // l == right (6 sub dom)
+ dSigmaExt~{i}~{right} = Region[{dSigmaExt~{i}~{right}~{0}}];
+
+ ListdSigmaInt~{i}~{right}() = {}; // get k and l for provided i and jerer k et l pour i et j donnes
+ dSigmaInt~{i}~{right}~{0} = Region[{(50+(i+1)%NDom)}];
+ ListdSigmaInt~{i}~{right}() += i; // k == i (6 sub dom)
+ ListdSigmaInt~{i}~{right}() += right; // l == right (6 sub dom)
+ dSigmaInt~{i}~{right} = Region[{dSigmaInt~{i}~{right}~{0}}];
+
+ dSigma~{i}~{right} = Region[{dSigmaExt~{i}~{right},dSigmaInt~{i}~{right}}];
+
+ //Sigma i = Sigma_{i, left} U Sigma_{i,right}
+ Sigma~{i} = Region[{Sigma~{i}~{left},Sigma~{i}~{right}}];
+ dSigmaExt~{i} = Region[{dSigmaExt~{i}~{left},dSigmaExt~{i}~{right}}];
+ dSigmaInt~{i} = Region[{dSigmaInt~{i}~{left},dSigmaInt~{i}~{right}}];
+ dSigma~{i} = Region[{dSigmaExt~{i},dSigmaInt~{i}}];
+ EndFor
+ }
+EndIf
+
+
+//===========================
+Include "ABC_MonoDomain.pro";
+Include "ABC_DDM.pro";
+//===========================
diff --git a/DDM-Corner-Helmholtz-2D/src/Common.pro b/DDM-Corner-Helmholtz-2D/src/Common.pro
new file mode 100644
index 0000000000000000000000000000000000000000..e1a1a739b4ff96abddb3c821d9584275da9d5cb8
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/src/Common.pro
@@ -0,0 +1,23 @@
+// Common quantities for every resoltion
+Jacobian {
+ { Name JVol ; Case { { Region All ; Jacobian Vol ; } } }
+ { Name JSur ; Case { { Region All ; Jacobian Sur ; } } }
+ { Name JLin ; Case { { Region All ; Jacobian Lin ; } } }
+}
+
+Integration {
+ { Name I1 ;
+ Case {
+ { Type Gauss ;
+ Case {
+ { GeoElement Point ; NumberOfPoints 1 ; }
+ { GeoElement Line ; NumberOfPoints 4 ; }
+ { GeoElement Triangle ; NumberOfPoints 6 ; }
+ { GeoElement Quadrangle ; NumberOfPoints 7 ; }
+ { GeoElement Tetrahedron ; NumberOfPoints 15 ; }
+ { GeoElement Hexahedron ; NumberOfPoints 34 ; }
+ }
+ }
+ }
+ }
+}
\ No newline at end of file
diff --git a/DDM-Corner-Helmholtz-2D/src/TC_Decomposition.pro b/DDM-Corner-Helmholtz-2D/src/TC_Decomposition.pro
new file mode 100644
index 0000000000000000000000000000000000000000..a5ec9cf1ad701387b98acbc050ba56d631e280c9
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/src/TC_Decomposition.pro
@@ -0,0 +1,46 @@
+Function{
+ myD = {} ; // the domains that I (as a MPI process) am in charge of
+
+ ListOfFields_g = {};
+ ListOfConnectedFields_g = {};
+
+// myD~{idom} : list of neightbor domain
+ For idom In {0:(NDom-1)}
+ myD~{idom} = {};
+ If (idom % MPI_Size == MPI_Rank)
+ myD() += D(idom); // D(idom) = index of subdomain (indexing could be different than 0,1,2,...)
+ myD~{idom} += D~{idom}();
+ EndIf
+ EndFor
+
+// Auxiliary functions
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+
+ For r In {0:(NDelta~{i}~{j}-1)}
+ rj = NDelta~{i}~{j}-1-r;
+
+ tag_g~{j}~{i}~{r} = 100 + j * 30 + r + i;
+ tag_g~{i}~{j}~{rj} = 100 + i * 30 + rj + j;
+
+ // Fields received / Needed
+ ListOfFields_g() += tag_g~{i}~{j}~{rj};
+ g~{i}~{j}~{rj}[ Delta~{j}~{i}~{rj} ] = ComplexScalarField[XYZ[]]{ tag_g~{i}~{j}~{rj} };
+
+ // Fields sent
+ ListOfConnectedFields_g() += 1;
+ ListOfConnectedFields_g() += tag_g~{j}~{i}~{r};
+
+ // Phi functions before jacobi
+ tag_phiInit~{i}~{j}~{r} = 10000 + i * 30 + rj + j;
+ phiInit~{i}~{j}~{r}[ Delta~{i}~{j}~{r} ] = ComplexScalarField[XYZ[]]{ tag_phiInit~{i}~{j}~{r} };
+ EndFor
+ EndFor
+ EndFor
+
+ //MPI_Printf["ListOfFields = ", ListOfFields_g(),ListOfFields_h()];
+ //MPI_Printf["ListOfConnectedFields = ", ListOfConnectedFields_g(),ListOfConnectedFields_h()];
+}
diff --git a/DDM-Corner-Helmholtz-2D/src/TC_WaveGuide.pro b/DDM-Corner-Helmholtz-2D/src/TC_WaveGuide.pro
new file mode 100644
index 0000000000000000000000000000000000000000..811afd663f401fe74c43e5ffae723f734fefd025
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/src/TC_WaveGuide.pro
@@ -0,0 +1,90 @@
+Constraint {
+ {Name DirichletIncoming; Type Assign; Case{{Region GammaIncoming; Value uInc[]; } } }
+ {Name DirichletOutgoing; Type Assign; Case{{Region GammaOutgoing; Value 0.; } } }
+ {Name DirichletTop; Type Assign; Case{{Region GammaTop; Value 0.; } } }
+ {Name DirichletBottom; Type Assign; Case{{Region GammaBottom; Value 0.; } } }
+}
+
+FunctionSpace{
+ {Name H_grad; Type Form0;
+ BasisFunction{
+ {Name u; NameOfCoef ui; Function BF_Node;
+ Support Region[{Omega, GammaIncoming, GammaOutgoing, GammaTop, GammaBottom}]; Entity NodesOf[All];}
+ }
+ If(StrCmp(INCOMING_CONDITION, "Dirichlet") == 0)
+ Constraint{
+ {NameOfCoef ui; EntityType NodesOf; NameOfConstraint DirichletIncoming;}
+ }
+ EndIf
+ If(StrCmp(OUTGOING_CONDITION, "Dirichlet") == 0)
+ Constraint{
+ {NameOfCoef ui; EntityType NodesOf; NameOfConstraint DirichletOutgoing;}
+ }
+ EndIf
+ If(StrCmp(TOP_CONDITION, "Dirichlet") == 0)
+ Constraint{
+ {NameOfCoef ui; EntityType NodesOf; NameOfConstraint DirichletTop;}
+ }
+ EndIf
+ If(StrCmp(BOTTOM_CONDITION, "Dirichlet") == 0)
+ Constraint{
+ {NameOfCoef ui; EntityType NodesOf; NameOfConstraint DirichletBottom;}
+ }
+ EndIf
+ }
+}
+
+Formulation {
+ { Name MonoDomain; Type FemEquation;
+ Quantity{
+ { Name u ; Type Local; NameOfSpace H_grad;}
+ }
+ Equation{
+ //Helmholtz equation
+ Galerkin{[Dof{Grad u}, {Grad u}];
+ In Omega; Jacobian JVol; Integration I1;}
+ Galerkin{[-kap^2*Dof{u}, {u}];
+ In Omega; Jacobian JVol; Integration I1;}
+ //Sommerfeld radiation condition (approx.)
+ If(StrCmp(OUTGOING_CONDITION, "Fourier") == 0)
+ Galerkin{[-I[]*kap*Dof{u}, {u}];
+ In GammaOutgoing; Jacobian JSur; Integration I1;}
+ EndIf
+ // Incoming wave is enforced through a Fourier-type condition
+ If(StrCmp(INCOMING_CONDITION, "Fourier") == 0)
+ Galerkin{[-I[]*kap*Dof{u}, {u}];
+ In GammaIncoming; Jacobian JSur; Integration I1;}
+ Galerkin{[-(-dx_uInc[]-I[]*kap*uInc[]), {u}];
+ In GammaIncoming; Jacobian JSur; Integration I1;}
+ EndIf
+ }
+ }
+}
+
+Resolution{
+ {Name MonoDomain;
+ System{ {Name A; NameOfFormulation MonoDomain; Type Complex; } }
+ Operation{
+ CreateDir[TC_DIR];
+ Generate[A];
+ Solve[A];
+ PostOperation[MonoDomain];
+ }
+ }
+}
+
+PostProcessing{
+ {Name MonoDomain; NameOfFormulation MonoDomain;
+ Quantity {
+ {Name u; Value {Local { [{u}] ; In Omega; Jacobian JVol; }}}
+ }
+ }
+}
+
+PostOperation{
+ {Name MonoDomain; NameOfPostProcessing MonoDomain;
+ Operation {
+ Print [u, OnElementsOf Omega, File StrCat[TC_DIR, StrCat[TC_PREFIX_,"u_mono.pos"]]];
+ }
+ }
+}
diff --git a/DDM-Corner-Helmholtz-2D/src/TC_WaveGuide_DDM.pro b/DDM-Corner-Helmholtz-2D/src/TC_WaveGuide_DDM.pro
new file mode 100644
index 0000000000000000000000000000000000000000..4e07efb190974857b507f64ae0b06b72e6b02339
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/src/TC_WaveGuide_DDM.pro
@@ -0,0 +1,414 @@
+Function{
+ //Angles
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ theta~{i}[] = ScalarField[XYZ[]]{i};
+ EndFor
+}
+
+Group {
+ TrGammaIncoming = ElementsOf[Omega, OnOneSideOf GammaIncoming];
+}
+
+Constraint {
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ {Name DirichletIncoming~{i}; Type Assign; Case{{Region GammaIncoming~{i}; Value $PhysicalSource?uInc[]:0.; } } }
+ {Name DirichletTop~{i}; Type Assign; Case{{Region GammaTop~{i}; Value 0.; } } }
+ {Name DirichletBottom~{i}; Type Assign; Case{{Region GammaBottom~{i}; Value 0.; } } }
+ {Name DirichletOutgoing~{i}; Type Assign; Case{{Region GammaOutgoing~{i}; Value 0. ;} } }
+ EndFor
+}
+
+FunctionSpace{
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ {Name H_grad~{i}; Type Form0;
+ BasisFunction{
+ {Name u~{i}; NameOfCoef ui; Function BF_Node;
+ Support Region[{Omega~{i}, GammaOutgoing~{i}, GammaIncoming~{i}, GammaTop~{i}, GammaBottom~{i}, Delta~{i}}]; Entity NodesOf[All];}
+ }
+ // Incoming wave if enforced as Dirichlet condition
+ If(StrCmp(INCOMING_CONDITION, "Dirichlet") == 0)
+ Constraint{
+ {NameOfCoef ui; EntityType NodesOf; NameOfConstraint DirichletIncoming~{i};}
+ }
+ EndIf
+ If(StrCmp(TOP_CONDITION, "Dirichlet") == 0)
+ Constraint{
+ {NameOfCoef ui; EntityType NodesOf; NameOfConstraint DirichletTop~{i};}
+ }
+ EndIf
+ If(StrCmp(BOTTOM_CONDITION, "Dirichlet") == 0)
+ Constraint{
+ {NameOfCoef ui; EntityType NodesOf; NameOfConstraint DirichletBottom~{i};}
+ }
+ EndIf
+ If(StrCmp(OUTGOING_CONDITION, "Dirichlet") == 0)
+ Constraint{
+ {NameOfCoef ui; EntityType NodesOf; NameOfConstraint DirichletOutgoing~{i};}
+ }
+ EndIf
+ }
+
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ For r In {0:(NDelta~{i}~{j}-1)}
+ {Name H_g~{j}~{i}~{r}; Type Form0;
+ BasisFunction{
+ {Name g~{j}~{i}~{r}; NameOfCoef gj; Function BF_Node;
+ Support Region[{Delta~{i}~{j}~{r}}];Entity NodesOf[All];}
+ }
+ }
+ {Name Hphi_grad~{i}~{j}~{r}; Type Form0;
+ BasisFunction{
+ {Name phi~{i}~{j}~{r}; NameOfCoef phiij; Function BF_Node;
+ Support Region[{Delta~{i}~{j}~{r}, dDelta~{i}~{j}~{r}}];Entity NodesOf[All];}
+ }
+ }
+ {Name Hpsi_grad~{i}~{j}~{r}; Type Form0;
+ BasisFunction{
+ {Name psi~{i}~{j}~{r}; NameOfCoef psiji; Function BF_Node;
+ Support Region[{Delta~{i}~{j}~{r}, dDelta~{i}~{j}~{r}}];Entity NodesOf[All];}
+ }
+ }
+ EndFor
+ EndFor
+ EndFor
+}
+
+Formulation {
+ { Name DDM; Type FemEquation;
+ Quantity{
+ { Name u ; Type Local; NameOfSpace H_grad;}
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ { Name u~{i} ; Type Local; NameOfSpace H_grad~{i};}
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ For r In {0:(NDelta~{i}~{j}-1)}
+ { Name phi~{i}~{j}~{r} ; Type Local; NameOfSpace Hphi_grad~{i}~{j}~{r};}
+ { Name psi~{i}~{j}~{r} ; Type Local; NameOfSpace Hpsi_grad~{i}~{j}~{r};}
+ EndFor
+ EndFor
+ EndFor
+ }
+ Equation{
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ //copy u~{i} in u
+ Galerkin{[Dof{u}, {u}];
+ In Omega~{i}; Jacobian JVol; Integration I1;}
+ Galerkin{[-Dof{u~{i}}, {u}];
+ In Omega~{i}; Jacobian JVol; Integration I1;}
+
+ //Helmholtz equation
+ Galerkin{[Dof{Grad u~{i}}, {Grad u~{i}}];
+ In Omega~{i}; Jacobian JVol; Integration I1;}
+ Galerkin{[-kap^2*Dof{u~{i}}, {u~{i}}];
+ In Omega~{i}; Jacobian JVol; Integration I1;}
+ Galerkin{[-I[]*kap*Dof{u~{i}}, {u~{i}}];
+ In GammaOutgoing~{i}; Jacobian JSur; Integration I1;}
+
+ // Incoming wave is enforced through a Fourier-type condition
+ If(StrCmp(INCOMING_CONDITION, "Fourier") == 0)
+ Galerkin{[-I[]*kap*Dof{u~{i}}, {u~{i}}];
+ In GammaIncoming~{i}; Jacobian JSur; Integration I1;}
+ Galerkin{[$PhysicalSource?-(-dx_uInc[]-I[]*kap*uInc[]):0, {u~{i}}];
+ In GammaIncoming~{i}; Jacobian JSur; Integration I1;}
+ EndIf
+
+ //Transmission condition
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ For r In {0:(NDelta~{i}~{j}-1)}
+ rj = (NDelta~{i}~{j}-1) - r; // Index from the other side
+ Galerkin{[-I[]*kap*Dof{phi~{i}~{j}~{r}}, {u~{i}}];
+ In Delta~{i}~{j}~{r}; Jacobian JSur; Integration I1;}
+ Galerkin{[$TCSource?-g~{i}~{j}~{rj}[]:0., {u~{i}}];
+ In Delta~{i}~{j}~{r}; Jacobian JSur; Integration I1;}
+
+ //Rij(ui)
+ Galerkin{[Dof{phi~{i}~{j}~{r}}, {phi~{i}~{j}~{r}}];
+ In Delta~{i}~{j}~{r}; Jacobian JSur; Integration I1;}
+ Galerkin{[-Dof{u~{i}}, {phi~{i}~{j}~{r}}];
+ In Delta~{i}~{j}~{r}; Jacobian JSur; Integration I1;}
+
+ //Rji(ui)
+ Galerkin{[Dof{psi~{i}~{j}~{r}}, {psi~{i}~{j}~{r}}];
+ In Delta~{i}~{j}~{r}; Jacobian JSur; Integration I1;}
+ Galerkin{[-Dof{u~{i}}, {psi~{i}~{j}~{r}}];
+ In Delta~{i}~{j}~{r}; Jacobian JSur; Integration I1;}
+
+ If (TC_ORDER==2)
+ //Rij(ui)
+ Galerkin{[1/(2*kap*kap)*Dof{d phi~{i}~{j}~{r}}, {d phi~{i}~{j}~{r}}];
+ In Delta~{i}~{j}~{r}; Jacobian JSur; Integration I1;}
+
+ //Rji(ui)
+ Galerkin{[1/(2*kap*kap)*Dof{d psi~{i}~{j}~{r}}, {d psi~{i}~{j}~{r}}];
+ In Delta~{i}~{j}~{r}; Jacobian JSur; Integration I1;}
+
+ If(CORNER_CONDITION == 2)
+ //Loop on Corner points (possibly empty list!)
+ For index In {0:#ListdDelta~{i}~{j}~{r}()-1}
+ s = ListdDelta~{i}~{j}~{r}(index);
+ //Rij(ui)
+ Galerkin{[-I[]/(4*kap)*(Cos[theta~{i}[]/2] + Cos[theta~{i}[]]/Cos[theta~{i}[]/2])*Dof{phi~{i}~{j}~{r}}, {phi~{i}~{j}~{r}}];
+ In Q~{i}~{j}~{r}~{s}; Jacobian JLin; Integration I1;}
+
+ Galerkin{[-I[]/(4*kap)*(Cos[theta~{i}[]/2] - Cos[theta~{i}[]]/Cos[theta~{i}[]/2])*Dof{phi~{i}~{j}~{s}}, {phi~{i}~{j}~{r}}];
+ In Q~{i}~{j}~{r}~{s}; Jacobian JLin; Integration I1;}
+
+ //Rji(ui) (same but conjugated coefficient)
+ Galerkin{[-I[]/(4*kap)*(-Cos[theta~{i}[]/2] - Cos[theta~{i}[]]/Cos[theta~{i}[]/2])*Dof{psi~{i}~{j}~{r}}, {psi~{i}~{j}~{r}}];
+ In Q~{i}~{j}~{r}~{s}; Jacobian JLin; Integration I1;}
+
+ Galerkin{[-I[]/(4*kap)*(-Cos[theta~{i}[]/2] + Cos[theta~{i}[]]/Cos[theta~{i}[]/2])*Dof{psi~{i}~{j}~{s}}, {psi~{i}~{j}~{r}}];
+ In Q~{i}~{j}~{r}~{s}; Jacobian JLin; Integration I1;}
+ EndFor
+ EndIf
+ EndIf
+ EndFor
+ EndFor
+ EndFor
+ }
+ }
+
+ //Resolution g
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ For r In {0:(NDelta~{i}~{j}-1)}
+ rj = (NDelta~{i}~{j}-1) - r; // Index from the other side
+ { Name G~{j}~{i}~{r}; Type FemEquation;
+ Quantity{
+ { Name u~{i} ; Type Local; NameOfSpace H_grad~{i};}
+ { Name g~{j}~{i}~{r} ; Type Local; NameOfSpace H_g~{j}~{i}~{r};}
+ { Name phi~{i}~{j}~{r} ; Type Local; NameOfSpace Hphi_grad~{i}~{j}~{r};}
+ { Name psi~{i}~{j}~{r} ; Type Local; NameOfSpace Hpsi_grad~{i}~{j}~{r};}
+ }
+ Equation{
+ Galerkin{[Dof{g~{j}~{i}~{r}},{g~{j}~{i}~{r}}];
+ In Delta~{i}~{j}~{r}; Jacobian JSur; Integration I1;}
+
+ Galerkin{[$TCSource?+g~{i}~{j}~{rj}[]:0.,{g~{j}~{i}~{r}}];
+ In Delta~{j}~{i}~{rj}; Jacobian JSur; Integration I1;}
+
+ Galerkin{[I[]*kap*{phi~{i}~{j}~{r}},{g~{j}~{i}~{r}}];
+ In Delta~{i}~{j}~{r}; Jacobian JSur; Integration I1;}
+
+ Galerkin{[I[]*kap*{psi~{i}~{j}~{r}},{g~{j}~{i}~{r}}];
+ In Delta~{i}~{j}~{r}; Jacobian JSur; Integration I1;}
+ }
+ }
+ EndFor
+ EndFor
+ EndFor
+}
+
+Resolution{
+ {Name DDM;
+ System{
+ {Name DDM; NameOfFormulation DDM; Type Complex; }
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ For r In {0:(NDelta~{i}~{j}-1)}
+ {Name G~{j}~{i}~{r}; NameOfFormulation G~{j}~{i}~{r}; Type Complex; }
+ EndFor
+ EndFor
+ EndFor
+ }
+ Operation{
+ // Initialisation
+ CreateDir[TC_DIR];
+ //Angles between segments
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ GmshRead[StrCat[WorkingDir, Sprintf["aux/TC_Theta_%g.pos",i+1]]];
+ EndFor
+ Evaluate[$PhysicalSource = 1];
+ Evaluate[$TCSource = 0];
+ UpdateConstraint[DDM, GammaIncoming, Assign];
+ Generate[DDM];
+ Solve[DDM];
+
+ Evaluate[$ItCount = 0];
+ If(PRINT_PHI)
+ //Iteration 0 value
+ PostOperation[Phi_Init];
+ EndIf
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ For r In {0:(NDelta~{i}~{j}-1)}
+ Generate[G~{j}~{i}~{r}];
+ Solve[G~{j}~{i}~{r}];
+ PostOperation[G~{j}~{i}~{r}];
+ EndFor
+ EndFor
+ EndFor
+ Evaluate[$PhysicalSource = 0];
+ Evaluate[$TCSource = 1];
+ If(StrCmp(INCOMING_CONDITION, "Dirichlet") == 0)
+ UpdateConstraint[DDM, GammaIncoming, Assign];
+ GenerateRHSGroup[DDM, Region[{TrGammaIncoming}]];
+ Else
+ GenerateRHSGroup[DDM, Region[{GammaIncoming}]];
+ EndIf
+
+ IterativeLinearSolver["I-A",SOLVER, TOL, MAXIT, RESTART, {ListOfFields_g()}, {ListOfConnectedFields_g()}, {}]
+ {
+ GenerateRHSGroup[DDM, Region[{Sigma}]];
+ SolveAgain[DDM];
+
+ Evaluate[$ItCount=$ItCount+1];
+ If(PRINT_PHI)
+ PostOperation[Phi];
+ EndIf
+
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ For r In {0:(NDelta~{i}~{j}-1)}
+ GenerateRHSGroup[G~{j}~{i}~{r}, Region[{Delta~{i}~{j}~{r}}]];
+ SolveAgain[G~{j}~{i}~{r}];
+ EndFor
+ EndFor
+ EndFor
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ For r In {0:(NDelta~{i}~{j}-1)}
+ PostOperation[G~{j}~{i}~{r}];
+ EndFor
+ EndFor
+ EndFor
+
+ }
+ // Compute solution
+ Evaluate[$PhysicalSource = 1];
+ Evaluate[$TCSource = 1];
+ If(StrCmp(INCOMING_CONDITION, "Dirichlet") == 0)
+ UpdateConstraint[DDM, GammaIncoming, Assign];
+ GenerateRHSGroup[DDM, Region[{Delta, TrGammaIncoming}]];
+ Else
+ GenerateRHSGroup[DDM, Region[{Delta, GammaIncoming}]];
+ EndIf
+ SolveAgain[DDM];
+ PostOperation[DDM];
+ }
+ }
+}
+
+PostProcessing{
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ For r In {0:(NDelta~{i}~{j}-1)}
+ {Name G~{j}~{i}~{r}; NameOfFormulation G~{j}~{i}~{r};
+ Quantity {
+ {Name g~{j}~{i}~{r}; Value {Local { [{g~{j}~{i}~{r}}] ; In Delta~{i}~{j}~{r}; Jacobian JSur; }}}
+ }
+ }
+ EndFor
+ EndFor
+ EndFor
+
+ {Name DDM; NameOfFormulation DDM;
+ Quantity {
+ {Name u_ddm; Value {
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ Local { [{u~{i}}] ; In Omega~{i}; Jacobian JVol; }
+ EndFor
+ }
+ }
+ }
+ }
+
+ {Name Phi_Init; NameOfFormulation DDM;
+ Quantity {
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ For r In {0:(NDelta~{i}~{j}-1)}
+ {Name phiInit~{i}~{j}~{r}; Value {
+ Local { [{phi~{i}~{j}~{r}}] ; In Delta~{i}~{j}~{r}; Jacobian JSur; }
+ } }
+ EndFor
+ EndFor
+ EndFor
+ }
+ }
+ {Name Phi; NameOfFormulation DDM;
+ Quantity {
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ For r In {0:(NDelta~{i}~{j}-1)}
+ {Name phi~{i}~{j}~{r}; Value {
+ Local { [{phi~{i}~{j}~{r}}+ phiInit~{i}~{j}~{r}[]] ; In Delta~{i}~{j}~{r}; Jacobian JSur; }
+ } }
+ EndFor
+ EndFor
+ EndFor
+ }
+ }
+}
+
+PostOperation{
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ For r In {0:(NDelta~{i}~{j}-1)}
+ {Name G~{j}~{i}~{r}; NameOfPostProcessing G~{j}~{i}~{r};
+ Operation { Print [g~{j}~{i}~{r}, OnElementsOf Delta~{i}~{j}~{r}, StoreInField tag_g~{j}~{i}~{r}];}
+ }
+ EndFor
+ EndFor
+ EndFor
+
+ {Name DDM; NameOfPostProcessing DDM;
+ Operation {
+ Print [u_ddm, OnElementsOf Omega, File StrCat[TC_DIR,StrCat[TC_PREFIX_,"u_ddm.pos"]]];
+ }
+ }
+
+ {Name Phi_Init; NameOfPostProcessing Phi_Init;
+ Operation {
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ For r In {0:(NDelta~{i}~{j}-1)}
+ Print [phiInit~{i}~{j}~{r}, OnElementsOf Delta~{i}~{j}~{r}, StoreInField tag_phiInit~{i}~{j}~{r}];
+ EndFor
+ EndFor
+ EndFor
+ }
+ }
+ {Name Phi; NameOfPostProcessing Phi;
+ Operation {
+ For ii In {0:#myD()-1}
+ i = myD(ii);
+ For jj In {0:#myD~{i}()-1}
+ j = myD~{i}(jj);
+ For r In {0:(NDelta~{i}~{j}-1)}
+ Print [phi~{i}~{j}~{r}, OnElementsOf Delta~{i}~{j}~{r}, Format SimpleTable, AppendExpressionToFileName $ItCount, File >> StrCat[TC_DIR,StrCat[TC_PREFIX_,Sprintf["phi_%g_%g_%g.pos", i,j,r]]]];
+ EndFor
+ EndFor
+ EndFor
+ }
+ }
+}
diff --git a/DDM-Corner-Helmholtz-2D/src/TC_main.data b/DDM-Corner-Helmholtz-2D/src/TC_main.data
new file mode 100644
index 0000000000000000000000000000000000000000..7fbab63bb693ca329506f7e024463a86d6df5f58
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/src/TC_main.data
@@ -0,0 +1,36 @@
+DefineConstant[
+ L = {10, Min 10, Max 1000, Step 0.1, Name "Input/05Geometry/10X-width"},
+ l = {10, Min 5, Max 100, Step 0.1, Name "Input/05Geometry/11Y-width"},
+ TC_BROKEN_LINE = {1, Choices{1="Broken Line", 0="Straight Line"}, Name "Input/05Geometry/15Type of border line"},
+ dx = {1, Min 0.1, Max L/4, Step 0.1, Name "Input/05Geometry/X-coord. of the pick point", Visible TC_BROKEN_LINE},
+ dy = {2, Min 0.1, Max l/2-0.1, Step 0.1, Name "Input/05Geometry/Y-coord. of bottom point", Visible TC_BROKEN_LINE},
+
+ INCOMING_CONDITION = {"Fourier", Choices {"Dirichlet", "Fourier"}, Name "Input/10Boundary Conditions/1Incoming (left)"},
+ OUTGOING_CONDITION = {"Fourier", Choices {"Dirichlet", "Neumann", "Fourier"}, Name "Input/10Boundary Conditions/2Outgoing (right, =0)"},
+ TOP_CONDITION = {"Neumann", Choices {"Dirichlet", "Neumann"}, Name "Input/10Boundary Conditions/3Top (=0)"},
+ BOTTOM_CONDITION = {"Neumann", Choices {"Dirichlet", "Neumann"}, Name "Input/10Boundary Conditions/4Bottom (=0)"},
+
+
+ kap = {Pi, Min 1, Max 30, Step 0.1, Name "Input/15Input/0Wavenumber"},
+ INCIDENT_WAVE = {"Plane Wave", Choices {"Eigenmode", "Plane Wave"}, Name "Input/15Input/2Type of incident Wave"},
+ alpha = {0, Min 0, Max 2*Pi, Step 0.1, Name "Input/15Input/3Incident angle", Visible (!StrCmp(INCIDENT_WAVE,"Plane Wave"))},
+ m_mode = {1, Min 0, Max 1000, Step 1, Name "Input/15Input/3Mode number", Visible (!StrCmp(INCIDENT_WAVE, "Eigenmode"))},
+
+ NLambda = {15, Min 10, Max 100, Step 1, Name "Input/Mesh/NLambda"},
+ h = {2*Pi/NLambda/kap, ReadOnly 1, Name "Input/Mesh/h"},
+
+ TC_ORDER = {2, Choices {0="Order 0", 2="Order 2"}, Name "Input/01DDM/05TC order"},
+ CORNER_CONDITION = {(!TC_BROKEN_LINE)?0:2, Choices {0 = "Dirichlet", 1="Homog. Neumann", 2="Corner Correction"}, Name "Input/01DDM/10Corner Condition", ReadOnly (TC_ORDER == 0 || !TC_BROKEN_LINE)},
+ NDom = {2, Choices {2}, ReadOnly 1, Visible 0, Name "Input/01DDM/15N sub domain"},
+
+ TC_DIRREL = {"out_TC/", Name "Input/Output/0Directory"},
+ TC_DIR = {StrCat[WorkingDir,TC_DIRREL], Visible 0, ReadOnly 1, Name "Input/Output/Output Directory (Absolute)"},
+ TC_PREFIX = {"", Name "Input/Output/05Prefix for filename"},
+ PRINT_PHI = {0, Choices {0,1}, Name "Input/Output/10Print Every Phi" },
+
+ SOLVER = {"jacobi", Choices {"jacobi", "gmres", "print"}, Name "Input/IterativeSolver/0Solver"},
+ TOLlog10 = {-6, Max -1, Min -16, Step -1, Name "Input/IterativeSolver/1Tolerance (log10)"},
+ TOL = 10^(TOLlog10),
+ MAXIT = {10, Min 10, Max 10000, Step 1, Name "Input/IterativeSolver/2Max it"},
+ RESTART = {0, Min 0, Max 1000, Step 1, Name "Input/IterativeSolver/3Restart"}
+];
diff --git a/DDM-Corner-Helmholtz-2D/src/TC_main.geo b/DDM-Corner-Helmholtz-2D/src/TC_main.geo
new file mode 100644
index 0000000000000000000000000000000000000000..dbdfcb1e89c75978d81b21e17a5de0dab83ca301
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/src/TC_main.geo
@@ -0,0 +1,72 @@
+//Rectangle separe en deux avec un coin
+
+//4 sommets
+Point(1) = {L, l/2, 0,h};
+Point(2) = {0, l/2, 0,h};
+Point(3) = {0, -l/2,0,h};
+Point(4) = {L, -l/2,0,h};
+
+dx_geo = TC_BROKEN_LINE?dx:0;
+dy_geo = TC_BROKEN_LINE?dy:l/2-1;
+//5 points interface
+Point(11) = {L/2, l/2, 0,h};
+Point(12) = {L/2, dy_geo,0,h};
+Point(13) = {L/2+dx_geo,0, 0,h}; //pointe
+Point(14) = {L/2,-dy_geo, 0,h};
+Point(15) = {L/2,-l/2, 0,h};
+// Point{13} In Surface{1}; //force pointe a etre noeud du maillage
+
+Line(2) = {2,3}; //segments bords rectangle
+Line(4) = {4,1}; //segments bords rectangle
+
+Line(21) = {11,2}; // Gamma Top inter. Omega_1
+Line(24) = {3,15}; // Gamma Bottom inter. Omega_1
+
+Line(22) = {1,11}; // Gamma Top inter. Omega_2
+Line(25) = {15,4}; // Gamma Bottom inter. Omega_2
+
+Line(30) = {11,12}; //interface Sigma
+Line(31) = {12,13};
+Line(32) = {13,14};
+Line(33) = {14,15};
+
+
+Curve Loop(1) = {-33,-32,-31,-30,21,2,24}; //bord Omega1
+Plane Surface(1) = {1}; //Omega1
+
+Curve Loop(2) = {4,22,30,31,32,33,25}; //bord Omega2
+Plane Surface(2) = {2}; //Omega2
+
+Physical Surface(0) = {1}; //Omega1
+Physical Surface(1) = {2}; //Omega2
+
+Physical Curve(31) = {2}; // Left Boundary (incoming)
+Physical Curve(33) = {4}; // Right Boundary (outcoming)
+
+Physical Curve(100) = {21}; // Gamma_Top on Omega_1
+Physical Curve(101) = {22}; // Gamma_Top on Omega_2
+
+Physical Curve(200) = {24}; // Gamma_Bottom on Omega_1
+Physical Curve(201) = {25}; // Gamma_Bottom on Omega_2
+
+For i In {0:3}
+ Physical Point(40+i) = {i+1}; //noeuds Gamma
+ Physical Point(50+i) = {10+i+1}; //noeuds Sigma
+ Physical Curve(20+i) = {30+i}; //interface Sigma
+EndFor
+Physical Point(54) = {15};
+
+
+// Due to TC_main.geo particular case, Mesh mush not be automatically computed
+Printf(OnelabAction);
+Solver.AutoMesh = -1; // the .geo file creates the mesh
+If(StrCmp(OnelabAction, "compute") == 0)
+ Mesh 2;
+ Save StrCat[WorkingDir, "main.msh"];
+ CreateDir StrCat[WorkingDir, "aux"];
+ Plugin(BoundaryAngles).Remove = 1;
+ Plugin(BoundaryAngles).Save = 1;
+ Plugin(BoundaryAngles).Dir = "aux";
+ Plugin(BoundaryAngles).Filename = "TC_Theta";
+ Plugin(BoundaryAngles).Run;
+EndIf
diff --git a/DDM-Corner-Helmholtz-2D/src/TC_main.pro b/DDM-Corner-Helmholtz-2D/src/TC_main.pro
new file mode 100644
index 0000000000000000000000000000000000000000..99c9f9d198c60310a86d7d66024edc27e779dc03
--- /dev/null
+++ b/DDM-Corner-Helmholtz-2D/src/TC_main.pro
@@ -0,0 +1,127 @@
+Include "TC_main.data";
+
+If(!StrCmp(TC_PREFIX,""))
+ TC_PREFIX_ = "";
+Else
+ TC_PREFIX_ = StrCat[TC_PREFIX, "_"];
+EndIf
+
+Function {
+ I[] = Complex[0.,1.]; //i complexe
+ alpha_vect[] = Vector[Cos[alpha],Sin[alpha],0]; //vecteur angle alpha
+ If(!StrCmp(INCIDENT_WAVE,"Plane Wave"))
+ //one plane incidente vect alpha
+ uInc[] = Complex[Cos[kap*(XYZ[]*alpha_vect[])],Sin[kap*(XYZ[]*alpha_vect[])]];
+ dx_uInc[] = I[]*kap*Cos[alpha]*uInc[];
+ ElseIf(!StrCmp(INCIDENT_WAVE,"Eigenmode"))
+ uInc[] = Cos[m_mode*Pi*(Y[]+l/2)/l];
+ dx_uInc[] = I[]*kap*uInc[];
+ EndIf
+}
+
+// 2 subdomains (DDM) case)
+Group {
+ D() = {};
+ For i In {0:(NDom-1)}
+ Omega~{i} = Region[{i}];
+ D() += i;
+ j = (i+1)%NDom; // neighbor
+ D~{i} = {j};
+
+ If (i==0)
+ GammaIncoming~{i} = Region[{31}];
+ GammaOutgoing~{i} = Region[{}];
+ Else
+ GammaOutgoing~{i} = Region[{33}];
+ GammaIncoming~{i} = Region[{}];
+ EndIf
+ GammaTop~{i} = Region[{(100+i)}];
+ GammaBottom~{i} = Region[{(200+i)}];
+
+ //Sigma_ij = dOmega1 cap dOmega2
+ Sigma~{i}~{j} = Region[{20,21,22,23}];
+ Delta~{i}~{j} = Region[{20,21,22,23}];
+ Sigma~{i} = Region[{20,21,22,23}];
+ Delta~{i} = Region[{20,21,22,23}];
+
+ If(CORNER_CONDITION == 0) //Dirichlet
+ // Segments are considered as "only one"
+ r = 0; // only one "segment"
+ NDelta~{i}~{j} = 1;
+ Delta~{i}~{j}~{r} = Region[{20,21,22,23}];
+ dDelta~{i}~{j}~{r} = Region[{}];
+ ListdDelta~{i}~{j}~{r}() = {}; // No corner point (empty list)
+ ListdDelta~{i}~{j}() = {}; // No corner point (empty list)
+ Else
+ // Sigma_{ij} is split into segments ("broken" H^1(Sigma_ij))
+ NDelta~{i}~{j} = 4;
+ // if i == 0 then r = {3,2,1,0}
+ // else i == 1 then r = {0,1,2,3}
+ For rr In {0:(NDelta~{i}~{j}-1)}
+ r = (i==0)?(NDelta~{i}~{j}-1-rr):rr;
+ s = (i==0)?(rr):(NDelta~{i}~{j}-1-rr); // indice of this segment from the other side
+
+ ListdDelta~{i}~{j}~{r}() = {}; // contains the indices r' of the adjacent segments (possibly unique)
+ Delta~{i}~{j}~{r} = Region[{(20+rr)}];
+
+ //Nods Q^ij_r = Delta^ij_r \cap Delta^ij_r'
+ If (r==0) // First segment
+ next = r+1;
+ Q~{i}~{j}~{r}~{next} = Region[{((i==0)?53-r:51+r)}];
+ dDelta~{i}~{j}~{r}~{0} = Region[{((i==0)?53-r:51+r)}];
+ ListdDelta~{i}~{j}~{r}() += next; // next segment
+
+ dDelta~{i}~{j}~{r} = Region[{((i==0)?53-r:51+r)}];
+ ElseIf (r==1) // second segment
+ next = r+1;
+ Q~{i}~{j}~{r}~{next} = Region[{((i==0)?53-r:51+r)}];
+ dDelta~{i}~{j}~{r}~{0} = Region[{((i==0)?53-r:51+r)}];
+ ListdDelta~{i}~{j}~{r}() += next; // next segment
+
+ prev = r-1;
+ Q~{i}~{j}~{r}~{prev} = Region[{((i==0)?53-prev:51+prev)}];
+ dDelta~{i}~{j}~{r}~{1} = Region[{((i==0)?53-prev:51+prev)}];
+ ListdDelta~{i}~{j}~{r}() += prev; // next segment
+
+ dDelta~{i}~{j}~{r} = Region[{((i==0)?53-r:51+r), ((i==0)?53-prev:51+prev)}];
+ ElseIf (r==2) // third segment
+ next = r+1;
+ Q~{i}~{j}~{r}~{next} = Region[{((i==0)?53-r:51+r)}];
+ dDelta~{i}~{j}~{r}~{0} = Region[{((i==0)?53-r:51+r)}];
+ ListdDelta~{i}~{j}~{r}() += next; // next segment
+
+ prev = r-1;
+ Q~{i}~{j}~{r}~{prev} = Region[{((i==0)?53-prev:51+prev)}];
+ dDelta~{i}~{j}~{r}~{1} = Region[{((i==0)?53-prev:51+prev)}];
+ ListdDelta~{i}~{j}~{r}() += prev; // next segment
+
+ dDelta~{i}~{j}~{r} = Region[{((i==0)?53-r:51+r), ((i==0)?53-prev:51+prev)}];
+ Else // last segment
+ prev = r-1;
+ Q~{i}~{j}~{r}~{prev} = Region[{((i==0)?53-prev:51+prev)}];
+ dDelta~{i}~{j}~{r}~{0} = Region[{((i==0)?53-prev:51+prev)}];
+ ListdDelta~{i}~{j}~{r}() += prev; // next segment
+
+ dDelta~{i}~{j}~{r} = Region[{((i==0)?53-prev:51+prev)}];
+ EndIf
+ EndFor
+ EndIf
+ EndFor
+}
+
+Group{
+ Omega = Region[{(0:(NDom-1))}];
+
+ Sigma = Region[{20,21,22,23}];
+ Delta = Region[{20,21,22,23}];
+
+ GammaIncoming = Region[{31}];
+ GammaOutgoing = Region[{33}];
+ GammaTop = Region[{100, 101}];
+ GammaBottom = Region[{200, 201}];
+}
+
+
+Include "TC_Decomposition.pro";
+Include "TC_WaveGuide.pro";
+Include "TC_WaveGuide_DDM.pro";
diff --git a/DiffractionGratings/grating2D_scalar.pro b/DiffractionGratings/grating2D_scalar.pro
index 3875c0a798a7483875ce6c7a7610f97e283e4238..9cb5b5eff650e3466f31dfa05407309a4f7efbb2 100644
--- a/DiffractionGratings/grating2D_scalar.pro
+++ b/DiffractionGratings/grating2D_scalar.pro
@@ -23,7 +23,7 @@ lambda0 = lambda0 * nm;
lambda_min = lambda_min * nm;
lambda_max = lambda_max * nm;
A = 1.;
-nb_orders = 2;
+// nb_orders = 2;
Group {
// Boundaries
@@ -334,7 +334,7 @@ FunctionSpace {
{ NameOfCoef un; EntityType NodesOf ; NameOfConstraint Bloch; }
{ NameOfCoef un2; EntityType EdgesOf ; NameOfConstraint Bloch; }
If (Flag_o2_interp==1)
- { NameOfCoef un3; EntityType EdgesOf ; NameOfConstraint Bloch; }
+ { NameOfCoef un4; EntityType EdgesOf ; NameOfConstraint Bloch; }
EndIf
}
}
@@ -389,8 +389,8 @@ PostProcessing {
EndFor
If (flag_polar==1)
For i In {0:2*nb_orders}
- { Name eff_r~{i} ; Value { Term{ Type Global; [ SquNorm[#i]*beta_super~{i}[]/beta1[] ] ; In SurfCutSuper1 ; } } }
- { Name eff_t~{i} ; Value { Term{ Type Global; [ SquNorm[#(2*nb_orders+1+i)]*(beta_subs~{i}[]/beta1[])*(epsr1[]/epsr2[]) ] ; In SurfCutSubs1 ; } } }
+ { Name eff_r~{i} ; Value { Term{ Type Global; [ SquNorm[$sr~{i}]*beta_super~{i}[]/beta1[] ] ; In SurfCutSuper1 ; } } }
+ { Name eff_t~{i} ; Value { Term{ Type Global; [ SquNorm[$st~{i}]*(beta_subs~{i}[]/beta1[])*(epsr1[]/epsr2[]) ] ; In SurfCutSubs1 ; } } }
EndFor
For i In {0:N_rods-1:1}
{ Name Q_rod~{i} ; Value { Integral { [ 0.5 * ep0*om0*Fabs[epsr_rods_im[]] * ( SquNorm[CompY[{Grad u2d}]*I[]/(om0*ep0*CompXX[epsilonr[]])+Ex1[]/CompXX[epsilonr[]]*CompXX[epsilonr_annex[]]] + SquNorm[-CompX[{Grad u2d}]*I[]/(om0*ep0*CompXX[epsilonr[]])+Ey1[]/CompXX[epsilonr[]]*CompXX[epsilonr_annex[]]] ) / (Pinc[]*d) ] ; In rod~{i} ; Integration Int_1 ; Jacobian JVol ; } } }
@@ -403,8 +403,8 @@ PostProcessing {
EndIf
If (flag_polar==0)
For i In {0:2*nb_orders}
- { Name eff_r~{i} ; Value { Term{ Type Global; [ SquNorm[#i]*beta_super~{i}[]/beta1[] ] ; In SurfCutSuper1 ; } } }
- { Name eff_t~{i} ; Value { Term{ Type Global; [ SquNorm[#(2*nb_orders+1+i)]*(beta_subs~{i}[]/beta1[])] ; In SurfCutSubs1 ; } } }
+ { Name eff_r~{i} ; Value { Term{ Type Global; [ SquNorm[$sr~{i}]*beta_super~{i}[]/beta1[] ] ; In SurfCutSuper1 ; } } }
+ { Name eff_t~{i} ; Value { Term{ Type Global; [ SquNorm[$st~{i}]*(beta_subs~{i}[]/beta1[])] ; In SurfCutSubs1 ; } } }
EndFor
For i In {0:N_rods-1:1}
{ Name Q_rod~{i} ; Value { Integral { [0.5 * ep0*om0*Fabs[epsr_rods_im[]] * (SquNorm[{u2d}+u1[]]) / (Pinc[]*d) ] ; In rod~{i} ; Integration Int_1 ; Jacobian JVol ; } } }
@@ -424,8 +424,8 @@ PostOperation {
Operation {
Print[ lambda_step, OnPoint{0,0,0}, Format Table, File > StrCat[myDir, "temp_lambda_step.txt"], SendToServer "GetDP/Lambda_step" ] ;
For i In {0:2*nb_orders}
- Print[ s_r~{i}[SurfCutSuper1], OnGlobal, Store i , Format Table , File > StrCat[myDir, Sprintf("temp_s_r_%g.txt", i-nb_orders)]];
- Print[ s_t~{i}[SurfCutSubs1] , OnGlobal, Store (2*nb_orders+1+i), Format Table , File > StrCat[myDir, Sprintf("temp_s_t_%g.txt", i-nb_orders)]];
+ Print[ s_r~{i}[SurfCutSuper1], OnGlobal, StoreInVariable $sr~{i}, Format Table , File > StrCat[myDir, Sprintf("temp_s_r_%g.txt", i-nb_orders)]];
+ Print[ s_t~{i}[SurfCutSubs1] , OnGlobal, StoreInVariable $st~{i}, Format Table , File > StrCat[myDir, Sprintf("temp_s_t_%g.txt", i-nb_orders)]];
EndFor
For i In {0:2*nb_orders}
Print[ eff_r~{i}[SurfCutSuper1], OnRegion SurfCutSuper1,Store (4*nb_orders+1+i), Format FrequencyTable, File > StrCat[myDir, Sprintf("efficiency_r_%g.txt", i-nb_orders)]];
@@ -468,7 +468,7 @@ PostOperation {
"Surface{36,48};}",
"Geometry.Color.Lines = {0,0,0};",
"l=PostProcessing.NbViews-1; View[l].ColorTable={Black}; ",
- "View[l-1].Visible=1; View[l-1].ShowScale=0;",
+ "View[l-1].Visible=1; View[l].Visible=1; View[l-1].ShowScale=0;",
"View[l].ShowScale=0; View[l].LineWidth=1.5; View[l].LineType=1;Geometry.LineWidth=0;"],
File StrCat[myDir,"tmp3.geo" ]] ;
EndIf
diff --git a/ECE_full_wave/FullWave_E_ece_SISO.pro b/ECE_full_wave/FullWave_E_ece_SISO.pro
new file mode 100644
index 0000000000000000000000000000000000000000..a8eb1b687ef79f1c61e450ff38678532843fc03c
--- /dev/null
+++ b/ECE_full_wave/FullWave_E_ece_SISO.pro
@@ -0,0 +1,204 @@
+/* FullWave_E_ece_SISO.pro
+
+ Problem independent pro file
+ for passive, linear domains in Full Wave with ECE boundary conditions.
+
+ It uses a formulation with vec{E} strictly inside the domain and V strictly on the boundary.
+ The domain is simply connected, it has only electric terminals.
+ The terminals can be voltage or current excited.
+ The material inside is linear from all points of view: electric, magnetic, conduction
+ It is compulsory that there exists a ground terminal (its voltage is set to zero).
+ The post-operation assumes that there is one excited (active) terminal (excitation equal to 1 - it can be in
+ voltage or current excited terminal).
+ Frequency domain simulations.
+*/
+
+
+Jacobian {
+ { Name Vol;
+ Case {
+ { Region All; Jacobian Vol; }
+ }
+ }
+ { Name Sur;
+ Case {
+ { Region All; Jacobian Sur; }
+ }
+ }
+}
+
+Integration {
+ { Name Int;
+ Case {
+ { Type Gauss;
+ Case {
+ { GeoElement Point; NumberOfPoints 1; }
+ { GeoElement Line; NumberOfPoints 3; }
+ { GeoElement Triangle; NumberOfPoints 3; }
+ { GeoElement Quadrangle; NumberOfPoints 4; }
+ { GeoElement Tetrahedron; NumberOfPoints 4; }
+ { GeoElement Hexahedron; NumberOfPoints 6; }
+ { GeoElement Prism; NumberOfPoints 9; }
+ { GeoElement Pyramid; NumberOfPoints 8; }
+ }
+ }
+ }
+ }
+}
+
+FunctionSpace {
+
+ { Name Hcurl_E; Type Form1;
+ BasisFunction {
+ { Name se; NameOfCoef ee; Function BF_Edge;
+ Support Dom_FW ; Entity EdgesOf[All, Not Sur_FW]; }
+ { Name sn; NameOfCoef vn; Function BF_GradNode;
+ Support Dom_FW ; Entity NodesOf[Sur_FW, Not Sur_Terminals_FWece]; }
+ { Name sf; NameOfCoef vf; Function BF_GradGroupOfNodes;
+ Support Dom_FW ; Entity GroupsOfNodesOf[Sur_Terminals_FWece]; }
+ }
+ GlobalQuantity {
+ { Name TerminalPotential; Type AliasOf ; NameOfCoef vf; }
+ { Name TerminalCurrent ; Type AssociatedWith; NameOfCoef vf; }
+ }
+
+ SubSpace {
+ { Name dv ; NameOfBasisFunction {sn}; } // Subspace, it maybe use in equations or post-pro
+ }
+
+ Constraint {
+ { NameOfCoef TerminalPotential; EntityType GroupsOfNodesOf; NameOfConstraint SetTerminalPotential; }
+ { NameOfCoef TerminalCurrent; EntityType GroupsOfNodesOf; NameOfConstraint SetTerminalCurrent; }
+ }
+ }
+
+}
+
+Formulation {
+
+ { Name FullWave_E_ece; Type FemEquation;
+ Quantity {
+ { Name e; Type Local; NameOfSpace Hcurl_E; }
+ { Name dv; Type Local; NameOfSpace Hcurl_E[dv]; } // Just for post-processing issues
+ { Name V; Type Global; NameOfSpace Hcurl_E[TerminalPotential]; }
+ { Name I; Type Global; NameOfSpace Hcurl_E[TerminalCurrent]; }
+ }
+ Equation {
+ // \int_D curl(\vec{E}) \cdot curl(\vec{e}) dv
+ Galerkin { [ nu[] * Dof{d e} , {d e} ]; In Vol_FW; Jacobian Vol; Integration Int; }
+
+ // \int_D j*\omega*(\sigma + j*\omega*\epsilon) \vec{E} \cdot \vec{e} dv
+ Galerkin { DtDof [ sigma[] * Dof{e} , {e} ]; In Vol_FW; Jacobian Vol; Integration Int; }
+ Galerkin { DtDtDof [ epsilon[] * Dof{e} , {e} ]; In Vol_FW; Jacobian Vol; Integration Int; }
+
+ // alternative // j*\omega*sum (vk Ik); for k - current excited terminals
+ // GlobalTerm {DtDof [ -Dof{I} , {V} ]; In SurBCec; }
+
+ // j*\omega*sum (vk Ik); for k - all terminals so that the currents through the terminals will be computed as well
+ GlobalTerm {DtDof [ -Dof{I} , {V} ]; In Sur_Terminals_FWece; }
+ }
+ }
+
+}
+
+
+Resolution {
+
+ { Name FullWave_E_ece;
+ System {
+ { Name Sys_Ele; NameOfFormulation FullWave_E_ece; Type Complex; Frequency Freq;}
+ }
+ Operation {
+ CreateDir[Dir];
+ SetTime[Freq]; // useful to save (and print) the current frequency
+ Generate[Sys_Ele]; Solve[Sys_Ele]; SaveSolution[Sys_Ele];
+ }
+ }
+
+}
+
+PostProcessing {
+
+ { Name FW_E_ece; NameOfFormulation FullWave_E_ece;
+ Quantity {
+ { Name E;
+ Value {
+ Local { [ {e} ]; In Vol_FW; Jacobian Vol; }
+ }
+ }
+
+ { Name normE;
+ Value {
+ Local { [ Norm[{e}] ]; In Vol_FW; Jacobian Vol; }
+ }
+ }
+
+
+ { Name J;
+ Value {
+ Local { [ sigma[]*{e} ]; In Vol_FW; Jacobian Vol; }
+ }
+ }
+
+ { Name rmsJ;
+ Value {
+ Local { [ Norm[sigma[]*{e}] ]; In Vol_FW; Jacobian Vol; }
+ }
+ }
+
+ { Name gradV;
+ Value {
+ Local { [ {dv} ]; In Vol_FW; Jacobian Vol; }
+ }
+ }
+
+ { Name Vterminals;
+ Value {
+ // This is a global variable, you do not need to indicate the Jacobian
+ // It is only defined at the terminal and it is only one value for the whole line (surface in 3D)
+ // If the support you give here is wider, you will get 0 where it is not defined
+ Term { [ -1*{V} ]; In Sur_Terminals_FWece; } // => unknowns only in Sur_Terminals_FWece, outside it will be zero
+ }
+ }
+
+ { Name I;
+ Value {
+ Term { [ -1*{I} ]; In Sur_Terminals_FWece; }
+ }
+ }
+
+ { Name VnotTerminals;
+ Value {
+ Local { [ -{dInv dv} ]; In Vol_FW; Jacobian Vol; }
+ }
+ }
+
+ { Name B;
+ Value {
+ Local { [ {d e}/(2*Pi*Freq*Complex[0,1]) ]; In Vol_FW; Jacobian Vol; }
+ }
+ }
+
+ { Name H;
+ Value {
+ Local { [ nu[]*{d e}/(2*Pi*Freq*Complex[0,1]) ]; In Vol_FW; Jacobian Vol; }
+ }
+ }
+
+
+
+ { Name Bz;
+ Value {
+ Local { [ CompZ[{d e}]/(2*Pi*Freq*Complex[0,1]) ]; In Vol_FW; Jacobian Vol; }
+ }
+ }
+
+ { Name Hz;
+ Value {
+ Local { [ nu[]*CompZ[{d e}]/(2*Pi*Freq*Complex[0,1]) ]; In Vol_FW; Jacobian Vol; }
+ }
+ }
+
+ }
+ }
+ }
diff --git a/ECE_full_wave/Ishape3d.geo b/ECE_full_wave/Ishape3d.geo
new file mode 100644
index 0000000000000000000000000000000000000000..8a95d1191c1d6bbaa628d00515adcd85484ac6dc
--- /dev/null
+++ b/ECE_full_wave/Ishape3d.geo
@@ -0,0 +1,123 @@
+/* Ishape3d.geo
+Geometrical description (for gmsh) of Ishape3D test for ECE
+For details, see comments in the Ishape3d_data.pro file
+Meshing information is also defined here.
+
+This uses OpenCascade
+*/
+
+
+Include "Ishape3d_data.pro";
+SetFactory("OpenCASCADE");
+
+xc = 0; yc = 0; zc = 0;
+vx = 0; vy = 0; vz = l;
+radius = a;
+
+volDom = newv; Cylinder(newv) = {xc, yc, zc, vx, vy, vz, radius};
+
+b() = Boundary{ Volume{volDom}; };
+Printf(" surfaces", b());
+
+// In order to identify which surface is which I played with the GUI!!!
+
+lateralCyl = b(0);
+bottomSurf = b(1);
+topSurf = b(2);
+
+
+//bs() = Boundary{ Surface{bottomSurf}; };
+//Printf(" curves", bs());
+//circle1 = bs(0);
+
+
+lc() = Boundary{ Surface{lateralCyl}; };
+Printf(" curves", lc());
+circle1 = lc(0);
+lineCyl = lc(1);
+circle2 = lc(2);
+//Transfinite Line {lineCyl} = 20;
+//Transfinite Curve{circle1} = 50;
+
+// Physical regions
+// --------------------------
+Physical Volume ("MaterialX", 100) = {volDom} ; /* MaterialX */
+
+Physical Surface ("Ground", 120) = {bottomSurf} ; /* Ground */
+Physical Surface ("Terminal", 121) = {topSurf} ; /* Terminal */
+Physical Surface ("BoundaryNotTerminal", 131) = {lateralCyl} ;
+
+
+/* Definition of parameters for local mesh dimensions */
+//lcar = s*l/10; // characteristic length of mesh element
+
+// lcar dep on Freq, wavelenth - 10 elements per wavelength and dimension
+//lambda = c0/Freq; // Label "Wavelength [m]"}
+//lcar = lambda/nbla
+// nbDelta from _data.geo, number of elements per skin depth
+
+delta = Sqrt(2.0/(2*Pi*Freq*mu*sigma));
+lcarDelta = delta/nbDelta;
+lcar = s*l/10;
+
+
+
+ //Field[1] = Distance;
+ //Field[1].CurvesList = {circle1};
+ //Field[1].SurfacesList = {lateralCyl};
+ //Field[1].Sampling = 200;
+
+ //Field[2] = Threshold;
+ //Field[2].InField = 1;
+ //Field[2].SizeMin = a/10; //lcar;
+ //Field[2].SizeMax = a/2;
+ //Field[2].DistMin = a/8; //delta;
+ //Field[2].DistMax = a/4; //delta;
+
+ //Field[2] = Box;
+ //Field[2].VIn = a/2;
+ //Field[2].VOut = a/10; //lcar;
+ //Field[2].XMin = -2*a/3;
+ //Field[2].XMax = 2*a/3;
+ //Field[2].YMin = -2*a/3;
+ //Field[2].YMax = 2*a/3;
+ //Field[2].ZMin = 0;
+ //Field[2].ZMax = l;
+ //Field[2].Thickness = 0.3;
+
+ Field[1] = Cylinder;
+ Field[1].VIn = lcar;
+ Field[1].VOut = lcar;
+ Field[1].Radius = a;
+ Field[1].XCenter = 0;
+ Field[1].YCenter = 0;
+ Field[1].ZCenter = l/2;
+ Field[1].XAxis = 0;
+ Field[1].YAxis = 0;
+ Field[1].ZAxis = l;
+
+ Field[2] = Cylinder;
+ Field[2].VIn = a/3;
+ Field[2].VOut = lcarDelta;
+ Field[2].Radius = a - delta;
+ Field[2].XCenter = 0;
+ Field[2].YCenter = 0;
+ Field[2].ZCenter = l/2;
+ Field[2].XAxis = 0;
+ Field[2].YAxis = 0;
+ Field[2].ZAxis = l;
+
+
+ Field[3] = Min;
+ Field[3].FieldsList = {1,2};
+ Background Field = 3;
+ Mesh.MeshSizeExtendFromBoundary = 0;
+ Mesh.MeshSizeFromPoints = 0;
+ Mesh.MeshSizeFromCurvature = 0;
+ Mesh.Algorithm = 5;
+
+
+/* Definition of parameters for local mesh dimensions */
+//lcar = s*l/10; // characteristic length of mesh element
+// Assign a mesh size to all the points of all the volumes:
+//MeshSize{ PointsOf{ Volume{:}; } } = lcar;
diff --git a/ECE_full_wave/Ishape3d.pro b/ECE_full_wave/Ishape3d.pro
new file mode 100644
index 0000000000000000000000000000000000000000..8ec428bc6d23bc18e2a8faf93b6c0fae874c89c3
--- /dev/null
+++ b/ECE_full_wave/Ishape3d.pro
@@ -0,0 +1,140 @@
+/* Ishape3d.pro
+Material description (for getdp) of Ishape3D test for ECE
+For details, see comments in the Ishape3d_data.pro file
+The Ishape3d geometry and meshing parameters are in the Ishape3d.geo file
+This file contains the setings that depend on the particular problem and
+it includes 1 general files
+*/
+
+Include "Ishape3d_data.pro"
+
+Group{
+ MaterialX = Region[100]; // MaterialX - homogenous domain
+ Ground = Region[120]; // Boundary - various parts
+ Terminal = Region[121];
+ BoundaryNotTerminal = Region[131];
+
+ Vol_FW = Region[{MaterialX}]; // domain without the boundary
+ Sur_Terminals_FWece = Region[{Ground, Terminal}]; // all terminals
+ Sur_FW = Region[{Sur_Terminals_FWece, BoundaryNotTerminal}]; //all boundary
+ Dom_FW = Region[ {Vol_FW, Sur_FW} ];
+ }
+
+
+ Function{
+ /*
+ Material properties are defined piecewise, for elementary groups
+ the values in the right hand side are defined in Ishape2d_data.pro
+ */
+
+ nu[#{MaterialX,Sur_FW}] = nu; // magnetic reluctivity [m/H]
+ epsilon[#{MaterialX,Sur_FW}] = eps; // permittivity [F/m]
+ sigma[#{MaterialX,Sur_FW}] = sigma; // conductivity [S/m]
+
+ // This is a problem with 2 terminals, out of which one is grounded.
+ // The non-grounded can be excited in voltage or in current.
+ // Depending on the excitation type, one of the following functions will be useful.
+ //
+ // When imposing voltage or current via a constraint, the region appears there
+ // If you have a complex, the value has to be a function => use square brackets []
+ If(Flag_AnalysisType==0)
+ VTerminal1[] = -VTermRMS*Complex[Cos[VTermPhase],Sin[VTermPhase]];
+ Else
+ ITerminal1[] = -ITermRMS*Complex[Cos[ITermPhase],Sin[ITermPhase]];
+ EndIf
+ }
+
+ Constraint{
+
+ // ece BC
+ { Name SetTerminalPotential; Type Assign; // voltage excited terminals
+ Case {
+ { Region Ground; Value 0.; }
+ If(Flag_AnalysisType==0)
+ { Region Terminal; Value VTerminal1[]; }
+ EndIf
+ }
+ }
+ { Name SetTerminalCurrent; Type Assign; // current excited terminals
+ Case {
+ If(Flag_AnalysisType==1)
+ { Region Terminal; Value ITerminal1[]; }
+ EndIf
+ }
+ }
+
+}
+
+// For convenience, saving results in different directories
+// Dir can be empty: Dir ="";
+ If (Flag_AnalysisType==0)
+ Dir = "res/FWeceBC_voltExc/";
+ Else
+ Dir = "res/FWeceBC_crtExc/";
+ EndIf
+
+ // The formulation and its tools
+Include "FullWave_E_ece_SISO.pro"
+
+
+// Some Macros for changing Gmsh options
+// Strictly not necessary => for aestetics or easying result treatment
+Macro Change_post_options
+Echo[Str[ "nv = PostProcessing.NbViews;",
+ "For v In {0:nv-1}",
+ "View[v].NbIso = 25;",
+ "View[v].RangeType = 3;" ,// per timestep
+ "View[v].ShowTime = 3;",
+ "View[v].IntervalsType = 3;",
+ "EndFor"
+ ], File "post.opt"];
+Return
+
+Macro WriteZ_header
+ Echo[ Str[Sprintf("# Hz Z RI R %g", 50)], Format Table, File > StrCat[Dir, "test_Z_RI.s1p"] ];
+Return
+Macro WriteY_header
+ Echo[ Str[Sprintf("# Hz Y RI R %g", 50)], Format Table, File > StrCat[Dir, "test_Y_RI.s1p"] ];
+Return
+
+
+
+PostOperation {
+ { Name Maps; NameOfPostProcessing FW_E_ece ;
+ Operation {
+ Print [ gradV, OnElementsOf ElementsOf[Vol_FW,OnOneSideOf Sur_FW], File StrCat[Dir,"map_gradV.pos" ]];
+
+ Print [ E, OnElementsOf Vol_FW, File StrCat[Dir,"map_E.pos" ]];
+ // Print [ J, OnElementsOf Vol_FW, File StrCat[Dir,"map_J.pos" ]];
+ // Print [ rmsJ, OnElementsOf Vol_FW, File StrCat[Dir,"map_absJ.pos" ]];
+
+ Print [ H, OnElementsOf Vol_FW, File StrCat[Dir,"map_H.pos" ]];
+ Print [ Vterminals, OnElementsOf ElementsOf[Sur_Terminals_FWece], File StrCat[Dir,"map_Vterminals.pos" ]];
+ Print [ VnotTerminals, OnElementsOf Vol_FW, File StrCat[Dir,"map_VnotTerminals.pos" ]];
+
+ Call Change_post_options;
+ }
+ }
+
+
+ { Name TransferMatrix; NameOfPostProcessing FW_E_ece ;
+ Operation {
+ If(Flag_AnalysisType==1) // current excitation
+ If (Freq==freqs(0))
+ Call WriteZ_header;
+ Printf("======================> Writting header with first Freq=%g",Freq);
+ EndIf
+ Print [ Vterminals, OnRegion Terminal,
+ Format Table , File > StrCat[Dir, "test_Z_RI.s1p"]] ;
+ Else
+ If (Freq==freqs(0))
+ Call WriteY_header;
+ Printf("======================> Writting header with first Freq=%g",Freq);
+ EndIf
+ Print [ I, OnRegion Terminal,
+ Format Table , File > StrCat[Dir, "test_Y_RI.s1p"]] ;
+ EndIf
+ }
+ }
+
+}
diff --git a/ECE_full_wave/Ishape3d_data.pro b/ECE_full_wave/Ishape3d_data.pro
new file mode 100644
index 0000000000000000000000000000000000000000..f5588e5082b2346df48de05dc3ffe8994ce7d33a
--- /dev/null
+++ b/ECE_full_wave/Ishape3d_data.pro
@@ -0,0 +1,122 @@
+/* Ishape3d_data.pro
+=========================== Ishape3D - test problem
+A cylindrical domain in space, one circular face in the plane z = 0, circle of radius a,
+axis of the cylinder is Oz, length = l
+
+The domain is filled with homogeneous and linear material, with epsilon, mu, sigma
+
+There is no no field source inside the domein (the "device" is passive).
+The field sources are only boundary conditions (BC) which are ECE.
+
+The problem has 2 terminals (on top and bottom), one has to be grounded, the other two can be either
+voltage excited or current excited.
+
+This is a test problem - used to validate the ECE implementation in onelab for a 3D problem
+
+===========================
+Names of input data - to be given by the user
+Geometry:
+a = radius of the cylinder [m]
+l = height of the cylinder [m]
+==
+Material
+epsr = relative permittivity
+mur = relative permeability
+sigma = conductivity [S/m]
+
+==
+Type of BC - always ece, top terminal is gnd; bottom terminal can be ev = electric voltage forced terminal; ec = electric current forced terminal
+typeBC = 0,1,
+0 = bottom ev
+1 = bottom ec
+==
+Excitation signals
+imposed by the user, on non-grounded terminals; default values - is 1 (V or A)
+=========================== */
+
+colorro = "LightGrey";
+
+/* new menu for the interface - holds geometrical data */
+cGUI= "{Ishape3D-ProblemData/";
+mGeo = StrCat[cGUI,"Geometrical parameters/0"];
+colorMGeo = "Ivory";
+close_menu = 1;
+DefineConstant[
+ a = {2.5e-6, Name StrCat[mGeo, "0a=0.5*Dimension along Ox"], Units "m", Highlight Str[colorMGeo], Closed close_menu},
+ l = {10e-6, Name StrCat[mGeo, "1l=Dimension along Oy"], Units "m", Highlight Str[colorMGeo]}
+];
+
+/* new menu for the interface - holds material data */
+mMat = StrCat[cGUI,"Material parameters/0"];
+colorMMat = "AliceBlue";
+DefineConstant[
+ epsr = {1, Name StrCat[mMat, "0Relative permittivity T part"], Units "-", Highlight Str[colorMMat], Closed close_menu},
+ mur = {1, Name StrCat[mMat, "1Relative permeability T part"], Units "-", Highlight Str[colorMMat]},
+ sigma = {6.6e7, Name StrCat[mMat, "2Conductivity T part"], Units "S/m", Highlight Str[colorMMat]}
+];
+
+eps0 = 8.854187818e-12; // F/m - absolute permitivity of vacuum
+mu0 = 4.e-7 * Pi; // H/m - absolute permeability of vacuum
+nu0 = 1/mu0; // m/H - absolute reluctivity of vacuum
+
+eps = eps0*epsr; // F/m - absolute permitivity
+mu = mu0*mur; // F/m - absolute permeability
+nu = 1/mu; // m/H - absolute reluctivity
+
+
+// new menu for the interface - type of BC
+mTypeBC = StrCat[cGUI,"Type of BC/0"];
+colorMTypeBC = "Red";
+DefineConstant[
+ Flag_AnalysisType = { 0,
+ Choices{
+ 0="bottomTerm ev",
+ 1="bottomTerm ec"},
+ Name Str[mTypeBC], Highlight Str[colorMTypeBC], Closed !close_menu,
+ ServerAction Str["Reset", "GetDP/1ResolutionChoices"]}
+];
+
+
+// new menu for the interface - values of excitations - significance depends on the type of BC
+mValuesBC = StrCat[cGUI,"Values of BC (frequency analysis)/0"];
+colorMValuesBC = "Ivory";
+
+fmin = 1e7; // Hz
+fmax = 100e9; // Hz
+
+nop = 10;
+//freqs()=LogSpace[Log10[fmin],Log10[fmax],nop];
+freqs()=LinSpace[fmin,fmax,nop];
+DefineConstant[
+ Freq = {freqs(0), Choices{freqs()}, Loop 0, Name StrCat[mValuesBC, "0Working Frequency"],
+ Units "Hz", Highlight Str[colorMValuesBC], Closed !close_menu }
+
+ // Flag_AnalysisType
+ // ==0 bottom ev
+ // ==1 bottom ec
+
+ VGroundRMS = {0, Name StrCat[mValuesBC, "2Top/1Potential on bottom (rms)"],
+ Units "V", ReadOnly 1, Highlight Str[colorro],
+ Visible (Flag_AnalysisType==0) || (Flag_AnalysisType==1)}
+ VGroundPhase = {0, Name StrCat[mValuesBC, "2Top/1Potential on bottom, phase"],
+ Units "rad", ReadOnly 1, Highlight Str[colorro],
+ Visible (Flag_AnalysisType==0) || (Flag_AnalysisType==1)}
+
+ VTermRMS = {1, Name StrCat[mValuesBC, "1Bottom/1Potential on Term1 (rms)"],
+ Units "V", ReadOnly 0, Highlight Str[colorMValuesBC],
+ Visible (Flag_AnalysisType==0)}
+ VTermPhase = {0, Name StrCat[mValuesBC, "1Bottom/1Potential on Term1, phase"],
+ Units "rad", ReadOnly 0, Highlight Str[colorMValuesBC],
+ Visible (Flag_AnalysisType==0)}
+
+ ITermRMS = {1, Name StrCat[mValuesBC, "1Bottom/1Current through Term1 (enters the domain) (rms)"],
+ Units "A", ReadOnly 0, Highlight Str[colorMValuesBC],
+ Visible (Flag_AnalysisType==1) }
+ ITermPhase = {0, Name StrCat[mValuesBC, "1Bottom/Current through Term1 (enters the domain), phase"],
+ Units "rad", ReadOnly 0, Highlight Str[colorMValuesBC],
+ Visible (Flag_AnalysisType==1) }
+
+ //_use_transfinite = {0, Choices{0,1}, Name "{MeshSettings/0Transfinite mesh?", Highlight "Yellow", Closed !close_menu}
+ s = {1, Name "{MeshSettings/1Mesh factor s"}
+ nbDelta = {1, Name "{MeshSettings/2Nb of elems per skin depth"}
+];
diff --git a/ECE_full_wave/LC.geo b/ECE_full_wave/LC.geo
new file mode 100644
index 0000000000000000000000000000000000000000..23d2e5988cc4d35289d8fd780e81c8942f657930
--- /dev/null
+++ b/ECE_full_wave/LC.geo
@@ -0,0 +1,79 @@
+Include "LC_data.pro";
+
+SetFactory("OpenCASCADE");
+
+// convert geometry read from STEP file to meters
+Geometry.OCCTargetUnit = "M";
+
+Geometry.NumSubEdges = 100; // Visualisation
+
+// We can activate the calculation of mesh element sizes based on curvature:
+Mesh.MeshSizeFromCurvature = 1; // Needed for spiral/helix
+
+// And we set the minimum number of elements per 2*Pi radians:
+Mesh.MinimumElementsPerTwoPi = 20/2;
+
+// We can constraint the min and max element sizes to stay within reasonnable
+// values (see `t10.geo' for more details):
+Mesh.MeshSizeMin = rw/4;
+Mesh.MeshSizeMax = rplateC;
+
+
+
+// read STEP file and store volume(s)
+v() = ShapeFromFile("LC_ostrowski.stp");
+
+vol_air() = v({10,11});
+vol_cond() = v({0,1,3:6,8,9});
+vol_diel() = v(7);
+vcore=v(2);
+
+// Doing intersections that are not in the initial step
+vol_aux()=BooleanFragments{Volume{vol_cond(),vol_diel()};Delete;}{}; //Plates and dielectric have to be intersected with connectors
+Coherence; // Air around
+
+// define physical groups
+Physical Volume("DomainAir", AIR) = vol_air();
+Physical Volume("DomainConductor", CONDUCTOR) = vol_cond(); // 6 and 8 are the capacitor plates
+Physical Volume("DomainDielectric", DIELECTRIC) = vol_diel();
+Physical Volume("DomainCore", CORE) = vcore;
+
+// outside boundaries
+bnd_air() = Abs(CombinedBoundary{Volume{Volume{:}};});
+surf_elec_in = 130; //side L
+surf_elec_out = 144; // side C
+bnd_air() -= {surf_elec_in,surf_elec_out};
+
+Physical Surface("Terminal", ELEC_IN) = surf_elec_in;
+Physical Surface("Ground", ELEC_OUT) = surf_elec_out;
+Physical Surface("SurBCnotTerminalAir", BND_AIR) = bnd_air();
+
+
+// Adapting the mesh
+// get bounding box
+bb() = BoundingBox Volume {v()};
+
+// size along axes (useful for adapting mesh)
+sizeX = bb(3)-bb(0);
+sizeY = bb(4)-bb(1);
+sizeZ = bb(5)-bb(2);
+
+
+scale_factor=2;
+lc_ref = scale_factor*sizeX/200;
+ptos_cond() = PointsOf{Volume{vol_cond()};};
+ptos_air_in() = PointsOf{Volume{v(10)};};
+ptos_core() = PointsOf{Volume{vcore};};
+ptos_air_in() -= {ptos_cond(),ptos_core()};
+ptos_air_out() = PointsOf{Surface{152,153};}; // only the side
+
+MeshSize{ptos_air_out()} = 10*lc_ref;
+MeshSize{ptos_air_in()} = 3*lc_ref;
+MeshSize{ptos_core()} = 1.5*lc_ref;
+MeshSize{ptos_cond()} = lc_ref;
+
+// For aestetics
+Recursive Color SkyBlue { Volume{vol_air()};}
+Recursive Color Green { Volume{vcore};}
+Recursive Color Red { Volume{vol_cond()};}
+Recursive Color Yellow { Volume{vol_diel()};}
diff --git a/ECE_full_wave/LC.pro b/ECE_full_wave/LC.pro
new file mode 100644
index 0000000000000000000000000000000000000000..ef6fbe2ceb104c2e9b2750bcb133a48759b1158d
--- /dev/null
+++ b/ECE_full_wave/LC.pro
@@ -0,0 +1,176 @@
+/* LC.pro
+Linked to step file from Joerg Ostrowski
+FW in E and V, ECE
+*/
+
+Include "LC_data.pro"
+
+Group{
+
+ Ground = Region[{ELEC_OUT}];
+ Terminal = Region[{ELEC_IN}];
+ SurBCnotTerminalAir = Region[{BND_AIR}];
+
+ DomainConductor = Region[{CONDUCTOR}];
+ DomainDielectric = Region[{DIELECTRIC}];
+ DomainCore = Region[{CORE}];
+ DomainAir = Region[{AIR}];
+
+ Vol_FW = Region[{DomainConductor,DomainDielectric,DomainCore,DomainAir}];
+ Sur_Terminals_FWece = Region[{Ground, Terminal}]; // all terminals
+ Sur_FW = Region[{Sur_Terminals_FWece, SurBCnotTerminalAir}]; //all boundary
+ Dom_FW = Region[ {Vol_FW, Sur_FW} ];
+ }
+
+
+ Function{
+ /*
+ Material properties are defined piecewise, for elementary groups
+ the values in the right hand side are defined in CL_data.pro
+ */
+
+ // conductor
+ nu[#{DomainConductor,Ground,Terminal}] = nuCond; // magnetic reluctivity [m/H]
+ epsilon[#{DomainConductor,Ground,Terminal}] = epsCond; // permittivity [F/m]
+ sigma[#{DomainConductor,Ground,Terminal}] = sigmaCond; // conductivity [S/m]
+
+ // dielectric
+ nu[#{DomainDielectric}] = nuDiel;
+ epsilon[#{DomainDielectric}] = epsDiel;
+ sigma[#{DomainDielectric}] = sigmaDiel;
+
+ // core
+ nu[#{DomainCore}] = nuCore;
+ epsilon[#{DomainCore}] = epsCore;
+ sigma[#{DomainCore}] = sigmaCore;
+
+ // air
+ nu[#{DomainAir,SurBCnotTerminalAir}] = nuAir;
+ epsilon[#{DomainAir,SurBCnotTerminalAir}] = epsAir;
+ sigma[#{DomainAir,SurBCnotTerminalAir}] = sigmaAir;
+
+ If(Flag_AnalysisType==0)
+ VTerminal1[] = -VTermRMS*Complex[Cos[VTermPhase],Sin[VTermPhase]];
+ Else
+ ITerminal1[] = -ITermRMS*Complex[Cos[ITermPhase],Sin[ITermPhase]];
+ EndIf
+ }
+
+ Constraint{
+
+ // ece BC
+ { Name SetTerminalPotential; Type Assign; // voltage excited terminals
+ Case {
+ { Region Ground; Value 0.; }
+ If(Flag_AnalysisType==0)
+ { Region Terminal; Value VTerminal1[]; }
+ EndIf
+ }
+ }
+ { Name SetTerminalCurrent; Type Assign; // current excited terminals
+ Case {
+ If(Flag_AnalysisType==1)
+ { Region Terminal; Value ITerminal1[]; }
+ EndIf
+ }
+ }
+
+}
+
+
+If (Flag_AnalysisType==0)
+ Dir = "res/FWeceBC_voltExc/";
+Else
+ Dir = "res/FWeceBC_crtExc/";
+EndIf
+
+// The formulation and its tools
+Include "FullWave_E_ece_SISO.pro"
+
+// Output results
+Macro Change_post_options
+Echo[Str[ "nv = PostProcessing.NbViews;",
+ "For v In {0:nv-1}",
+ "View[v].NbIso = 25;",
+ "View[v].RangeType = 3;" ,// per timestep
+ "View[v].ShowTime = 3;",
+ "View[v].IntervalsType = 3;",
+ "EndFor"
+ ], File "post.opt"];
+Return
+
+Macro WriteZ_header
+ Echo[ Str[Sprintf("# Hz Z RI R %g", 50)], Format Table, File > StrCat[Dir, "test_Z_RI.s1p"] ];
+Return
+Macro WriteY_header
+ Echo[ Str[Sprintf("# Hz Y RI R %g", 50)], Format Table, File > StrCat[Dir, "test_Y_RI.s1p"] ];
+Return
+
+
+Macro Plugin_cuts
+ Echo[ Str[
+ "nview = PostProcessing.NbViews-1;",
+ "vname = Str[View[nview].Name];",
+ "Plugin(CutPlane).A = 1;",
+ "Plugin(CutPlane).B = 0;",
+ "Plugin(CutPlane).C = 0;",
+ "Plugin(CutPlane).D = -0.0289;", // half wire L side
+ "Plugin(CutPlane).View = nview;",
+ "Plugin(CutPlane).Run;",
+ "View[nview+1].RangeType = 2;", // custom
+ "View[nview+1].CustomMax = View[nview+1].Max;", // max
+ "View[nview+1].CustomMin = View[nview+1].MinVisible;", // min
+ "View[nview+1].ScaleType = 2;", // logarithmic scale
+ "View[nview+1].Name = StrCat[vname, ' on YZ plane'];"
+ ], File StrCat[Dir,"cuts.geo"] ] ;
+Return
+
+PostOperation {
+
+ { Name Maps; NameOfPostProcessing FW_E_ece ;
+ Operation {
+ Print [ gradV, OnElementsOf ElementsOf[Vol_FW,OnOneSideOf Sur_FW], File StrCat[Dir,"map_gradV.pos" ]];
+
+ Print [ Vterminals, OnElementsOf ElementsOf[Sur_FW], File StrCat[Dir,"map_Vterminals.pos" ]];
+ Print [ VnotTerminals, OnElementsOf Vol_FW, File StrCat[Dir,"map_VnotTerminals.pos" ]];
+ Print [ H, OnElementsOf Vol_FW, File StrCat[Dir,"map_H.pos" ]];
+ Print [ E, OnElementsOf Vol_FW, File StrCat[Dir,"map_E.pos" ]];
+ Call Change_post_options;
+
+ Print [ normE, OnElementsOf Vol_FW, File StrCat[Dir,"map_normE.pos" ]];
+ Call Plugin_cuts;
+ }
+ }
+
+ { Name TransferMatrix; NameOfPostProcessing FW_E_ece ;
+ Operation {
+ If(Flag_AnalysisType==1) // current excitation
+ If (Freq==freqs(0))
+ Call WriteZ_header;
+ Printf("======================> Writting header with first Freq=%g",Freq);
+ EndIf
+ Print [ Vterminals, OnRegion Terminal,
+ Format Table , File > StrCat[Dir, "test_Z_RI.s1p"]] ;
+ Else
+ If (Freq==freqs(0))
+ Call WriteY_header;
+ Printf("======================> Writting header with first Freq=%g",Freq);
+ EndIf
+ Print [ I, OnRegion Terminal,
+ Format Table , File > StrCat[Dir, "test_Y_RI.s1p"]] ;
+ EndIf
+ }
+ }
+
+}
+
+// What follows only works if your solver is GetDP => adapt name if necessary
+
+DefineConstant[
+ // always solve this resolution (it's the only one provided)
+ // R_ = {"Analysis", Name "GetDP/1ResolutionChoices", Visible 1}
+ // set some command-line options for getdp
+ C_ = {"-solve -v 4 -pos -v2", Name "GetDP/9ComputeCommand", Visible 1}
+ // don't do the post-processing pass (some already included in Resolution)
+ P_ = {"Maps", Name "GetDP/2PostOperationChoices", Visible 1}
+];
diff --git a/ECE_full_wave/LC_data.pro b/ECE_full_wave/LC_data.pro
new file mode 100644
index 0000000000000000000000000000000000000000..b04a7b7acbe0b5bf8d6edab96367b84a32488553
--- /dev/null
+++ b/ECE_full_wave/LC_data.pro
@@ -0,0 +1,94 @@
+DefineConstant[
+ cm = 1e-2,
+ mm = 1e-3
+ rw = {5*mm/2, Name "Param. Geometry/03radius or wire", Highlight "Pink", ReadOnly}
+ rplateC = {6*cm, Name "Param. Geometry/10radius of capacitor plates", Highlight "LightCyan", ReadOnly}
+ dplateC = {3*mm, Name "Param. Geometry/11distance between plates", Highlight "LightCyan", ReadOnly}
+];
+
+sigma_cond = 1e7;
+mur_core = 1000;
+epsr_diel = 1e6;
+sigma_diel = 0;
+
+mu0 = 4.e-7 * Pi ;
+nu0 = 1/mu0;
+eps0 = 8.854187818e-12;
+
+// --------------------
+
+nuAir = nu0;
+epsAir = eps0;
+sigmaAir = 0;
+
+nuCore = 1/(mu0*mur_core);
+epsCore = eps0;
+sigmaCore = 0;
+
+nuDiel = nu0;
+epsDiel = eps0*epsr_diel;
+sigmaDiel = sigma_diel;
+
+nuCond = nu0;
+epsCond = eps0;
+sigmaCond = sigma_cond;
+
+
+//----------------------
+// Physical numbers...
+//----------------------
+CONDUCTOR = 1000; // volume, conductor touching the boundary at the excited termimnal, including the coil wire and one plate
+BND_CONDUCTOR = 1111; // volume, conductor touching the boundary at the grounded terminal and including the other plate
+
+ELEC_IN = 111; // surface, excited terminal
+ELEC_OUT = 112; // surface, grounded terminal
+
+DIELECTRIC = 2000; // volume, the dielectric of the capacitor
+ELEC_DIEL_IN = 221;
+ELEC_DIEL_OUT = 222;
+
+CORE = 3000; // volume, the core of the coil
+
+AIR = 4000; // volume, the air
+BND_AIR = 4444; // surface, boundary touched by air
+
+// -----------------------
+cGUI= "{CL - Excitation/";
+close_menu = 1;
+colorro = "LightGrey";
+mTypeBC = StrCat[cGUI,"Type of ECE Excitation/0"];
+
+colorMTypeBC = "Red";
+DefineConstant[
+ Flag_AnalysisType = { 0,
+ Choices{
+ 0="ev",
+ 1="ec"},
+ Name Str[mTypeBC], Highlight Str[colorMTypeBC], Closed !close_menu,
+ ServerAction Str["Reset", "GetDP/1ResolutionChoices"]}
+];
+
+/* new menu for the interface - values of excitations - significance depends on the type of BC */
+mValuesBC = StrCat[cGUI,"Frequency values/0"];
+colorMValuesBC = "Ivory";
+
+fmin = 1000; // Hz
+fmax = 80000; // Hz
+
+nop = 10;
+freqs()=LogSpace[Log10[fmin],Log10[fmax],nop];
+//freqs()=LinSpace[fmin,fmax,nop];
+DefineConstant[
+ Freq = {freqs(0), Choices{freqs()}, Loop 0, Name StrCat[mValuesBC, "0Working Frequency"], Units "Hz", Highlight Str[colorMValuesBC], Closed !close_menu }
+];
+
+
+If (Flag_AnalysisType==1) // current exc
+ Printf("======================> Terminal is current => Z transfer function");
+ ITermRMS = 1;
+ ITermPhase = 0;
+Else // voltage exc
+ Printf("======================> Terminal is voltage excited => Y transfer function");
+ VTermRMS = 1;
+ VTermPhase = 0;
+EndIf
diff --git a/ECE_full_wave/LC_ostrowski.stp b/ECE_full_wave/LC_ostrowski.stp
new file mode 100644
index 0000000000000000000000000000000000000000..41dbfcba4ee49d107468b7b02d3e0c63e9c5bad2
--- /dev/null
+++ b/ECE_full_wave/LC_ostrowski.stp
@@ -0,0 +1,28652 @@
+ISO-10303-21;
+HEADER;
+FILE_DESCRIPTION((''),'2;1');
+FILE_NAME('LC_ASM','2021-07-08T11:46:31',('CHJOOST1'),(''),
+'CREO PARAMETRIC BY PTC INC, 2017110','CREO PARAMETRIC BY PTC INC, 2017110','');
+FILE_SCHEMA(('CONFIG_CONTROL_DESIGN'));
+ENDSEC;
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diff --git a/ECE_full_wave/README.txt b/ECE_full_wave/README.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7c6aec2c86695cf3e32dc0115182c82df0549a0c
--- /dev/null
+++ b/ECE_full_wave/README.txt
@@ -0,0 +1,31 @@
+Electric circuit element (ECE) boundary conditions in full-wave electromagnetic problems.
+
+ Models developed by G. Ciuprina, D. Ioan and R.V. Sabariego.
+
+This directory contains the pro and geo files necessary to run the test cases in article:
+
+G. Ciuprina, D. Ioan, and R.V. Sabariego. Electric circuit element boundary conditions
+in the finite element method for full-wave passive electromagnetic devices.
+Journal of Mathematics in Industry, 12:1-13, Art no. 7, 2022. DOI: 10.1186/s13362-022-00122-1.
+
+Common formulation files:
+-------------------------
+ "FullWave_E_ece_SISO.pro" - file with function spaces, formulation, resolution and postprocessing.
+
+Cylinder benchmark:
+-------------------
+ "Ishape3D_data.pro" - contains geometrical and physical parameters used by the geo and pro files.
+ "Ishape3D.geo" - contains the geometry description.
+ "Ishape3D.pro" - contains the problem definition.
+
+Inductor-Capacitor (LC) benchmark:
+-------------
+ "LC_data.pro" - contains geometrical and physical parameters used by the geo and pro files.
+ "LC_ostrowski.stp" - STEP geometry courtesy of J. Ostrowski.
+ "LC.geo" - adapts STEP file to use with Gmsh. Note that the computation of BooleanFragments is very slow.
+ "LC.pro" - contains the problem definition.
+
+Quick start
+-----------
+ Open "Ishape3D.pro" with Gmsh.
+ Open "LC.pro" with Gmsh.
diff --git a/ElectromagneticScattering/scattererTmatrix.geo b/ElectromagneticScattering/scattererTmatrix.geo
index 01c68c93867729f200a00f3e4258f45d23584907..422a50ce9d8a761ee88a5d74bbee5ab45ac5d35b 100644
--- a/ElectromagneticScattering/scattererTmatrix.geo
+++ b/ElectromagneticScattering/scattererTmatrix.geo
@@ -74,3 +74,9 @@ Mesh.VolumeEdges = 0;
Mesh.ElementOrder = 2;
Mesh.HighOrderOptimize = 1;
+//+
+Hide "*";
+//+
+Show {
+ Point{1}; Point{2}; Curve{1}; Curve{2}; Curve{3}; Surface{1}; Surface{2}; Volume{1};
+}
diff --git a/QuasiNormalModeExpansion/QNM_expansion_DtN.geo b/QuasiNormalModeExpansion/QNM_expansion_DtN.geo
new file mode 100644
index 0000000000000000000000000000000000000000..619575eaff68155d06eea11ef30543094621b4f1
--- /dev/null
+++ b/QuasiNormalModeExpansion/QNM_expansion_DtN.geo
@@ -0,0 +1,51 @@
+///////////////////////////////
+// Author : Guillaume Demesy //
+///////////////////////////////
+
+Include "QNM_expansion_DtN_data.geo";
+SetFactory("OpenCASCADE");
+lc_bg = lambda0/paramaille;
+lc_sc = lambda0/(paramaille*3);
+
+Rectangle(1) = {-dx_scat/2, -dy_scat/2, 0, dx_scat, dy_scat, 0};
+Disk(2) = {0, 0, 0, r_domain, r_domain};
+If (flag_PML==1)
+ Disk(3) = {0, 0, 0, r_pml, r_pml};
+EndIf
+Coherence;
+
+Physical Point("PrintPoint",100) = {1};
+
+Physical Surface("SCAT",1) = {1};
+If (flag_PML==1)
+ Physical Surface("BG",2) = {2};
+ Characteristic Length {6} = lc_bg;
+ Physical Surface("PML",3) = {3};
+ Physical Surface("SRC",4) = {};
+ Characteristic Length {2,3,4,5} = lc_sc;
+ Characteristic Length {1} = lc_bg;
+ Characteristic Length {7} = lc_bg;
+ Physical Line("SURF_SM",10) = {};
+ Else
+ Physical Surface("BG",2) = {2};
+ Physical Surface("SRC",4) = {};
+ Characteristic Length {2,3,4,5} = lc_sc;
+ Characteristic Length {1} = lc_bg;
+ Physical Line("SURF_SM",10) = {1};
+EndIf
+
+Rectangle(10) = {-dx_scat/2+domain_tot*yshift, -dy_scat/2, 0, dx_scat, dy_scat, 0};
+Disk(20) = {domain_tot*yshift, 0, 0, r_domain, r_domain};
+Delete{Surface{10,20};}
+If (flag_PML==1)
+ Disk(30) = {domain_tot*yshift, 0, 0, r_pml, r_pml};
+ Delete{Surface{30};}
+EndIf
+
+If (flag_PML==1)
+ Point(newp) = {-dx_scat/2+domain_tot*yshift, 2*r_pml, 0};
+Else
+ Point(newp) = {-dx_scat/2+domain_tot*yshift, 2*r_domain, 0};
+EndIf
+Geometry.Points = 0;
+
diff --git a/QuasiNormalModeExpansion/QNM_expansion_DtN.pro b/QuasiNormalModeExpansion/QNM_expansion_DtN.pro
new file mode 100644
index 0000000000000000000000000000000000000000..8ca575f0c1f3ccfe5d7dfcf6f2041b90449e2c57
--- /dev/null
+++ b/QuasiNormalModeExpansion/QNM_expansion_DtN.pro
@@ -0,0 +1,561 @@
+///////////////////////////////
+// Author : Guillaume Demesy //
+///////////////////////////////
+
+Include "QNM_expansion_DtN_data.geo";
+stored_exp_field_AR_PML = 10000;
+stored_exp_field_AR_mur = 20000;
+stored_exp_field_AR_BT2 = 30000;
+stored_exp_field_manual_PML = 40000;
+CreateDir["out"];
+
+Group {
+ // Domains
+ Scat = Region[1];
+ Bg = Region[2];
+ Src = Region[4];
+ If (flag_PML==0)
+ PML = Region[{}];
+ Surf = Region[10];
+ Else
+ PML = Region[{3}];
+ Surf = Region[{10}];
+ EndIf
+ Omega = Region[{Bg,Scat,PML,Src}];
+ PrintPoint = Region[100];
+}
+
+Function{
+ I[] = Complex[0.0,1.0];
+
+ k0[] = $realomega/cel;
+ omega0[] = k0[]*cel;
+
+ spml_re = 1;
+ spml_im = 1;
+
+ R_pml_in = r_domain;
+ sr[] = Complex[spml_re,spml_im];
+ rho[] = Sqrt[X[]*X[]+Y[]*Y[]];// Norm[ XYZ[ ] ];
+ phi[] = Atan2[ Y[] , X[] ];
+ rr[] = R_pml_in + (rho[] - R_pml_in) * sr[];
+ drr[] = sr[];
+ pmlcirctens[] = Rotate[TensorDiag[rr[]/(drr[]*rho[]), (drr[]*rho[])/rr[], (drr[]*rr[])/rho[]],0,0,-phi[]];
+
+ epsr[Scat] = Complex[epsr_scat_re,epsr_scat_im];
+ epsr[Bg] = epsr_bg;
+ epsr[Src] = epsr_bg;
+ epsr[PML] = pmlcirctens[];
+
+ epsr_annex[Scat] = epsr_bg;
+ epsr_annex[Bg] = epsr_bg;
+ epsr_annex[Src] = epsr_bg;
+ epsr_annex[PML] = pmlcirctens[];
+
+ mur[Scat] = 1;
+ mur[Bg] = 1;
+ mur[Src] = 1;
+ mur[PML] = pmlcirctens[];
+
+ alpha[] = k0[]*Cos[theta0];
+ beta[] = k0[]*Sin[theta0];
+ siwt = 1;
+ ui[] = Vector[0, 0, Exp[I[]*siwt*(alpha[]*X[]+beta[]*Y[])] ];
+ Hi[] = I[]/(omega0[]*mu0) * Vector[alpha[],beta[],0] /\ ui[];
+ Pinc[] = 0.5*1^2*Sqrt[eps0*epsr_bg/mu0] * 2*r_domain;
+
+ THETA[] = Atan2[Y[],X[]];
+ TG[] = Vector[-Sin[THETA[]], Cos[THETA[]],0];
+
+ source_PW[] = k0[]^2 * (epsr_annex[]-epsr[]) * ui[];
+
+ For k In {0:#tabrealomegasexpansion()-1}
+ k0~{k}[] = tabrealomegasexpansion(k)/cel;
+ alpha~{k}[] = k0~{k}[]*Cos[theta0];
+ beta~{k}[] = k0~{k}[]*Sin[theta0];
+ ui~{k}[] = Vector[0, 0, Exp[I[]*siwt*(alpha~{k}[]*X[]+beta~{k}[]*Y[])] ];
+ source_PW~{k}[] = k0~{k}[]^2 * (epsr_annex[]-epsr[]) * ui~{k}[];
+ us_exp_PML_modal_manual~{k}[] = ComplexScalarField[XYZ[]]{stored_exp_field_manual_PML+k};
+ us_exp_PML_modal~{k}[] = ComplexScalarField[XYZ[]]{stored_exp_field_AR_PML+k};
+ us_exp_mur_modal~{k}[] = ComplexScalarField[XYZ[]]{stored_exp_field_AR_mur+k};
+ us_exp_BT2_modal~{k}[] = ComplexScalarField[XYZ[]]{stored_exp_field_AR_BT2+k};
+ EndFor
+
+
+ source_G[Src] = Vector[0, 0, 1];
+ source_G[Scat] = 0;
+ source_G[Bg] = 0;
+ source_G[PML] = 0;
+
+ Rout = r_domain;
+
+ alphaBT[] = 1/(2*Rout) - I[]/(8*k0[]*Rout^2*(1+I[]/(k0[]*Rout)));
+ betaBT[] = - 1/(2*I[]*k0[]*(1+I[]/(k0[]*Rout)));
+}
+
+Constraint {
+}
+
+Jacobian {
+ { Name JVol ;
+ Case {
+ { Region All ; Jacobian Vol ; }
+ }
+ }
+ { Name JSur ;
+ Case {
+ { Region All ; Jacobian Sur ; }
+ }
+ }
+}
+
+Integration {
+ { Name Int_1 ;
+ Case {
+ { Type Gauss ;
+ Case {
+ { GeoElement Point ; NumberOfPoints 1 ; }
+ { GeoElement Line ; NumberOfPoints 4 ; }
+ { GeoElement Triangle ; NumberOfPoints 12 ; }
+ }
+ }
+ }
+ }
+}
+
+FunctionSpace {
+ { Name Hgrad_P; Type Form1P;
+ BasisFunction {
+ { Name sn; NameOfCoef un; Function BF_PerpendicularEdge_1N; Support Region[{Omega,Surf}]; Entity NodesOf[Omega]; }
+ { Name sn2; NameOfCoef un2; Function BF_PerpendicularEdge_2E; Support Region[{Omega,Surf}]; Entity EdgesOf[Omega]; }
+ }
+ Constraint {
+ }
+ }
+}
+
+Formulation {
+ {Name form_direct_PML; Type FemEquation;
+ Quantity{{ Name u; Type Local; NameOfSpace Hgrad_P;}}
+ Equation{
+ Galerkin{[ k0[]^2*epsr[]*Dof{u} , {u}]; In Omega; Jacobian JVol; Integration Int_1;}
+ Galerkin{[ -1/mur[]*Dof{Curl u} , {Curl u}]; In Omega; Jacobian JVol; Integration Int_1;}
+ Galerkin{[ -source_PW[] , {u}]; In Omega; Jacobian JVol; Integration Int_1;}
+ }
+ }
+
+ {Name form_direct_mur; Type FemEquation;
+ Quantity{{ Name u; Type Local; NameOfSpace Hgrad_P;}}
+ Equation{
+ Galerkin{[ k0[]^2*epsr[]*Dof{u} , {u}]; In Omega; Jacobian JVol; Integration Int_1;}
+ Galerkin{[ -1/mur[]*Dof{Curl u} , {Curl u}]; In Omega; Jacobian JVol; Integration Int_1;}
+ Galerkin{[ -source_PW[] , {u}]; In Omega; Jacobian JVol; Integration Int_1;}
+ Galerkin{[ I[]*k0[]*Dof{u} , {u}]; In Surf; Jacobian JSur; Integration Int_1;}
+ }
+ }
+
+ {Name form_direct_BT2; Type FemEquation;
+ Quantity{{ Name u; Type Local; NameOfSpace Hgrad_P;}}
+ Equation{
+ Galerkin{[ k0[]^2*epsr[]*Dof{u} , {u}]; In Omega; Jacobian JVol; Integration Int_1;}
+ Galerkin{[ -1/mur[]*Dof{Curl u} , {Curl u}]; In Omega; Jacobian JVol; Integration Int_1;}
+ Galerkin{[ -source_PW[] , {u}]; In Omega; Jacobian JVol; Integration Int_1;}
+ Galerkin{[ I[]*k0[]*Dof{u} , {u}]; In Surf; Jacobian JSur; Integration Int_1;}
+ Galerkin{[ -alphaBT[] * Dof{u} , {u}]; In Surf; Jacobian JSur; Integration Int_1;}
+ Galerkin{[ -betaBT[] * Dof{Curl u} , {Curl u}]; In Surf; Jacobian JSur; Integration Int_1;}
+ }
+ }
+
+ {Name form_modal_linear_PML; Type FemEquation;
+ Quantity{{ Name u; Type Local; NameOfSpace Hgrad_P;}}
+ Equation{
+ Galerkin{Eig[-1/cel^2*epsr[]*Dof{u} , {u}]; Order 2 ; In Omega; Jacobian JVol; Integration Int_1;}
+ Galerkin{ [ -1/mur[]*Dof{Curl u} , {Curl u}]; In Omega; Jacobian JVol; Integration Int_1;}
+ }
+ }
+
+ {Name form_modal_PML; Type FemEquation;
+ Quantity{{ Name u; Type Local; NameOfSpace Hgrad_P;}}
+ Equation{
+ Galerkin{Eig[-1/cel^2*epsr[]*Dof{u} , {u}]; Rational 1 ; In Omega; Jacobian JVol; Integration Int_1;}
+ Galerkin{Eig[ -1/mur[]*Dof{Curl u} , {Curl u}]; Rational 2 ; In Omega; Jacobian JVol; Integration Int_1;}
+ }
+ }
+ {Name form_modal_mur_poly; Type FemEquation;
+ Quantity{{ Name u; Type Local; NameOfSpace Hgrad_P;}}
+ Equation{
+ Galerkin{ Eig[-1/cel^2*epsr[]*Dof{u} , {u}]; Order 2 ; In Omega; Jacobian JVol; Integration Int_1;}
+ Galerkin{ [-1/mur[]*Dof{Curl u} , {Curl u}]; In Omega; Jacobian JVol; Integration Int_1;}
+ Galerkin{ Eig[ 1/cel*Dof{u} , {u}]; Order 1 ; In Surf ; Jacobian JSur; Integration Int_1;}
+ }
+ }
+ {Name form_modal_mur; Type FemEquation;
+ Quantity{{ Name u; Type Local; NameOfSpace Hgrad_P;}}
+ Equation{
+ Galerkin{ Eig[-1/cel^2*epsr[]*Dof{u} , {u}]; Rational 1 ; In Omega; Jacobian JVol; Integration Int_1;}
+ Galerkin{ Eig[-1/mur[]*Dof{Curl u} , {Curl u}]; Rational 2 ; In Omega; Jacobian JVol; Integration Int_1;}
+ Galerkin{ Eig[ 1/cel*Dof{u} , {u}]; Rational 3 ; In Surf ; Jacobian JSur; Integration Int_1;}
+ }
+ }
+ {Name form_modal_BT2; Type FemEquation;
+ Quantity{{ Name u; Type Local; NameOfSpace Hgrad_P;}}
+ Equation{
+ // {-1/cel^2,0,0}/{1} --------- (i\omega)^2/c^2
+ Galerkin{Eig[ epsr[]* Dof{u} , {u}]; Rational 1; In Omega; Jacobian JVol; Integration Int_1;}
+ // {1}/{1} 1
+ Galerkin{Eig[ -1/mur[]*Dof{Curl u} , {Curl u}]; Rational 2; In Omega; Jacobian JVol; Integration Int_1;}
+ // {1/cel,0}/{1} --------- i\omega/c
+ Galerkin{Eig[ Dof{u} , {u}]; Rational 3; In Surf ; Jacobian JSur; Integration Int_1;}
+ // {-4*Rout/cel,3}/{-8*Rout^2/cel,8*Rout} --------- \frac{-4Ri\omega/c+3}{-8R^2i\omega/c+8R}
+ Galerkin{Eig[ Dof{u} , {u}]; Rational 4; In Surf ; Jacobian JSur; Integration Int_1;}
+ // {-Rout}/{2*Rout/cel,-2} --------- \frac{-R}{2Ri\omega/c-2}
+ Galerkin{Eig[ Dof{Curl u} , {Curl u}]; Rational 5; In Surf ; Jacobian JSur; Integration Int_1;}
+ }
+ }
+ {Name form_RHS; Type FemEquation;
+ Quantity{{ Name u; Type Local; NameOfSpace Hgrad_P;}}
+ Equation{
+ // Galerkin { [ 1. * Dof{u} , { u} ]; In Omega ; Jacobian JSur; Integration Int_1;}
+ Galerkin{[-source_PW[] , {u}]; In Omega; Jacobian JVol; Integration Int_1;}
+
+ }
+ }
+}
+
+Resolution {
+ { Name res_modal_PML;
+ System {
+ { Name M1; NameOfFormulation form_modal_linear_PML; Type ComplexValue; }
+ { Name M2; NameOfFormulation form_direct_PML ; Type ComplexValue; }
+ }
+ Operation {
+ GenerateSeparate[M1] ;
+ EigenSolve[M1,neig_PML,target_re_PML,target_im_PML];
+ PostOperation[postop_modal_PML];
+ For k In {0:#tabrealomegasexpansion()-1}
+ Evaluate[$realomega=tabrealomegasexpansion(k)];
+ Generate[M2];
+ Solve[M2];
+ PostOperation[postop_direct_PML];
+ EndFor
+ For k In {0:#tabrealomegasexpansion()-1}
+ PostOperation[postop_gmsh~{k}];
+ Sleep[0.3];
+ EndFor
+ }
+ }
+
+ { Name res_modal_AR_BT2;
+ System{
+ { Name V ; NameOfFormulation form_RHS ; Type ComplexValue; }
+ { Name M1; NameOfFormulation form_modal_BT2 ; Type ComplexValue; }
+ { Name M2; NameOfFormulation form_direct_BT2 ; Type ComplexValue; }
+
+ }
+ Operation{
+ For k In {0:#tabrealomegasexpansion()-1}
+ Evaluate[$realomega=tabrealomegasexpansion(k)];
+ GenerateListOfRHS[V,Omega,#tabrealomegasexpansion()];
+ EndFor
+ GenerateSeparate[M1];
+ EigenSolveAndExpand[M1,neig_BT,target_re_BT,target_im_BT,
+ {{-1/cel^2,0,0},{1},{1/cel,0},{ 4*Rout/cel,-3} ,{Rout}},
+ { {1},{1}, {1},{-8*Rout^2/cel,8*Rout},{2*Rout/cel,-2}},
+ tabrealomegasexpansion(),
+ V];
+ PostOperation[postop_modal_AR_BT2];
+ For k In {0:#tabrealomegasexpansion()-1}
+ Evaluate[$realomega=tabrealomegasexpansion(k)];
+ Generate[M2];
+ Solve[M2];
+ PostOperation[postop_direct_BT2];
+ EndFor
+ For k In {0:#tabrealomegasexpansion()-1}
+ PostOperation[postop_gmsh~{k}];
+ Sleep[0.5];
+ EndFor
+ }
+ }
+
+ { Name res_modal_AR_PML;
+ System{
+ { Name M1; NameOfFormulation form_modal_PML ; Type ComplexValue; }
+ { Name V ; NameOfFormulation form_RHS ; Type ComplexValue; }
+ }
+ Operation{
+ For k In {0:#tabrealomegasexpansion()-1}
+ Evaluate[$realomega=tabrealomegasexpansion(k)];
+ GenerateListOfRHS[V,Omega,#tabrealomegasexpansion()];
+ EndFor
+ GenerateSeparate[M1];
+ EigenSolveAndExpand[M1,neig_PML,target_re_BT,target_im_BT,
+ {{1,0,0},{1}},
+ { {1},{1}},
+ tabrealomegasexpansion(),
+ V];
+ }
+ }
+ { Name res_modal_AR_mur;
+ System{
+ { Name V; NameOfFormulation form_RHS ; Type ComplexValue; }
+ { Name M1; NameOfFormulation form_modal_mur ; Type ComplexValue; }
+ { Name M2; NameOfFormulation form_direct_mur ; Type ComplexValue; }
+ }
+ Operation{
+ For k In {0:#tabrealomegasexpansion()-1}
+ Evaluate[$realomega=tabrealomegasexpansion(k)];
+ GenerateListOfRHS[V,Omega,#tabrealomegasexpansion()];
+ EndFor
+ GenerateSeparate[M1];
+ EigenSolveAndExpand[M1,neig_BT,target_re_BT,target_im_BT,
+ {{1,0,0},{1},{1,0}},
+ { {1},{1}, {1}},
+ tabrealomegasexpansion(),
+ V];
+ PostOperation[postop_modal_AR_mur];
+ For k In {0:#tabrealomegasexpansion()-1}
+ Evaluate[$realomega=tabrealomegasexpansion(k)];
+ Generate[M2];
+ Solve[M2];
+ PostOperation[postop_direct_mur];
+ EndFor
+ For k In {0:#tabrealomegasexpansion()-2}
+ PostOperation[postop_gmsh~{k}];
+ Sleep[0.5];
+ EndFor
+ }
+ }
+}
+
+PostProcessing {
+ { Name postpro_direct_PML; NameOfFormulation form_direct_PML;
+ Quantity {
+ { Name us ; Value { Local{ [CompZ[{u} ]]; In Omega; Jacobian JVol; } } }
+ { Name ut ; Value { Local{ [CompZ[{u}+ui[]]]; In Omega; Jacobian JVol; } } }
+ { Name intnorm2utot ; Value { Integral { [SquNorm[{u}+ui[]]]; In Scat ; Jacobian JVol; Integration Int_1 ; } } }
+ }
+ }
+ { Name postpro_direct_mur; NameOfFormulation form_direct_mur;
+ Quantity {
+ { Name us ; Value { Local{ [CompZ[{u} ]]; In Omega; Jacobian JVol; } } }
+ { Name ut ; Value { Local{ [CompZ[{u}+ui[]]]; In Omega; Jacobian JVol; } } }
+ { Name intnorm2utot ; Value { Integral { [SquNorm[{u}+ui[]]]; In Scat ; Jacobian JVol; Integration Int_1 ; } } }
+ }
+ }
+ { Name postpro_direct_BT2; NameOfFormulation form_direct_BT2;
+ Quantity {
+ { Name us ; Value { Local{ [CompZ[{u} ]]; In Omega; Jacobian JVol; } } }
+ { Name ut ; Value { Local{ [CompZ[{u}+ui[]]]; In Omega; Jacobian JVol; } } }
+ { Name intnorm2utot ; Value { Integral { [SquNorm[{u}+ui[]]]; In Scat ; Jacobian JVol; Integration Int_1 ; } } }
+ }
+ }
+
+ // ANCHOR POSTPRO_modal_PML
+ { Name postpro_modal_PML; NameOfFormulation form_modal_PML;
+ Quantity {
+ { Name u ; Value { Local{ [CompZ[{u}] ] ; In Omega ; Jacobian JVol; } } }
+ { Name normu ; Value { Local{ [ Norm[{u}] ] ; In Omega ; Jacobian JVol; } } }
+ { Name ev_re ; Value { Local{ [$EigenvalueReal] ; In PrintPoint; Jacobian JVol; } } }
+ { Name ev_im ; Value { Local{ [$EigenvalueImag] ; In PrintPoint; Jacobian JVol; } } }
+ { Name vol ; Value { Integral { [1] ; In PrintPoint ; Jacobian JVol; Integration Int_1 ; } } }
+ { Name eig_re ; Value { Integral { [$EigenvalueReal/$vol] ; In PrintPoint ; Jacobian JVol; Integration Int_1 ; } } }
+ { Name eig_im ; Value { Integral { [$EigenvalueImag/$vol] ; In PrintPoint ; Jacobian JVol; Integration Int_1 ; } } }
+ { Name ev ; Value { Integral { [Complex[$EigenvalueReal,$EigenvalueImag]/$vol] ; In PrintPoint; Jacobian JVol; Integration Int_1 ; } } }
+ For i In {0:#tabrealomegasexpansion()-1}
+ { Name overlap~{i} ; Value { Integral { [{u}*source_PW~{i}[]] ; In Scat ; Jacobian JVol; Integration Int_1 ; } } }
+ EndFor
+ { Name den ; Value { Integral { [{u}*epsr[]*{u}] ; In Omega ; Jacobian JVol; Integration Int_1 ; } } }
+ For i In {0:#tabrealomegasexpansion()-1}
+ { Name us_PML_modal_manual~{i};
+ Value {
+ For j In {0:(neig_PML-1)}
+ // cel^2/(w^2-w_k^2)
+ Local { [ CompZ[cel^2/(tabrealomegasexpansion(i)^2-$ev~{j}^2) * $overlap~{i}~{j}/$den~{j} * {u}[neig_PML-1-j]]] ; In Omega; Jacobian JVol; }
+ // // cel^2/(2*w*(w-w_k))
+ // Local { [ CompZ[cel^2/(2*tabrealomegasexpansion(i)*(tabrealomegasexpansion(i)-$ev~{j})) * $overlap~{i}~{j}/$den~{j} * {u}[neig_PML-1-j]]] ; In Omega; Jacobian JVol; }
+ // // NEP style : cel^2/(2*w_k*(w-w_k))
+ // Local { [ CompZ[cel^2/(2*$ev~{j}*(tabrealomegasexpansion(i)-$ev~{j})) * $overlap~{i}~{j}/$den~{j} * {u}[neig_PML-1-j]]] ; In Omega; Jacobian JVol; }
+ EndFor
+ }
+ }
+ { Name us_PML_modal_manual_stored~{i}; Value {Local { [us_exp_PML_modal_manual~{i}[]] ; In Omega; Jacobian JVol; } } }
+ EndFor
+ For i In {0:#tabrealomegasexpansion()-1}
+ { Name intnorm2utot~{i} ; Value { Integral { [SquNorm[us_exp_PML_modal_manual~{i}[] + CompZ[ui~{i}[]]]]; In Scat; Jacobian JVol; Integration Int_1 ; } } }
+ EndFor
+ }
+ }
+
+ { Name postpro_modal_AR_BT2; NameOfFormulation form_modal_BT2;
+ Quantity {
+ { Name u ; Value { Local{ [CompZ[{u}] ] ; In Omega ; Jacobian JVol; } } }
+ { Name normu ; Value { Local{ [ Norm[{u}] ] ; In Omega ; Jacobian JVol; } } }
+ { Name ev_re ; Value { Local{ [$EigenvalueReal] ; In PrintPoint; Jacobian JVol; } } }
+ { Name ev_im ; Value { Local{ [$EigenvalueImag] ; In PrintPoint; Jacobian JVol; } } }
+ { Name vol ; Value { Integral { [1] ; In PrintPoint ; Jacobian JVol; Integration Int_1 ; } } }
+ { Name eig_re ; Value { Integral { [$EigenvalueReal/$vol] ; In PrintPoint ; Jacobian JVol; Integration Int_1 ; } } }
+ { Name eig_im ; Value { Integral { [$EigenvalueImag/$vol] ; In PrintPoint ; Jacobian JVol; Integration Int_1 ; } } }
+ For i In {0:#tabrealomegasexpansion()-1}
+ { Name intnorm2utot~{i} ; Value { Integral { [SquNorm[us_exp_BT2_modal~{i}[] + CompZ[ui~{i}[]]]] ; In Scat ; Jacobian JVol; Integration Int_1 ; } } }
+ EndFor
+ }
+ }
+ { Name postpro_modal_AR_PML; NameOfFormulation form_modal_PML;
+ Quantity {
+ { Name u ; Value { Local{ [CompZ[{u}] ] ; In Omega ; Jacobian JVol; } } }
+ { Name ev_re ; Value { Local{ [$EigenvalueReal] ; In PrintPoint; Jacobian JVol; } } }
+ { Name ev_im ; Value { Local{ [$EigenvalueImag] ; In PrintPoint; Jacobian JVol; } } }
+ For i In {0:#tabrealomegasexpansion()-1}
+ { Name intnorm2utot~{i} ; Value { Integral { [SquNorm[us_exp_PML_modal~{i}[] + CompZ[ui~{i}[]]]] ; In Scat ; Jacobian JVol; Integration Int_1 ; } } }
+ EndFor
+ }
+ }
+ { Name postpro_modal_AR_mur; NameOfFormulation form_modal_mur;
+ Quantity {
+ { Name u ; Value { Local{ [CompZ[{u}] ] ; In Omega ; Jacobian JVol; } } }
+ { Name ev_re ; Value { Local{ [$EigenvalueReal] ; In PrintPoint; Jacobian JVol; } } }
+ { Name ev_im ; Value { Local{ [$EigenvalueImag] ; In PrintPoint; Jacobian JVol; } } }
+ { Name vol ; Value { Integral { [1] ; In PrintPoint ; Jacobian JVol; Integration Int_1 ; } } }
+ { Name eig_re ; Value { Integral { [$EigenvalueReal/$vol] ; In PrintPoint ; Jacobian JVol; Integration Int_1 ; } } }
+ { Name eig_im ; Value { Integral { [$EigenvalueImag/$vol] ; In PrintPoint ; Jacobian JVol; Integration Int_1 ; } } }
+ For i In {0:#tabrealomegasexpansion()-1}
+ { Name intnorm2utot~{i} ; Value { Integral { [SquNorm[us_exp_mur_modal~{i}[] + CompZ[ui~{i}[]]]] ; In Scat ; Jacobian JVol; Integration Int_1 ; } } }
+ EndFor
+ }
+ }
+}
+
+PostOperation {
+ { Name postop_direct_PML; NameOfPostProcessing postpro_direct_PML ;
+ Operation {
+ Print[ us , OnElementsOf Omega, File "out/us_PML_direct.pos", ChangeOfCoordinates {$X+domain_tot*yshift,$Y,$Z}, Name "us_PML_direct"];
+ Print[ intnorm2utot[Scat] , OnGlobal, File "out/ACC_PML_direct.out", Format SimpleTable];
+ If(flag_PRINTFIELDS==1)
+ Print[ us , OnElementsOf Omega, File "out/us_PML.pos", Name "us_PML"];
+ EndIf
+ }
+ }
+ { Name postop_direct_mur; NameOfPostProcessing postpro_direct_mur ;
+ Operation {
+ Print[ us , OnElementsOf Omega, File "out/us_mur_direct.pos", ChangeOfCoordinates {$X+domain_tot*yshift,$Y,$Z} , Name "us_mur_direct"];
+ Print[ intnorm2utot[Scat] , OnGlobal, File "out/ACC_mur_direct.out", Format SimpleTable];
+ If(flag_PRINTFIELDS==1)
+ Print[ us , OnElementsOf Omega, File "out/us_mur.pos", Name "us_mur"];
+ EndIf
+ }
+ }
+ { Name postop_direct_BT2; NameOfPostProcessing postpro_direct_BT2 ;
+ Operation {
+ Print[ us , OnElementsOf Omega, File "out/us_BT2_direct.pos", ChangeOfCoordinates {$X+domain_tot*yshift,$Y,$Z} , Name "us_BT2_direct"];
+ Print[ intnorm2utot[Scat] , OnGlobal, File "out/ACC_BT2_direct.out", Format SimpleTable];
+ If(flag_PRINTFIELDS==1)
+ Print[ us , OnElementsOf Omega, File "out/us_BT2.pos", Name "us_BT2"];
+ EndIf
+ }
+ }
+ { Name postop_modal_PML; NameOfPostProcessing postpro_modal_PML ;
+ Operation {
+ Print [ev_re , OnElementsOf PrintPoint , Format TimeTable, File "out/EigenValuesReal_PML.txt"];
+ Print [ev_im , OnElementsOf PrintPoint , Format TimeTable, File "out/EigenValuesImag_PML.txt"];
+ Print [vol[PrintPoint] , OnGlobal, TimeStep 0, StoreInVariable $vol,Format Table];
+ For j In {0:(neig-1)}
+ Print [eig_re[PrintPoint] , OnGlobal, TimeStep j , Format Table , SendToServer "GetDP/eig_re"];
+ Print [eig_im[PrintPoint] , OnGlobal, TimeStep j , Format Table , SendToServer "GetDP/eig_im"];
+ EndFor
+ Print [u , OnElementsOf Omega, File "out/u_PML.pos", Name "u_PML"];
+ If (flag_manualexp==1)
+ Print [vol[PrintPoint] , OnGlobal, TimeStep 0, StoreInVariable $vol,Format Table];
+ For i In {0:#tabrealomegasexpansion()-1}
+ For j In {0:(neig_PML-1)}
+ Print [overlap~{i}[Scat] , OnGlobal, TimeStep j, StoreInVariable $overlap~{i}~{j},Format Table];
+ EndFor
+ EndFor
+ For j In {0:(neig_PML-1)}
+ Print [den[Omega] , OnGlobal, TimeStep j, StoreInVariable $den~{j},Format Table];
+ EndFor
+ For j In {0:(neig_PML-1)}
+ Print [ev[PrintPoint] , OnGlobal, TimeStep j, StoreInVariable $ev~{j}, Format SimpleTable];
+ EndFor
+ For i In {0:(#tabrealomegasexpansion()-1)}
+ Print [us_PML_modal_manual~{i} , OnElementsOf Omega, StoreInField (stored_exp_field_manual_PML+i), File Sprintf["out/us_PML_modal_manual_%03g.pos",i], Name Sprintf["us_PML_modal_manual_%03g.pos",i], LastTimeStepOnly];
+ EndFor
+ For i In {0:(#tabrealomegasexpansion()-1)}
+ Print [intnorm2utot~{i}[Scat] , OnGlobal , Format SimpleTable,File Sprintf["out/ACC_PML_modal_manual_%03g.out",i],LastTimeStepOnly];
+ EndFor
+ EndIf
+ }
+ }
+ { Name postop_modal_AR_BT2; NameOfPostProcessing postpro_modal_AR_BT2 ;
+ Operation {
+ Print [ev_re , OnElementsOf PrintPoint , Format TimeTable, File "out/EigenValuesReal_BT2.txt"];
+ Print [ev_im , OnElementsOf PrintPoint , Format TimeTable, File "out/EigenValuesImag_BT2.txt"];
+ Print [vol[PrintPoint] , OnGlobal, TimeStep 0, StoreInVariable $vol,Format Table];
+ For j In {0:(neig-1)}
+ Print [eig_re[PrintPoint] , OnGlobal, TimeStep j , Format Table , SendToServer "GetDP/eig_re"];
+ Print [eig_im[PrintPoint] , OnGlobal, TimeStep j , Format Table , SendToServer "GetDP/eig_im"];
+ EndFor
+ Print [u , OnElementsOf Omega, File "out/u_BT2.pos", Name "u_BT2"];
+ For k In {0:#tabrealomegasexpansion()-1}
+ Print [u , OnElementsOf Omega, StoreInField (stored_exp_field_AR_BT2+k), File Sprintf["out/us_BT2_modal_%03g.pos",k],Name "us_BT2_modal",TimeStep {neig_BT+k}];
+ Print [intnorm2utot~{k}[Scat] , OnGlobal, File Sprintf["out/ACC_BT2_modal_%03g.out",k], Format SimpleTable, TimeStep {neig_BT+k}];
+ EndFor
+ }
+ }
+ { Name postop_modal_AR_PML; NameOfPostProcessing postpro_modal_AR_PML ;
+ Operation {
+ Print [ev_re , OnElementsOf PrintPoint , Format TimeTable, File "out/EigenValuesReal_PML.txt"];
+ Print [ev_im , OnElementsOf PrintPoint , Format TimeTable, File "out/EigenValuesImag_PML.txt"];
+ // Print [u , OnElementsOf Omega, File "out/u_PML.pos", Name "u_BT2"];
+ For k In {0:#tabrealomegasexpansion()-1}
+ Print [u , OnElementsOf Omega, StoreInField (stored_exp_field_AR_PML+k), File Sprintf["out/us_PML_modal_%03g.pos",k], Name "us_pml_modal",TimeStep {neig_PML+k}];
+ Print [intnorm2utot~{k}[Scat], OnGlobal , Format SimpleTable,File Sprintf["out/ACC_PML_modal_%03g.out",k],LastTimeStepOnly];
+ EndFor
+ }
+ }
+ { Name postop_modal_AR_mur; NameOfPostProcessing postpro_modal_AR_mur ;
+ Operation {
+ Print [ev_re , OnElementsOf PrintPoint , Format TimeTable, File "out/EigenValuesReal_mur.txt"];
+ Print [ev_im , OnElementsOf PrintPoint , Format TimeTable, File "out/EigenValuesImag_mur.txt"];
+ Print [vol[PrintPoint] , OnGlobal, TimeStep 0, StoreInVariable $vol,Format Table];
+ For j In {0:(neig-1)}
+ Print [eig_re[PrintPoint] , OnGlobal, TimeStep j , Format Table , SendToServer "GetDP/eig_re"];
+ Print [eig_im[PrintPoint] , OnGlobal, TimeStep j , Format Table , SendToServer "GetDP/eig_im"];
+ EndFor
+ // Print [u , OnElementsOf Omega, File "out/u_mur.pos", Name "u_BT2"];
+ For k In {0:#tabrealomegasexpansion()-1}
+ Print [u , OnElementsOf Omega,StoreInField (stored_exp_field_AR_mur+k), File Sprintf["out/us_mur_modal_%03g.pos",k], Name "us_mur_modal",TimeStep {neig_BT+k}];
+ Print [intnorm2utot~{k}[Scat] , OnGlobal, File Sprintf["out/ACC_mur_modal_%03g.out",k], Format SimpleTable, TimeStep {neig_BT+k}];
+ EndFor
+ }
+ }
+ For k In {0:#tabrealomegasexpansion()-1}
+ { Name postop_gmsh~{k} ; NameOfPostProcessing postpro_modal_AR_BT2;
+ Operation {
+ Echo[Str["Geometry.Points = 0;","Geometry.Color.Curves = {0,0,0};","Mesh.SurfaceEdges = 0;",
+ "k=PostProcessing.NbViews-1;","View[k].Visible = 0;","View.Visible = 0;","View[0].Visible = 1;",
+ Sprintf["View[%g].Visible = 0;",k],
+ Sprintf["View[%g].Visible = 0;",nb_Omegas+k],
+ Sprintf["View[%g].Visible = 1;",k+1],
+ Sprintf["View[%g].ColormapNumber = 7;",k+1],
+ Sprintf["View[%g].IntervalsType = 3;",k+1],
+ Sprintf["View[%g].NbIso = 30;",k+1],
+ Sprintf["View[%g].Visible = 1;",nb_Omegas+k+1],
+ Sprintf["View[%g].ColormapNumber = 7;",nb_Omegas+k+1],
+ Sprintf["View[%g].IntervalsType = 3;",nb_Omegas+k+1],
+ Sprintf["View[%g].NbIso = 30;",nb_Omegas+k+1]], File "tmp0.geo"];
+ // Echo[Str["Plugin(Annotate).Text= \"TOP : DIRECT -- BOTTOM : EXPANSION\";" , "Plugin(Annotate).Run;"]];
+ }
+ }
+ EndFor
+}
+
+slepc_options_rg = Sprintf[" -rg_interval_endpoints %.8lf,%.8lf,%.8lf,%.8lf ",eig_min_re,eig_max_re,eig_min_im,eig_max_im];
+DefineConstant[
+ R_ = {"res_nleig_rat_exp", Name "GetDP/1ResolutionChoices", Visible 1},
+ C_ = {StrCat["-pre ",str_res," -cal -slepc ",str_slepc_solver," ",slepc_options_rg] , Name "GetDP/9ComputeCommand", Visible 1}
+];
+
+DefineConstant[
+ eig_re_ = {0, Name "GetDP/eig_re", ReadOnly 1, Graph "10", Visible 1},
+ eig_im_ = {0, Name "GetDP/eig_im", ReadOnly 1, Graph "01", Visible 1}
+];
diff --git a/QuasiNormalModeExpansion/QNM_expansion_DtN_data.geo b/QuasiNormalModeExpansion/QNM_expansion_DtN_data.geo
new file mode 100644
index 0000000000000000000000000000000000000000..3ceb72459cc1fa7112aede78d6401edf1a8df8b3
--- /dev/null
+++ b/QuasiNormalModeExpansion/QNM_expansion_DtN_data.geo
@@ -0,0 +1,85 @@
+///////////////////////////////
+// Author : Guillaume Demesy //
+///////////////////////////////
+
+pp = "Model Options/";
+DefineConstant[
+ flag_DtN = {2 , Name StrCat[pp, "0DtN"], Choices {0="PML",1="ABC",2="BT2"} , ServerAction "Reset"},
+ flag_vector_case = {0 , Name StrCat[pp, "1polarization case"], Choices {0="(0,0,Ez)",1="(Ex,Ey,0)"} },
+ flag_o2 = {1 , Name StrCat[pp, "2FE order"], Choices {0="order 1",1="order 2"} },
+ neig = {120 , Name StrCat[pp, "3number of eigenvalues"] }
+];
+
+nm = 0.1;
+paramaille = 10;
+
+neig_PML = neig;
+neig_BT = neig;
+
+a_lat = 482.5*nm;
+lambda_m = a_lat;
+
+lambda0 = 500*nm;
+dx_scat = 200*nm;
+dy_scat = 400*nm;
+epsr_scat_re = 9;
+epsr_scat_im = 0.5;
+epsr_bg = 1;
+
+r_domain = 0.5*Sqrt[dx_scat^2+dy_scat^2]+100*nm;
+r_pml = r_domain+lambda0;
+
+eps0 = 8.854187817e-3*nm;
+mu0 = 400.*Pi*nm;
+cel = 1.0/Sqrt[eps0 * mu0];
+
+norm = dy_scat/(Pi*cel);
+
+omega_target_re = 0.7/norm;
+omega_target_im = 1/norm;
+
+target_re_PML = omega_target_re^2 - omega_target_im^2;
+target_im_PML = 2*omega_target_re*omega_target_im;
+target_re_BT = omega_target_im;
+target_im_BT = omega_target_re;
+
+eig_min_re = -5/norm;
+eig_max_re = 5/norm;
+eig_min_im = -8/norm;
+eig_max_im = 8/norm;
+
+If (flag_DtN==0)
+ flag_PML = 1;
+ flag_ABC_BAYLISS = 0;
+ slepc_options_rg = Sprintf[" -rg_interval_endpoints %.8lf,%.8lf,%.8lf,%.8lf ",eig_min_re,eig_max_re,eig_min_im,eig_max_im];
+ str_res = "res_modal_PML";
+ str_slepc_solver = " ";
+ domain_tot = 2*r_pml;
+Else
+ flag_PML = 0;
+ flag_ABC_BAYLISS = 1;
+ slepc_options_rg = " ";
+ If (flag_DtN==1)
+ str_res = "res_modal_AR_mur";
+ Else
+ str_res = "res_modal_AR_BT2";
+ EndIf
+ str_slepc_solver = " -nep_type nleigs -nep_rational -nep_target_magnitude -nep_view_pre -nep_monitor_all :temp_eigenvalues.txt ";
+ domain_tot = 2*r_domain;
+EndIf
+
+flag_PRINTVECTOR = 1;
+flag_PRINTFIELDS = 0;
+
+nb_Omegas = 60;
+RealOmega_min = 0.5 / norm;
+RealOmega_max = 3 / norm;
+theta0 = 30 * Pi/180;
+
+tabrealomegasexpansion = LinSpace[RealOmega_min,RealOmega_max,nb_Omegas];
+// Freq = 0;
+
+// FIXME
+flag_manualexp = 1;
+
+yshift = 1.1;
diff --git a/QuasiNormalModeExpansion/QNM_expansion_dispersive_media.geo b/QuasiNormalModeExpansion/QNM_expansion_dispersive_media.geo
new file mode 100644
index 0000000000000000000000000000000000000000..ab4fa7271b6bb78b98c9a60a32b8ed90b403ed54
--- /dev/null
+++ b/QuasiNormalModeExpansion/QNM_expansion_dispersive_media.geo
@@ -0,0 +1,98 @@
+///////////////////////////////
+// Author : Guillaume Demesy //
+///////////////////////////////
+
+Include "QNM_expansion_dispersive_media_data.geo";
+lc_cell = lambda_m/paramaille;
+lc_sq = lc_cell/2.;
+lc_src = lc_cell;
+
+Point(1) = {-a_lat , -a_lat/2, 0. , lc_cell};
+Point(2) = {-a_lat , a_lat/2, 0. , lc_cell};
+Point(3) = { 0 , -a_lat/2, 0. , lc_sq};
+Point(4) = { 0 , a_lat/2, 0. , lc_sq};
+Point(5) = { a_lat , -a_lat/2, 0. , lc_cell};
+Point(6) = { a_lat , a_lat/2, 0. , lc_cell};
+Point(12) = {-a_lat+0.7 *2*a_lat , -a_lat/2, 0. , lc_sq};
+Point(13) = {-a_lat+0.48*2*a_lat , a_lat/2, 0. , lc_sq};
+
+Point(7) = { cx_src , cy_src , 0. , lc_src};
+Point(8) = { cx_src+r_src , cy_src , 0. , lc_src};
+Point(9) = { cx_src , cy_src+r_src , 0. , lc_src};
+Point(10) = { cx_src-r_src , cy_src , 0. , lc_src};
+Point(11) = { cx_src , cy_src-r_src , 0. , lc_src};
+
+Circle(8) = {10, 7, 9};
+Circle(9) = {9, 7, 8};
+Circle(10) = {8, 7, 11};
+Circle(11) = {11, 7, 10};
+
+Line(12) = {7, 8};
+Line(13) = {7, 9};
+Line(14) = {7, 10};
+Line(15) = {7, 11};
+
+Line Loop(1) = {8, -13, 14};
+Plane Surface(1) = {-1};
+Line Loop(2) = {13, 9, -12};
+Plane Surface(2) = {-2};
+Line Loop(3) = {10, -15, 12};
+Plane Surface(3) = {-3};
+Line Loop(4) = {14, -11, -15};
+Plane Surface(4) = {4};
+
+Line(16) = {1, 3};
+Line(17) = {3, 12};
+Line(18) = {12, 5};
+Line(19) = {5, 6};
+Line(20) = {6, 4};
+Line(21) = {4, 13};
+Line(22) = {13, 2};
+Line(23) = {2, 1};
+Line(24) = {3, 13};
+Line(25) = {12, 4};
+Curve Loop(5) = {23, 16, 24, 22};
+Plane Surface(5) = {5};
+Curve Loop(6) = {24, -21, -25, -17};
+Plane Surface(6) = {-6};
+Curve Loop(7) = {25, -20, -19, -18};
+Curve Loop(8) = {8, 9, 10, 11};
+Plane Surface(7) = {-7, 8};
+
+Physical Surface(1) = {6}; // Dispersive medium
+Physical Surface(2) = {5,7}; // Background
+Physical Surface(3) = {1,2,3,4}; // disk green
+Physical Line(10) = {16,17,18,19,20,21,22,23}; // Outer box
+Physical Line(20) = {24,25}; // bound lag
+Physical Line(30) = {12}; // Edge Source Green X
+Physical Line(31) = {13}; // Edge Source Green Y
+Physical Point(100) = {7};
+
+// dummy lines to see expansion and direct solutions side by side
+pp=newp;
+Point(pp+1) = {-a_lat+ xshift*2*a_lat , -a_lat/2 , 0. , lc_cell};
+Point(pp+2) = {-a_lat+ xshift*2*a_lat , a_lat/2 , 0. , lc_cell};
+Point(pp+3) = { 0+ xshift*2*a_lat , -a_lat/2 , 0. , lc_sq};
+Point(pp+4) = { 0+ xshift*2*a_lat , a_lat/2 , 0. , lc_sq};
+Point(pp+5) = { a_lat+ xshift*2*a_lat , -a_lat/2 , 0. , lc_cell};
+Point(pp+6) = { a_lat+ xshift*2*a_lat , a_lat/2 , 0. , lc_cell};
+Point(pp+12) = {-a_lat+0.7 *2*a_lat+ xshift*2*a_lat , -a_lat/2, 0. , lc_sq};
+Point(pp+13) = {-a_lat+0.48*2*a_lat+ xshift*2*a_lat , a_lat/2, 0. , lc_sq};
+
+c=newl;
+Line(c+16) = {pp+1, pp+3};
+Line(c+17) = {pp+3, pp+12};
+Line(c+18) = {pp+12, pp+5};
+Line(c+19) = {pp+5, pp+6};
+Line(c+20) = {pp+6, pp+4};
+Line(c+21) = {pp+4, pp+13};
+Line(c+22) = {pp+13, pp+2};
+Line(c+23) = {pp+2, pp+1};
+Line(c+24) = {pp+3, pp+13};
+Line(c+25) = {pp+12, pp+4};
+
+// dummy point to enforce window center
+pp=newp;
+Point(pp+1) = {-a_lat+ xshift*2*a_lat , 1.5*a_lat , 0. , lc_cell};
+
+Geometry.Points = 0;
diff --git a/QuasiNormalModeExpansion/QNM_expansion_dispersive_media.pro b/QuasiNormalModeExpansion/QNM_expansion_dispersive_media.pro
new file mode 100644
index 0000000000000000000000000000000000000000..1af0bc3affbb27e2b405d2cd2af3de6490310845
--- /dev/null
+++ b/QuasiNormalModeExpansion/QNM_expansion_dispersive_media.pro
@@ -0,0 +1,307 @@
+///////////////////////////////
+// Author : Guillaume Demesy //
+///////////////////////////////
+
+Include "QNM_expansion_dispersive_media_data.geo";
+
+Group {
+ // Domains
+ Om_1 = Region[1];
+ Om_src = Region[3];
+ Om_2 = Region[{2,3}];
+ Om = Region[{Om_1,Om_2}];
+ Om_but_src = Region[{Om,-Om_src}];
+
+ Surfdiri = Region[10];
+ Bound = Region[20];
+ pt_src = Region[100];
+ green_x_src = Region[30];
+ green_y_src = Region[31];
+ PrintPoint = Region[100];
+ Om_plot = Region[{Om,-Om_src}];
+}
+
+Function{
+ I[] = Complex[0,1];
+ k0[] = $realomega/cel;
+ mur[] = TensorDiag[1,1,1];
+ epsr_nod[] = TensorDiag[1,1,1];
+ om_lorentz_1[] = Complex[om_lorentz_1_re,om_lorentz_1_im];
+ mur_direct[] = 1;
+ epsr_direct[Om_1] = 1 + a_lorentz_1/($realomega-om_lorentz_1[]) - a_lorentz_1/($realomega+Conj[om_lorentz_1[]]);
+ epsr_direct[Om_2] = 1;
+ epsr_mau1[] = 1 + I[]*a_lorentz_1/($Eigenvalue-I[]*om_lorentz_1[]) - I[]*a_lorentz_1/($Eigenvalue+I[]*Conj[om_lorentz_1[]]);
+
+ If (flag_vector_case==0)
+ source_RHS[Om_src] = Vector[0,0,1];
+ source_RHS[Om_but_src] = Vector[0,0,0];
+ Else
+ source_RHS[Om_src] = Vector[1,0,0];
+ source_RHS[Om_but_src] = Vector[0,0,0];
+ EndIf
+}
+
+Constraint {
+ {Name Dirichlet; Type Assign;
+ Case {
+ { Region Surfdiri ; Value 0.; }
+ }
+ }
+
+ { Name Dirichlet_src;
+ Case {
+ { Region green_x_src;
+ Type Assign; Value 0. ;
+ }
+ }
+ }
+}
+
+Jacobian {
+ {Name JVol ; Case { { Region All ; Jacobian Vol ; } } }
+ {Name JSur ; Case { { Region All ; Jacobian Sur ; } } }
+ {Name JLin ; Case { { Region All ; Jacobian Lin ; } } }
+}
+
+Integration {
+ { Name Int_1 ;
+ Case {
+ { Type Gauss ;
+ Case {
+ { GeoElement Point ; NumberOfPoints 1 ; }
+ { GeoElement Line ; NumberOfPoints 4 ; }
+ { GeoElement Triangle ; NumberOfPoints 12 ; }
+ }
+ }
+ }
+ }
+}
+
+FunctionSpace {
+ { Name Hgrad_perp; Type Form1P;
+ BasisFunction {
+ { Name un; NameOfCoef un; Function BF_PerpendicularEdge_1N; Support Region[Om]; Entity NodesOf[All]; }
+ { Name un2; NameOfCoef un2; Function BF_PerpendicularEdge_2E; Support Region[Om]; Entity EdgesOf[All]; }
+ If(flag_o2==1)
+ { Name un3; NameOfCoef un3; Function BF_PerpendicularEdge_2F; Support Region[Om]; Entity FacetsOf[All]; }
+ { Name un4; NameOfCoef un4; Function BF_PerpendicularEdge_3E; Support Region[Om]; Entity EdgesOf[All]; }
+ { Name un5; NameOfCoef un5; Function BF_PerpendicularEdge_3F; Support Region[Om]; Entity FacetsOf[All]; }
+ EndIf
+ }
+ Constraint {
+ { NameOfCoef un; EntityType NodesOf ; NameOfConstraint Dirichlet; }
+ { NameOfCoef un2; EntityType EdgesOf ; NameOfConstraint Dirichlet; }
+ If(flag_o2==1)
+ { NameOfCoef un3; EntityType FacetsOf ; NameOfConstraint Dirichlet; }
+ { NameOfCoef un4; EntityType EdgesOf ; NameOfConstraint Dirichlet; }
+ { NameOfCoef un5; EntityType FacetsOf ; NameOfConstraint Dirichlet; }
+ EndIf
+ }
+ }
+
+ { Name Hcurl; Type Form1;
+ BasisFunction {
+ { Name sn; NameOfCoef un; Function BF_Edge ; Support Region[Om]; Entity EdgesOf[All]; }
+ { Name sn2; NameOfCoef un2; Function BF_Edge_2E; Support Region[Om]; Entity EdgesOf[All]; }
+ If(flag_o2==1)
+ { Name sn3; NameOfCoef un3; Function BF_Edge_3F_a; Support Region[Om]; Entity FacetsOf[All]; }
+ { Name sn4; NameOfCoef un4; Function BF_Edge_3F_b; Support Region[Om]; Entity FacetsOf[All]; }
+ { Name sn5; NameOfCoef un5; Function BF_Edge_4E ; Support Region[Om]; Entity EdgesOf[All]; }
+ EndIf
+ }
+ Constraint {
+ { NameOfCoef un ; EntityType EdgesOf ; NameOfConstraint Dirichlet; }
+ { NameOfCoef un2; EntityType EdgesOf ; NameOfConstraint Dirichlet; }
+ { NameOfCoef un3; EntityType FacetsOf; NameOfConstraint Dirichlet; }
+ { NameOfCoef un4; EntityType FacetsOf; NameOfConstraint Dirichlet; }
+ { NameOfCoef un5; EntityType EdgesOf ; NameOfConstraint Dirichlet; }
+
+ }
+ }
+
+ { Name Hcurl_direct_green_lin; Type Form1;
+ BasisFunction {
+ { Name sn; NameOfCoef un ; Function BF_Edge ; Support Region[{Om,green_x_src}]; Entity EdgesOf[All]; }
+ { Name sn2; NameOfCoef un2; Function BF_Edge_2E; Support Region[{Om,green_x_src}]; Entity EdgesOf[All]; }
+ If(flag_o2==1)
+ { Name sn3; NameOfCoef un3; Function BF_Edge_3F_a; Support Region[Om]; Entity FacetsOf[All]; }
+ { Name sn4; NameOfCoef un4; Function BF_Edge_3F_b; Support Region[Om]; Entity FacetsOf[All]; }
+ { Name sn5; NameOfCoef un5; Function BF_Edge_4E ; Support Region[Om]; Entity EdgesOf[All]; }
+ EndIf
+ }
+ Constraint{
+ { NameOfCoef un2; EntityType EdgesOf ; NameOfConstraint Dirichlet_src; }
+ { NameOfCoef un3; EntityType FacetsOf; NameOfConstraint Dirichlet_src; }
+ { NameOfCoef un4; EntityType FacetsOf; NameOfConstraint Dirichlet_src; }
+ { NameOfCoef un5; EntityType EdgesOf ; NameOfConstraint Dirichlet_src; }
+ }
+ }
+}
+
+Formulation {
+ {Name modal_helmholtz; Type FemEquation;
+ Quantity{
+ If (flag_vector_case==0)
+ { Name u; Type Local; NameOfSpace Hgrad_perp;}
+ Else
+ { Name u; Type Local; NameOfSpace Hcurl;}
+ EndIf
+ }
+ Equation {
+ Galerkin { Eig[ 1/mur[] * Dof{Curl u}, {Curl u} ]; Rational 1; In Om ; Jacobian JSur; Integration Int_1;}
+ Galerkin { Eig[ epsr_nod[]/cel^2 * Dof{u}, {u} ]; Rational 2; In Om_1; Jacobian JSur; Integration Int_1;}
+ Galerkin { Eig[ epsr_nod[]/cel^2 * Dof{u}, {u} ]; Rational 3; In Om_2; Jacobian JSur; Integration Int_1;}
+ }
+ }
+
+ // if other matrices, fails to print eigs (conflict between M1 matrices)
+ {Name form_RHS; Type FemEquation;
+ Quantity{
+ If (flag_vector_case==0)
+ { Name u; Type Local; NameOfSpace Hgrad_perp;}
+ Else
+ { Name u; Type Local; NameOfSpace Hcurl;}
+ EndIf
+ }
+ Equation{
+ Galerkin { [ 1. * Dof{u} , {u} ]; In Om; Jacobian JVol; Integration Int_1;}
+ Galerkin { [ source_RHS[] , {u} ]; In Om; Jacobian JVol; Integration Int_1; }
+ }
+ }
+
+ {Name direct_helmholtz; Type FemEquation;
+ Quantity{
+ If (flag_vector_case==0)
+ { Name u; Type Local; NameOfSpace Hgrad_perp;}
+ Else
+ { Name u; Type Local; NameOfSpace Hcurl;}
+ EndIf
+ }
+ Equation {
+ Galerkin { [ -1/mur_direct[]*Dof{Curl u} , {Curl u}]; In Om ; Jacobian JSur; Integration Int_1; }
+ Galerkin { [ k0[]^2*epsr_direct[]*Dof{u} , {u}] ; In Om ; Jacobian JSur; Integration Int_1; }
+ Galerkin { [ -source_RHS[] , {u}] ; In Om_src; Jacobian JVol; Integration Int_1; }
+ }
+ }
+}
+
+Resolution {
+ { Name res_nleig_rat_exp;
+ System{
+ { Name V ; NameOfFormulation form_RHS ; Type ComplexValue; }
+ { Name M1; NameOfFormulation modal_helmholtz ; Type ComplexValue; }
+ { Name M2; NameOfFormulation direct_helmholtz ; Type ComplexValue; }
+ }
+ Operation{
+ CreateDir["out"];
+ For k In {0:#tabrealomegasexpansion()-1}
+ Evaluate[$realomega=tabrealomegasexpansion(k)];
+ GenerateListOfRHS[V,Om,#tabrealomegasexpansion()];
+ EndFor
+ GenerateSeparate[M1];
+ EigenSolveAndExpand[M1,neig,eig_target_re,eig_target_im,
+ { {1}, {-1,-2*om_lorentz_1_im,2*a_lorentz_1*om_lorentz_1_re-om_lorentz_1_mod^2,0,0}, {1,0,0} } ,
+ { {1}, {-1,-2*om_lorentz_1_im,-om_lorentz_1_mod^2}, {1} } ,
+ tabrealomegasexpansion(),
+ V];
+ PostOperation[postop_lorentz_nleig_rat_exp];
+ For k In {0:#tabrealomegasexpansion()-1}
+ Evaluate[$realomega=tabrealomegasexpansion(k)];
+ Generate[M2];
+ Solve[M2];
+ PostOperation[postop_direct_helmholtz];
+ EndFor
+ For k In {0:#tabrealomegasexpansion()-1}
+ PostOperation[postop_gmsh~{k}];
+ Sleep[0.3];
+ EndFor
+ }
+ }
+}
+
+PostProcessing {
+ { Name postpro_lorentz_nleig_rat_exp; NameOfFormulation modal_helmholtz;
+ Quantity {
+ { Name intnormu ; Value { Integral { [ Norm[{u}] ] ; In Om ; Jacobian JSur; Integration Int_1 ; } } }
+ { Name intnormu_rod ; Value { Integral { [ Norm[{u}] ] ; In Om_1 ; Jacobian JSur; Integration Int_1 ;} } }
+ { Name u ; Value { Local { [ {u} ] ; In Om; Jacobian JSur; } } }
+ { Name u_im; Value { Local { [ Im[{u}] ] ; In Om; Jacobian JSur; } } }
+ { Name EigenValuesReal; Value { Local{ [$EigenvalueReal]; In PrintPoint; Jacobian JSur; } } }
+ { Name EigenValuesImag; Value { Local{ [$EigenvalueImag]; In PrintPoint; Jacobian JSur; } } }
+ { Name vol ; Value { Integral { [1] ; In PrintPoint ; Jacobian JVol; Integration Int_1 ; } } }
+ { Name eig_re ; Value { Integral { [$EigenvalueReal/$vol] ; In PrintPoint ; Jacobian JVol; Integration Int_1 ; } } }
+ { Name eig_im ; Value { Integral { [$EigenvalueImag/$vol] ; In PrintPoint ; Jacobian JVol; Integration Int_1 ; } } }
+ }
+ }
+
+ { Name postpro_direct_helmholtz; NameOfFormulation direct_helmholtz;
+ Quantity {
+ { Name eps ; Value { Local { [ epsr_direct[]] ; In Om ; Jacobian JSur; } } }
+ { Name source_RHS ; Value { Local { [ source_RHS[] ] ; In Om; Jacobian JSur; } } }
+ { Name u_direct ; Value { Local { [ {u} ] ; In Om; Jacobian JSur; } } }
+ { Name u_direct_im ; Value { Local { [ Im[{u}] ] ; In Om; Jacobian JSur; } } }
+ { Name intnormu_rod ; Value { Integral { [ Norm[{u}] ] ; In Om_1 ; Jacobian JSur; Integration Int_1 ;} } }
+ }
+ }
+}
+
+
+PostOperation {
+ { Name postop_lorentz_nleig_rat_exp; NameOfPostProcessing postpro_lorentz_nleig_rat_exp ;
+ Operation {
+ Print [vol[PrintPoint] , OnGlobal, TimeStep 0, StoreInVariable $vol,Format Table];
+ For j In {0:(neig-1)}
+ Print [eig_re[PrintPoint] , OnGlobal, TimeStep j , Format Table , SendToServer "GetDP/eig_re"];
+ Print [eig_im[PrintPoint] , OnGlobal, TimeStep j , Format Table , SendToServer "GetDP/eig_im"];
+ EndFor
+ Print [EigenValuesReal, OnElementsOf PrintPoint, Format TimeTable, File "out/EigenValuesReal.txt"];
+ Print [EigenValuesImag, OnElementsOf PrintPoint, Format TimeTable, File "out/EigenValuesImag.txt"];
+ Print [ u , OnElementsOf Om, File Sprintf["out/u.pos"], EigenvalueLegend];
+ Print [ u , OnPoint {cx_src,-cy_src,0}, Format TimeTable, File "out/u_expand_on_probe_point.txt"];
+ For k In {0:#tabrealomegasexpansion()-1}
+ // Print [ u_im, OnElementsOf Om, File Sprintf["out/u_exp_%03g.out",k], Name Sprintf["u_expand_imag_%03g (left)",k] , EigenvalueLegend, TimeStep {neig+k}];
+ Print [ u_im, OnGrid {$A,$B, 0} {-a_lat:a_lat:a_lat/30, -a_lat/2:a_lat/2:a_lat/15, 0}, File Sprintf["out/u_exp_%03g.out",k], Name Sprintf["u_expand_imag_%03g (left)",k] , EigenvalueLegend, TimeStep {neig+k}];
+ EndFor
+ }
+ }
+ { Name postop_direct_helmholtz; NameOfPostProcessing postpro_direct_helmholtz ;
+ Operation {
+ Print[ u_direct_im, OnGrid {$A,$B, 0} {-a_lat:a_lat:a_lat/30, -a_lat/2:a_lat/2:a_lat/15, 0}, File "out/u_direct.pos" , ChangeOfCoordinates {$X+xshift*2*a_lat,$Y,$Z} , Name "u_direct_imag (right)"];
+ Print[ u_direct , OnPoint {cx_src,-cy_src,0}, Format TimeTable, File >> "out/u_direct_on_probe_point.txt"];
+ Print [intnormu_rod[Om_1], OnGlobal, Format TimeTable, File "out/intnormu_direct_on_src_point.out" ];
+ }
+ }
+ For k In {0:#tabrealomegasexpansion()-1}
+ { Name postop_gmsh~{k}; NameOfPostProcessing postpro_direct_helmholtz ;
+ Operation {
+ Echo[Str["Geometry.Points = 0;","Geometry.Color.Curves = {0,0,0};","Mesh.SurfaceEdges = 0;",
+ "k=PostProcessing.NbViews-1;","View[k].Visible = 0;",
+ "View.Visible = 0;","View[0].Visible = 1;", "View[0].ColormapNumber = 7;",
+ Sprintf["View[%g].Visible = 0;",k],
+ Sprintf["View[%g].Visible = 0;",nb_Omegas+k],
+ Sprintf["View[%g].ColormapNumber = 7;",k+1],
+ Sprintf["View[%g].ColormapNumber = 7;",nb_Omegas+k+1],
+ Sprintf["View[%g].Visible = 1;",k+1],
+ Sprintf["View[%g].Visible = 1;",nb_Omegas+k+1]], File "tmp0.geo"];
+ // Echo[Str["Plugin(Annotate).Text= "TOP : DIRECT -- BOTTOM : EXPANSION\";" , "Plugin(Annotate).Run;"]];
+ }
+ }
+ EndFor
+}
+
+
+slepc_options_rg = Sprintf[" -rg_interval_endpoints %.8lf,%.8lf,%.8lf,%.8lf ",eig_min_re,eig_max_re,eig_min_im,eig_max_im];
+DefineConstant[
+ R_ = {"res_nleig_rat_exp", Name "GetDP/1ResolutionChoices", Visible 1},
+ C_ = {StrCat["-pre res_nleig_rat_exp -cal -slepc -nep_type nleigs -nep_rational -nep_target_magnitude -nep_view_pre -nep_ncv 300 -nep_monitor_all :temp_eigenvalues.txt",slepc_options_rg] , Name "GetDP/9ComputeCommand", Visible 1}
+];
+
+DefineConstant[
+ eig_re_ = {0, Name "GetDP/eig_re", ReadOnly 1, Graph "10", Visible 0},
+ eig_im_ = {0, Name "GetDP/eig_im", ReadOnly 1, Graph "01", Visible 0}
+];
+
+// DefineConstant[
+// R_ = {"res_nleig_rat_exp", Name "GetDP/1ResolutionChoices", Visible 1},
+// C_ = {"-pre res_nleig_rat_exp -cal -slepc -nep_max_it 1000 -nep_type nleigs -nep_rational -nep_target_magnitude -nep_ncv 100 -rg_interval_endpoints 0.00000000,0.05763407,0.00390394,3.12315286 -nep_view_pre -nep_monitor_all :temp_eigenvalues.txt", Name "GetDP/9ComputeCommand", Visible 1}
+// ];
diff --git a/QuasiNormalModeExpansion/QNM_expansion_dispersive_media_data.geo b/QuasiNormalModeExpansion/QNM_expansion_dispersive_media_data.geo
new file mode 100644
index 0000000000000000000000000000000000000000..25e6ceb285fadd2fafcd9ca40897940b2ea8932d
--- /dev/null
+++ b/QuasiNormalModeExpansion/QNM_expansion_dispersive_media_data.geo
@@ -0,0 +1,49 @@
+///////////////////////////////
+// Author : Guillaume Demesy //
+///////////////////////////////
+
+pp = "Model Options/";
+DefineConstant[
+ flag_vector_case = {1 , Name StrCat[pp, "0polarization case"], Choices {0="(0,0,Ez)",1="(Ex,Ey,0)"} },
+ flag_o2 = {1 , Name StrCat[pp, "1FE order"], Choices {0="order 1",1="order 2"} },
+ neig = {100 , Name StrCat[pp, "0number of eigenvalues"]}
+];
+
+nm = 0.1;
+N_true_poles = 1;
+paramaille = 5;
+
+a_lat = 482.5*nm;
+lambda_m = a_lat;
+
+eps0 = 8.854187817e-3*nm;
+mu0 = 400.*Pi*nm;
+cel = 1.0/Sqrt[eps0 * mu0];
+norm = a_lat/(2.*Pi*cel);
+
+om_p_josab = .4*norm;
+om_0_josab = 0.3*norm;
+gama_josab = 0.05*norm;
+om_lorentz_1_im = -gama_josab/2;
+om_lorentz_1_re = Sqrt[om_0_josab^2-om_lorentz_1_im^2];
+a_lorentz_1 = -om_p_josab^2/(2*om_lorentz_1_re);
+om_lorentz_1_mod = Sqrt[om_lorentz_1_re^2+om_lorentz_1_im^2];
+
+eig_target_re = om_lorentz_1_im/4;
+eig_target_im = 1/norm;
+eig_max_im = 8/norm;
+eig_min_im = 0.01/norm;
+eig_min_re = 0;
+eig_max_re = 0.8*Fabs[om_lorentz_1_im];
+
+cx_src = 0.75*2*a_lat - a_lat;
+cy_src = 0.75*a_lat - a_lat/2;
+r_src = a_lat/100;
+
+nb_Omegas = 50;
+RealOmega_min = 0.1;
+RealOmega_max = 1.1;
+tabrealomegasexpansion = LinSpace[RealOmega_min,RealOmega_max,nb_Omegas];
+Freq = 0;
+
+xshift = 1.1;
diff --git a/QuasiNormalModeExpansion/README.md b/QuasiNormalModeExpansion/README.md
new file mode 100644
index 0000000000000000000000000000000000000000..ad26131ca07fe9ba36000e6ee00fd76593aaff08
--- /dev/null
+++ b/QuasiNormalModeExpansion/README.md
@@ -0,0 +1,17 @@
+ONELAB models for the expansion of electromagnetic problems in Quasi-Normal Modes in open and/or dispersive media.
+
+## Quick Install
+Open `QNM_expansion_dispersive_media.pro` with e.g. your precompiled version of [ONELAB](https://onelab.info) to compute Quasi-Normal Modes of a dispersive structure. The numerical resolvent [1] is then applied to a specific source and the results are compared to those of the corresponding direct problem side by side [2].
+
+## What's inside
+These models heavily rely on slepc for the solving of non-linear eigenvalue problems [1-3].
+
+## Authors
+Guillaume Demésy
+
+## References
+[1] See [slepc doc](https://slepc.upv.es/documentation/current/docs/manualpages/NEP/NEPApplyResolvent.html).
+
+[2] See "[Photonics in highly dispersive media: The exact modal expansion](https://arxiv.org/abs/1807.02355)" for details about Dispersive QNMs.
+
+[3] See "[NEP: a module for the parallel solution of nonlinear eigenvalue problems in SLEPc](https://arxiv.org/abs/1910.11712)".
diff --git a/QuasiNormalModeExpansion/screenshot1_512.png b/QuasiNormalModeExpansion/screenshot1_512.png
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diff --git a/QuasiNormalModeExpansion/screenshot2_512.png b/QuasiNormalModeExpansion/screenshot2_512.png
new file mode 100644
index 0000000000000000000000000000000000000000..c311e5c4872a76510467a0626c6a8e3e7218398a
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diff --git a/TimeReversal/.gitignore b/TimeReversal/.gitignore
new file mode 100644
index 0000000000000000000000000000000000000000..547656a59b8d2e8b9c682a94e237906e5f0cd737
--- /dev/null
+++ b/TimeReversal/.gitignore
@@ -0,0 +1,4 @@
+*.pos
+*.msh
+*.pre
+*.db