Add Laplace equation example

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

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"}];

Examples/laplace.par

@@ -0,0 +1,91 @@
+
+Cactus::cctk_final_time = 1
+Cactus::terminate = "time"
+
+ActiveThorns = "IOUtil Carpet CarpetLib CarpetSlab CoordBase CoordBase SymBase CartGrid3D Slab CarpetIOBasic CarpetIOASCII CarpetIOScalar Laplace Time MoL Boundary GenericFD CarpetReduce LoopControl CarpetIOHDF5 HDF5"
+
+CoordBase::domainsize                   = minmax
+
+CoordBase::boundary_size_x_lower        = 1
+CoordBase::boundary_size_y_lower        = 1
+CoordBase::boundary_size_z_lower        = 0
+CoordBase::boundary_shiftout_x_lower    = 0
+CoordBase::boundary_shiftout_y_lower    = 0
+CoordBase::boundary_shiftout_z_lower    = 1
+
+CoordBase::boundary_size_x_upper        = 1
+CoordBase::boundary_size_y_upper        = 1
+CoordBase::boundary_size_z_upper        = 0
+CoordBase::boundary_shiftout_x_upper    = 0
+CoordBase::boundary_shiftout_y_upper    = 0
+CoordBase::boundary_shiftout_z_upper    = 1
+
+CartGrid3D::type                        = "coordbase"
+CartGrid3D::domain                      = "full"
+CartGrid3D::avoid_origin                = "no"
+
+CoordBase::xmin                         = 0
+CoordBase::ymin                         = 0
+CoordBase::zmin                         = 0
+CoordBase::xmax                         = 1
+CoordBase::ymax                         = 1
+CoordBase::zmax                         = 0
+CoordBase::dx                           = 0.02
+CoordBase::dy                           = 0.02
+CoordBase::dz                           = 0.02
+
+driver::ghost_size_x = 1
+driver::ghost_size_y = 1
+driver::ghost_size_z = 0
+
+Carpet::domain_from_coordbase           = "yes"
+Carpet::poison_new_timelevels           = "yes"
+Carpet::check_for_poison                = "no"
+
+Carpet::max_refinement_levels = 1
+Carpet::prolongation_order_space = 3
+Carpet::prolongation_order_time = 2
+Carpet::init_each_timelevel = no
+Carpet::print_timestats_every = 0
+
+Time::timestep = 0.0001
+Time::timestep_method                   = "given"
+
+MethodOfLines::ode_method             = "generic"
+MethodOfLines::generic_type             = "RK"
+MethodOfLines::MoL_Intermediate_Steps = 1
+MethodOfLines::MoL_Num_Scratch_Levels = 1
+
+# MethodOfLines::ode_method             = "RK2"
+# MethodOfLines::MoL_NaN_Check          = "no"
+# MethodOfLines::initial_data_is_crap   = "yes"
+# MethodOfLines::MoL_Intermediate_Steps = 2
+# MethodOfLines::MoL_Num_Scratch_Levels = 1
+
+IO::out_dir = $parfile
+
+IOBasic::outInfo_every                  = 100
+IOBasic::outInfo_reductions             = "minimum maximum"
+IOBasic::outInfo_vars                   = "
+  Carpet::physical_time_per_hour
+  Laplace::phi
+  Laplace::phirhs
+"
+
+IOScalar::outScalar_every               = 10
+IOScalar::outScalar_reductions          = "norm2"
+IOScalar::outScalar_vars                = "Laplace::phirhs"
+
+Laplace::Lx = 1
+Laplace::Ly = 1
+Laplace::phi0 = 1
+Laplace::mu = 1
+
+IOHDF5::out_every                       = 100
+IOHDF5::out_vars                        = "
+  Laplace::phi
+  Laplace::phirhs
+"
+
+# TimerReport::out_every = 0
+# TimerReport::n_top_timers = 50