Add Laplace equation example

This uses Jacobi iteration to solve Laplace's equation in 2D on a square grid.

1 files changed, 68 insertions, 0 deletions

diff --git a/Examples/Laplace.m b/Examples/Laplace.m
new file mode 100644
index 0000000..ad8a28f
--- /dev/null
+++ b/Examples/Laplace.m
@@ -0,0 +1,68 @@
+
+groups = {{"phi_group", {phi}}};
+
+derivatives =
+{
+  PDstandard[i_] ->
+    StandardCenteredDifferenceOperator[1,fdOrder/2,i],
+  PDstandard[i_, i_] ->
+    StandardCenteredDifferenceOperator[2,fdOrder/2,i],
+  PDstandard[i_, j_] ->
+    StandardCenteredDifferenceOperator[1,fdOrder/2,i] StandardCenteredDifferenceOperator[1,fdOrder/2,j]
+};
+
+PD = PDstandard;
+
+initialCalc = 
+{
+  Name -> "Laplace_initial",
+  Schedule -> {"AT INITIAL"},
+  Where -> Interior,
+  Equations -> 
+  {
+    phi -> phi0 Sum[4/(Pi n) Sin[n Pi x/Lx] Sinh[n Pi y/Lx]/Sinh[n Pi Ly/Lx], {n, 1, 1, 2}]
+  }
+};
+
+initialBoundaryCalc = 
+{
+  Name -> "Laplace_initial_boundary",
+  Schedule -> {"AT INITIAL after Laplace_initial"},
+  Where -> Boundary,
+  Equations -> 
+  {
+    phi -> IfThen[Abs[y-Ly]<10^-10, phi0, 0]
+  }
+};
+
+evolveCalc = 
+{
+  Name -> "Laplace_relax",
+  Schedule -> {"in MoL_CalcRHS", "AT ANALYSIS"},
+  Equations ->
+  {
+    dot[phi] -> mu Euc[ui,uj] PD[phi,li,lj]
+  }
+};
+
+boundaryCalc = 
+{
+  Name -> "Laplace_boundary",
+  Schedule -> {"in MoL_RHSBoundaries", "AT ANALYSIS"},
+  Where -> Boundary,
+  Equations ->
+  {
+    dot[phi] -> 0
+  }
+};
+
+
+CreateKrancThornTT[
+  groups, ".", 
+  "Laplace", 
+  Calculations -> {initialCalc, initialBoundaryCalc, evolveCalc, boundaryCalc},
+  PartialDerivatives -> derivatives,
+  ZeroDimensions -> {3},
+  RealParameters -> {Lx,Ly,phi0,mu},
+  IntParameters -> {{Name -> fdOrder, Default -> 2, AllowedValues -> {2, 4}}},
+  DeclaredGroups -> {"phi_group"}];