From ac0efbe338abc872056c6b479526e6212cd461b3 Mon Sep 17 00:00:00 2001 From: Bertrand Thierry <bthierry@math.cnrs.fr> Date: Thu, 2 Sep 2021 15:29:45 +0200 Subject: [PATCH] Helmholtz Model : Corner Condition for ABC and DDM --- HelmholtzCornerCondition/ABC_norm.py | 48 ++ HelmholtzCornerCondition/README.md | 84 ++++ HelmholtzCornerCondition/img/ABC.png | Bin 0 -> 199066 bytes HelmholtzCornerCondition/img/TC.png | Bin 0 -> 204753 bytes HelmholtzCornerCondition/main.data | 12 + HelmholtzCornerCondition/main.geo | 10 + HelmholtzCornerCondition/main.pro | 14 + HelmholtzCornerCondition/notes.md | 51 +++ HelmholtzCornerCondition/src/ABC_DDM.pro | 131 ++++++ HelmholtzCornerCondition/src/ABC_DDM_1.pro | 172 ++++++++ HelmholtzCornerCondition/src/ABC_DDM_2.pro | 283 ++++++++++++ .../src/ABC_Decomposition.pro | 57 +++ .../src/ABC_MonoDomain.pro | 102 +++++ HelmholtzCornerCondition/src/ABC_main.data | 17 + HelmholtzCornerCondition/src/ABC_main.geo | 90 ++++ HelmholtzCornerCondition/src/ABC_main.pro | 325 ++++++++++++++ HelmholtzCornerCondition/src/Common.pro | 23 + .../src/TC_Decomposition.pro | 46 ++ HelmholtzCornerCondition/src/TC_WaveGuide.pro | 90 ++++ .../src/TC_WaveGuide_DDM.pro | 414 ++++++++++++++++++ HelmholtzCornerCondition/src/TC_main.data | 36 ++ HelmholtzCornerCondition/src/TC_main.geo | 72 +++ HelmholtzCornerCondition/src/TC_main.pro | 127 ++++++ 23 files changed, 2204 insertions(+) create mode 100644 HelmholtzCornerCondition/ABC_norm.py create mode 100644 HelmholtzCornerCondition/README.md create mode 100644 HelmholtzCornerCondition/img/ABC.png create mode 100644 HelmholtzCornerCondition/img/TC.png create mode 100644 HelmholtzCornerCondition/main.data create mode 100644 HelmholtzCornerCondition/main.geo create mode 100644 HelmholtzCornerCondition/main.pro create mode 100644 HelmholtzCornerCondition/notes.md create mode 100644 HelmholtzCornerCondition/src/ABC_DDM.pro create mode 100644 HelmholtzCornerCondition/src/ABC_DDM_1.pro create mode 100644 HelmholtzCornerCondition/src/ABC_DDM_2.pro create mode 100644 HelmholtzCornerCondition/src/ABC_Decomposition.pro create mode 100644 HelmholtzCornerCondition/src/ABC_MonoDomain.pro create mode 100644 HelmholtzCornerCondition/src/ABC_main.data create mode 100644 HelmholtzCornerCondition/src/ABC_main.geo create mode 100644 HelmholtzCornerCondition/src/ABC_main.pro create mode 100644 HelmholtzCornerCondition/src/Common.pro create mode 100644 HelmholtzCornerCondition/src/TC_Decomposition.pro create mode 100644 HelmholtzCornerCondition/src/TC_WaveGuide.pro create mode 100644 HelmholtzCornerCondition/src/TC_WaveGuide_DDM.pro create mode 100644 HelmholtzCornerCondition/src/TC_main.data create mode 100644 HelmholtzCornerCondition/src/TC_main.geo create mode 100644 HelmholtzCornerCondition/src/TC_main.pro diff --git a/HelmholtzCornerCondition/ABC_norm.py b/HelmholtzCornerCondition/ABC_norm.py new file mode 100644 index 0000000..cbcd962 --- /dev/null +++ b/HelmholtzCornerCondition/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/HelmholtzCornerCondition/README.md b/HelmholtzCornerCondition/README.md new file mode 100644 index 0000000..c11f630 --- /dev/null +++ b/HelmholtzCornerCondition/README.md @@ -0,0 +1,84 @@ +# 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: + +- `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`). + - `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 +- `GetDP`: The `Resolution` value: + - `MonoDomain`: Direct solver / Mono domain problem (every sub-domains are merged) + - `DDM`: Domain Decomposition Algorithm +- `GMSH`: nothing +- `Input`: + - `wavenumber` + - `Type of Condition (left side)`: on the left side, `Dirichlet` or `Fourier`. Both conditions are such that the solution remain the same. + - `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` (for GMRES) are classical parameter +- `Mesh`: `NLambda` is the number of discretization points per wavelength +- `Output`: + - `Prefix for filename`: prefix applied to every saved file + - `Output Directory` of the results + - `Print every phi`: print on disk every auxiliary functions + diff --git a/HelmholtzCornerCondition/img/ABC.png b/HelmholtzCornerCondition/img/ABC.png new file mode 100644 index 0000000000000000000000000000000000000000..1e9c22868fbf4054309b122af92aa4a797eeae54 GIT binary patch literal 199066 zcmaI71yodT)IK^iND4}qq)Ll)Dj)(PCEYFEodSYLcZVX~-5o;@f-v*|Ll0d;&z+z6 z{qMc&uKS&}Sm&%6&Uw%KzI#9W+0Wh+uKZCJ{}JUQ004k5_g-2R06<4xqViy4B2QDW z;cDaw(?mg58hJ(@S5mD3$P<p^du<m00GH&yKNLWECOPs$ELS;28LV}58hjG8%~9<! z0DvAKC;jG==ltH1M<%t~9q<_JVbP#3*L+444=5%g3ZbWAl78}suKmR$>|3HFmi9*| z($X#O$zp$AqUFP1a=2m((W9t7A7cKc=iKPgD#8na&}q&tWN=t9b;D1OXV>i;M)yV+ 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zc{nsuKorU&r&V1qA1Xva_}vhW|Cch~<+Y?f%>M0FW9MI0PXSTT_*;fyWjkq_ilz@+ z9UUDV9UUE=hZcRCM(5!|)Bfv>%>NYr8~a85PYP)Nmyeyl&G`S1YbPBY9UUDV9i9JT sM7;@gbaZrdbaZrdbaZrdbpHSIzsb72J|w&_1^@s607*qoM6N<$f|g6%r2qf` literal 0 HcmV?d00001 diff --git a/HelmholtzCornerCondition/main.data b/HelmholtzCornerCondition/main.data new file mode 100644 index 0000000..9be4111 --- /dev/null +++ b/HelmholtzCornerCondition/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/HelmholtzCornerCondition/main.geo b/HelmholtzCornerCondition/main.geo new file mode 100644 index 0000000..cf39f62 --- /dev/null +++ b/HelmholtzCornerCondition/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/HelmholtzCornerCondition/main.pro b/HelmholtzCornerCondition/main.pro new file mode 100644 index 0000000..7e8f6c3 --- /dev/null +++ b/HelmholtzCornerCondition/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/HelmholtzCornerCondition/notes.md b/HelmholtzCornerCondition/notes.md new file mode 100644 index 0000000..64a8976 --- /dev/null +++ b/HelmholtzCornerCondition/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/HelmholtzCornerCondition/src/ABC_DDM.pro b/HelmholtzCornerCondition/src/ABC_DDM.pro new file mode 100644 index 0000000..fe07e3b --- /dev/null +++ b/HelmholtzCornerCondition/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 $ItCount, File >> StrCat[ABC_DIR,"ABC_DDM_normg.pos"]]; + } + } + EndFor + EndFor + // Print the solution on HDD + error wrt exact solution + {Name DDM; NameOfPostProcessing DDM; + Operation { + Print [u_ddm, OnElementsOf Omega, File StrCat[ABC_DIR, StrCat[ABC_PREFIX, "DDM_Scattered_Field.pos"]]]; + Print [u_ddm_abs, OnElementsOf Omega, File StrCat[ABC_DIR, StrCat[ABC_PREFIX, "DDM_Scattered_Field_(abs._value).pos"]]]; + Print [uerr_ddm, OnElementsOf Omega, File StrCat[ABC_DIR, StrCat[ABC_PREFIX, "DDM_Error_numeric_vs_analytic.pos"]]]; + } + } +} diff --git a/HelmholtzCornerCondition/src/ABC_DDM_1.pro b/HelmholtzCornerCondition/src/ABC_DDM_1.pro new file mode 100644 index 0000000..fff9eb8 --- /dev/null +++ b/HelmholtzCornerCondition/src/ABC_DDM_1.pro @@ -0,0 +1,172 @@ +// First algorithm + +Formulation { + { Name DDM_1; Type FemEquation; + Quantity{ + For ii In {0:#myD()-1} + i = myD(ii); + { Name u~{i} ; Type Local; NameOfSpace H_grad~{i};} + EndFor + For k In {0:#ListGammaExt()-1} + { Name phi~{k} ; Type Local; NameOfSpace H_phi~{k};} + EndFor + } + Equation{ + For ii In {0:#myD()-1} + i = myD(ii); + // PDE on u_i + //Helmholtz equation + Galerkin{[Dof{Grad u~{i}}, {Grad u~{i}}]; + In Omega~{i}; Jacobian JVol; Integration I1;} + Galerkin{[-kap^2*Dof{u~{i}}, {u~{i}}]; + In Omega~{i}; Jacobian JVol; Integration I1;} + // dni ui -i*kap ui = gij on Sigma ij + For jj In {0:#myD~{i}()-1} + j = myD~{i}(jj); + Galerkin{[-I[]*kap*Dof{u~{i}}, {u~{i}}]; + In Sigma~{i}~{j}; Jacobian JSur; Integration I1;} + Galerkin{[$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/HelmholtzCornerCondition/src/ABC_DDM_2.pro b/HelmholtzCornerCondition/src/ABC_DDM_2.pro new file mode 100644 index 0000000..3d3ab40 --- /dev/null +++ b/HelmholtzCornerCondition/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/HelmholtzCornerCondition/src/ABC_Decomposition.pro b/HelmholtzCornerCondition/src/ABC_Decomposition.pro new file mode 100644 index 0000000..9cca9eb --- /dev/null +++ b/HelmholtzCornerCondition/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/HelmholtzCornerCondition/src/ABC_MonoDomain.pro b/HelmholtzCornerCondition/src/ABC_MonoDomain.pro new file mode 100644 index 0000000..463a0b3 --- /dev/null +++ b/HelmholtzCornerCondition/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/HelmholtzCornerCondition/src/ABC_main.data b/HelmholtzCornerCondition/src/ABC_main.data new file mode 100644 index 0000000..83ac5a1 --- /dev/null +++ b/HelmholtzCornerCondition/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/HelmholtzCornerCondition/src/ABC_main.geo b/HelmholtzCornerCondition/src/ABC_main.geo new file mode 100644 index 0000000..f0c7746 --- /dev/null +++ b/HelmholtzCornerCondition/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/HelmholtzCornerCondition/src/ABC_main.pro b/HelmholtzCornerCondition/src/ABC_main.pro new file mode 100644 index 0000000..4e56c82 --- /dev/null +++ b/HelmholtzCornerCondition/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="Ordre 0", 2="Ordre 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/HelmholtzCornerCondition/src/Common.pro b/HelmholtzCornerCondition/src/Common.pro new file mode 100644 index 0000000..e1a1a73 --- /dev/null +++ b/HelmholtzCornerCondition/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/HelmholtzCornerCondition/src/TC_Decomposition.pro b/HelmholtzCornerCondition/src/TC_Decomposition.pro new file mode 100644 index 0000000..a5ec9cf --- /dev/null +++ b/HelmholtzCornerCondition/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/HelmholtzCornerCondition/src/TC_WaveGuide.pro b/HelmholtzCornerCondition/src/TC_WaveGuide.pro new file mode 100644 index 0000000..811afd6 --- /dev/null +++ b/HelmholtzCornerCondition/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/HelmholtzCornerCondition/src/TC_WaveGuide_DDM.pro b/HelmholtzCornerCondition/src/TC_WaveGuide_DDM.pro new file mode 100644 index 0000000..4e07efb --- /dev/null +++ b/HelmholtzCornerCondition/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/HelmholtzCornerCondition/src/TC_main.data b/HelmholtzCornerCondition/src/TC_main.data new file mode 100644 index 0000000..92a73e8 --- /dev/null +++ b/HelmholtzCornerCondition/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="Ordre 0", 2="Ordre 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/HelmholtzCornerCondition/src/TC_main.geo b/HelmholtzCornerCondition/src/TC_main.geo new file mode 100644 index 0000000..dbdfcb1 --- /dev/null +++ b/HelmholtzCornerCondition/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/HelmholtzCornerCondition/src/TC_main.pro b/HelmholtzCornerCondition/src/TC_main.pro new file mode 100644 index 0000000..99c9f9d --- /dev/null +++ b/HelmholtzCornerCondition/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"; -- GitLab