/// <summary>
/// Poisson Equation on a (-1,1)x(-1,1), Dirichlet everywhere
/// </summary>
public static SipControl Square(int xRes = 5, int yRes = 5, int deg = 5)
{
//Func<double[], double> exRhs = X => 2 * X[0] * X[0] + 2 * X[1] * X[1] - 4;
//Func<double[], double> exSol = X => (1.0 - X[0] * X[0]) * (1.0 - X[1] * X[1]);
//Func<double[], double> exSol = X => (1.0 - X[1]);
//Func<double[], double> exRhs = X => 0.0;
Func <double[], double> exSol = X => - Math.Cos(X[0] * Math.PI * 0.5) * Math.Cos(X[1] * Math.PI * 0.5);
Func <double[], double> exRhs = X => (Math.PI * Math.PI * 0.5 * Math.Cos(X[0] * Math.PI * 0.5) * Math.Cos(X[1] * Math.PI * 0.5)); // == - /\ exSol
var R = new SipControl();
R.ProjectName = "ipPoison/square";
R.savetodb = false;
//R.DbPath = "D:\\BoSSS-db";
R.FieldOptions.Add("T", new FieldOpts()
{
Degree = deg, SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Tex", new FieldOpts()
{
Degree = 4
});
R.InitialValues_Evaluators.Add("RHS", exRhs);
R.InitialValues_Evaluators.Add("Tex", exSol);
R.ExactSolution_provided = true;
//R.LinearSolver.NoOfMultigridLevels = 2;
//R.LinearSolver.SolverCode = LinearSolverCode.exp_softpcg_mg;
R.LinearSolver.SolverCode = LinearSolverCode.exp_softpcg_schwarz_directcoarse;
R.SuppressExceptionPrompt = true;
//R.LinearSolver.SolverCode = LinearSolverCode.classic_mumps;
R.GridFunc = delegate() {
double[] xNodes = GenericBlas.Linspace(-1, 1, xRes);
double[] yNodes = GenericBlas.Linspace(-1, 1, yRes);
var grd = Grid2D.Cartesian2DGrid(xNodes, yNodes);
grd.EdgeTagNames.Add(1, BoundaryType.Dirichlet.ToString());
grd.DefineEdgeTags(delegate(double[] X) {
byte ret = 1;
return(ret);
});
return(grd);
};
R.AddBoundaryValue(BoundaryType.Dirichlet.ToString(), "T", exSol);
R.NoOfSolverRuns = 1;
R.AdaptiveMeshRefinement = true;
R.NoOfTimesteps = 5;
return(R);
}
/// <summary>
/// Test on a curved grid.
/// </summary>
public static SipControl TestCurved()
{
var R = new SipControl();
R.ProjectName = "ipPoison/curved";
R.savetodb = false;
R.FieldOptions.Add("T", new FieldOpts()
{
Degree = 2, SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Tex", new FieldOpts()
{
Degree = 15
});
R.InitialValues_Evaluators.Add("RHS", X => 0.0);
R.InitialValues_Evaluators.Add("Tex", X => (Math.Log(X[0].Pow2() + X[1].Pow2()) / Math.Log(4.0)) + 1.0);
R.ExactSolution_provided = true;
R.GridFunc = delegate() {
var grd = Grid2D.CurvedSquareGrid(GenericBlas.Linspace(1, 2, 3), GenericBlas.Linspace(0, 1, 11), CellType.Square_9, true);
grd.EdgeTagNames.Add(1, BoundaryType.Dirichlet.ToString());
grd.DefineEdgeTags(X => 1);
return(grd);
};
R.AddBoundaryValue(BoundaryType.Dirichlet.ToString(), "T",
delegate(double[] X) {
double x = X[0], y = X[1];
return(Math.Sqrt(x * x + y * y));
});
return(R);
}
/// <summary>
/// Test on a Cartesian grid, with an exact polynomial solution.
/// </summary>
public static SipControl TestCartesian1(int xRes = 32, double xStretch = 1.0, int yRes = 16, double yStretch = 1.01, int pDG = 2)
{
//BoSSS.Application.SipPoisson.SipHardcodedControl.TestCartesian1()
var RR = new SipControl();
RR.ProjectName = "ipPoison/cartesian";
RR.savetodb = false;
RR.FieldOptions.Add("T", new FieldOpts()
{
Degree = pDG, SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
RR.FieldOptions.Add("Tex", new FieldOpts()
{
Degree = pDG * 2
});
RR.InitialValues_Evaluators.Add("RHS", X => 1.0);
RR.InitialValues_Evaluators.Add("Tex", X => (0.5 * X[0].Pow2() - 10 * X[0]));
RR.ExactSolution_provided = true;
RR.GridFunc = delegate()
{
double[] xNodes = CreateNodes(xRes, xStretch, 0, 10);
double[] yNodes = CreateNodes(yRes, yStretch, -1, +1);
var grd = Grid2D.Cartesian2DGrid(xNodes, yNodes);
grd.EdgeTagNames.Add(1, BoundaryType.Dirichlet.ToString());
grd.EdgeTagNames.Add(2, BoundaryType.Neumann.ToString());
grd.DefineEdgeTags(delegate(double[] X)
{
byte ret;
if (Math.Abs(X[0] - 0.0) <= 1.0e-6)
{
ret = 1;
}
else
{
ret = 2;
}
return(ret);
});
return(grd);
};
RR.AddBoundaryValue(BoundaryType.Dirichlet.ToString());
RR.AddBoundaryValue(BoundaryType.Neumann.ToString());
RR.GridPartType = BoSSS.Foundation.Grid.GridPartType.none;
return(RR);
}
public static SipControl JumpingSquare(int xRes = 5, int yRes = 5, int deg = 3)
{
var R = new SipControl();
R.ProjectName = "ipPoison/square";
R.savetodb = false;
R.FieldOptions.Add("T", new FieldOpts()
{
Degree = deg
});
R.FieldOptions.Add("Tex", new FieldOpts()
{
Degree = 4
});
R.InitialValues_Evaluators.Add("RHS", X => 0.0);
R.InitialValues_Evaluators.Add("Tex", X => 0.1);
R.ExactSolution_provided = true;
R.SuppressExceptionPrompt = true;
R.AddBoundaryValue(BoundaryType.Dirichlet.ToString(), "T",
X => {
if (X[0] > 0.9999)
{
return(0.1);
}
else
{
return(0.1);
}
});
R.NoOfSolverRuns = 1;
R.AdaptiveMeshRefinement = true;
R.NoOfTimesteps = 1;
R.ImmediatePlotPeriod = 1;
R.SuperSampling = 2;
R.GridFunc = delegate() {
double[] xNodes = GenericBlas.Linspace(-1, 1, xRes);
double[] yNodes = GenericBlas.Linspace(-1, 1, yRes);
var grd = Grid2D.Cartesian2DGrid(xNodes, yNodes);
grd.EdgeTagNames.Add(1, BoundaryType.Dirichlet.ToString());
grd.DefineEdgeTags(delegate(double[] X) {
byte ret = 1;
return(ret);
});
return(grd);
};
return(R);
}
/// <summary>
/// Poisson Equation on a (-1,1)x(-1,1), Dirichlet everywhere
/// </summary>
public static SipControl Square(int xRes = 21, int yRes = 16, int deg = 5)
{
//Func<double[], double> exRhs = X => 2 * X[0] * X[0] + 2 * X[1] * X[1] - 4;
//Func<double[], double> exSol = X => (1.0 - X[0] * X[0]) * (1.0 - X[1] * X[1]);
//Func<double[], double> exSol = X => (1.0 - X[1]);
//Func<double[], double> exRhs = X => 0.0;
Func <double[], double> exSol = X => - Math.Cos(X[0] * Math.PI * 0.5) * Math.Cos(X[1] * Math.PI * 0.5);
Func <double[], double> exRhs = X => (Math.PI * Math.PI * 0.5 * Math.Cos(X[0] * Math.PI * 0.5) * Math.Cos(X[1] * Math.PI * 0.5)); // == - /\ exSol
var R = new SipControl();
R.ProjectName = "ipPoison/square";
R.savetodb = false;
//R.DbPath = "D:\\BoSSS-db";
R.FieldOptions.Add("T", new FieldOpts()
{
Degree = deg, SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Tex", new FieldOpts()
{
Degree = 4
});
R.InitialValues_Evaluators.Add("RHS", exRhs);
R.InitialValues_Evaluators.Add("Tex", exSol);
R.ExactSolution_provided = true;
R.GridFunc = delegate() {
double[] xNodes = GenericBlas.Linspace(-1, 1, xRes);
double[] yNodes = GenericBlas.Linspace(-1, 1, yRes);
var grd = Grid2D.Cartesian2DGrid(xNodes, yNodes);
grd.EdgeTagNames.Add(1, BoundaryType.Dirichlet.ToString());
grd.DefineEdgeTags(delegate(double[] X) {
byte ret = 1;
return(ret);
});
return(grd);
};
R.AddBoundaryCondition(BoundaryType.Dirichlet.ToString(), "T", exSol);
R.NoOfSolverRuns = 1;
return(R);
}
/// <summary>
/// Test on a Cartesian grid, with an exact polynomial solution.
/// </summary>
public static SipControl TestCartesian3D(int xRes = 32, double xStretch = 1.0, int yRes = 16, double yStretch = 1.0, int zRes = 16, double zStretch = 1.0)
{
var R = new SipControl();
R.ProjectName = "ipPoison/cartesian";
R.savetodb = false;
R.FieldOptions.Add("T", new FieldOpts()
{
Degree = 6, SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Tex", new FieldOpts()
{
Degree = 6
});
R.InitialValues_Evaluators.Add("RHS", X => 1.0);
R.InitialValues_Evaluators.Add("Tex", X => (0.5 * X[0].Pow2() - 10 * X[0]));
R.ExactSolution_provided = true;
R.GridFunc = delegate() {
double[] xNodes = CreateNodes(xRes, xStretch, 0, 10);
double[] yNodes = CreateNodes(yRes, yStretch, -1, +1);
double[] zNodes = CreateNodes(zRes, zStretch, -1, +1);
var grd = Grid3D.Cartesian3DGrid(xNodes, yNodes, zNodes);
grd.EdgeTagNames.Add(1, BoundaryType.Dirichlet.ToString());
grd.EdgeTagNames.Add(2, BoundaryType.Neumann.ToString());
grd.DefineEdgeTags(delegate(double[] X) {
byte ret;
if (Math.Abs(X[0] - 0.0) <= 1.0e-6)
{
ret = 1;
}
else
{
ret = 2;
}
return(ret);
});
return(grd);
};
R.AddBoundaryCondition(BoundaryType.Dirichlet.ToString());
R.AddBoundaryCondition(BoundaryType.Neumann.ToString());
return(R);
}
/// <summary>
/// Poisson Equation on a (-1,1)x(-1,1), Dirichlet everywhere
/// </summary>
public static SipControl RegularSquare(int xRes = 5, int yRes = 5, int deg = 2)
{
Func <double[], double> exSol =
X => - Math.Cos(X[0] * Math.PI * 0.5) * Math.Cos(X[1] * Math.PI * 0.5);
Func <double[], double> exRhs =
X => (Math.PI * Math.PI * 0.5 * Math.Cos(X[0] * Math.PI * 0.5) * Math.Cos(X[1] * Math.PI * 0.5)); // == - /\ exSol
var R = new SipControl();
R.ProjectName = "ipPoison/square";
R.savetodb = false;
R.FieldOptions.Add("T", new FieldOpts()
{
Degree = deg
});
R.FieldOptions.Add("Tex", new FieldOpts()
{
Degree = 4
});
R.InitialValues_Evaluators.Add("RHS", exRhs);
R.InitialValues_Evaluators.Add("Tex", exSol);
R.ExactSolution_provided = true;
R.SuppressExceptionPrompt = true;
R.AddBoundaryValue(BoundaryType.Dirichlet.ToString(), "T", exSol);
R.NoOfSolverRuns = 1;
R.AdaptiveMeshRefinement = true;
R.NoOfTimesteps = 1;
R.ImmediatePlotPeriod = 1;
R.SuperSampling = 2;
R.GridFunc = delegate() {
double[] xNodes = GenericBlas.Linspace(-1, 1, xRes);
double[] yNodes = GenericBlas.Linspace(-1, 1, yRes);
var grd = Grid2D.Cartesian2DGrid(xNodes, yNodes);
grd.EdgeTagNames.Add(1, BoundaryType.Dirichlet.ToString());
grd.DefineEdgeTags(delegate(double[] X) {
byte ret = 1;
return(ret);
});
return(grd);
};
return(R);
}
public static SipControl VoronoiSquare(int res = 50, int deg = 2)
{
var R = new SipControl
{
ProjectName = "SipPoisson-Voronoi",
SessionName = "testrun",
ImmediatePlotPeriod = 1,
SuperSampling = 2,
savetodb = false,
ExactSolution_provided = false,
};
R.FieldOptions.Add("T", new FieldOpts()
{
Degree = deg, SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Tex", new FieldOpts()
{
Degree = deg * 2
});
R.InitialValues_Evaluators.Add("RHS", X => X[0] * X[0]);
R.InitialValues_Evaluators.Add("Tex", X => X[0]);
Func <double[], double> dirichletBoundary =
X => 0.0;
// X => Math.Pow(X[0], 2) + Math.Pow(X[1], 2);
R.AddBoundaryValue(BoundaryType.Dirichlet.ToString(), "T", dirichletBoundary);
R.GridFunc = delegate(){
Vector[] DomainBndyPolygon = new[] {
new Vector(-1, 1),
new Vector(1, 1),
new Vector(1, -1),
new Vector(-1, -1)
};
AggregationGrid grid;
grid = BoSSS.Foundation.Grid.Voronoi.VoronoiGrid2D.Polygonal(DomainBndyPolygon, 10, res);
grid.EdgeTagNames.Add(1, BoundaryType.Dirichlet.ToString());
grid.DefineEdgeTags((double[] X) => (byte)1);
return(grid);
};
return(R);
}
//Base case for Voronoi Testing
static SipControl TestGrid(
VoronoiGrid grid,
int deg = 1,
LinearSolverCode solver_name = LinearSolverCode.classic_pardiso,
Foundation.IO.IDatabaseInfo db = null)
{
var R = new SipControl
{
ProjectName = "SipPoisson-Voronoi",
SessionName = "testrun"
};
R.ImmediatePlotPeriod = 1;
if (db != null)
{
R.savetodb = true;
R.SetDatabase(db);
}
R.FieldOptions.Add("T", new FieldOpts()
{
Degree = deg, SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Tex", new FieldOpts()
{
Degree = deg * 2
});
R.InitialValues_Evaluators.Add("RHS", X => 1.0);
R.InitialValues_Evaluators.Add("Tex", X => X[0]);
R.ExactSolution_provided = false;
R.LinearSolver.NoOfMultigridLevels = int.MaxValue;
R.LinearSolver.SolverCode = solver_name;
R.LinearSolver.NoOfMultigridLevels = 1;
//R.TargetBlockSize = 100;
grid.SetGridAndBoundaries(R);
return(R);
}
/// <summary>
/// Test on a Cartesian grid, with an exact polynomial solution.
/// </summary>
public static SipControl TestCartesian3D(int PowRes = 5, int DGdegree = 1, string blapath = null, int xRes = 2, double xStretch = 1.0, int yRes = 2, double yStretch = 1.0, int zRes = 2, double zStretch = 1.0)
{
xRes = (int)Math.Pow(xRes, PowRes);
yRes = (int)Math.Pow(yRes, PowRes);
zRes = (int)Math.Pow(zRes, PowRes);
var R = new SipControl();
R.ProjectName = "ipPoison/cartesian";
R.savetodb = false;
R.WriteMeSomeAnalyse = @"D:\Analysis\CCpoisson\Study0_vary_Mlevel_n_blocks\";
R.FieldOptions.Add("T", new FieldOpts()
{
Degree = DGdegree, SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Tex", new FieldOpts()
{
Degree = DGdegree
});
R.InitialValues_Evaluators.Add("RHS", X => 1.0);
R.InitialValues_Evaluators.Add("Tex", X => (0.5 * X[0].Pow2() - 10 * X[0]));
R.ExactSolution_provided = true;
R.GridFunc = delegate() {
double[] xNodes = CreateNodes(xRes, xStretch, 0, 10);
//double[] xNodes = CreateNodes(xRes, xStretch, -1, +1);
double[] yNodes = CreateNodes(yRes, yStretch, -1, +1);
//double[] zNodes = CreateNodes(zRes, zStretch, -1, +1);
//var grd = Grid3D.Cartesian3DGrid(xNodes, yNodes, zNodes);
var grd = Grid2D.Cartesian2DGrid(xNodes, yNodes);
grd.EdgeTagNames.Add(1, BoundaryType.Dirichlet.ToString());
grd.EdgeTagNames.Add(2, BoundaryType.Neumann.ToString());
grd.DefineEdgeTags(delegate(double[] X) {
byte ret;
if (Math.Abs(X[0] - 0.0) <= 1.0e-6)
{
ret = 1;
}
else
{
ret = 2;
}
return(ret);
});
return(grd);
};
//R.LinearSolver.SolverCode = LinearSolverConfig.Code.exp_softpcg_jacobi_mg;
R.LinearSolver.SolverCode = LinearSolverConfig.Code.exp_decomposedMG_OrthoScheme;
//R.LinearSolver.SolverCode = LinearSolverConfig.Code.classic_mumps;
R.LinearSolver.NoOfMultigridLevels = 10;
R.LinearSolver.TargetBlockSize = 40;
//R.LinearSolver.MaxSolverIterations = 1;
//R.LinearSolver.MaxSolverIterations = 10;
R.AddBoundaryValue(BoundaryType.Dirichlet.ToString());
R.AddBoundaryValue(BoundaryType.Neumann.ToString());
return(R);
}
/// <summary>
/// Test on a 2D Voronoi mesh
/// </summary>
/// <param name="Res">
/// number of randomly chosen Delaunay vertices
/// </param>
/// <param name="deg">
/// polynomial degree
/// </param>
/// <param name="solver_name">
/// Name of solver to use.
/// </param>
public static SipControl TestVoronoi(int Res, SolverCodes solver_name = SolverCodes.classic_pardiso, int deg = 3)
{
if (System.Environment.MachineName.ToLowerInvariant().EndsWith("rennmaschin")
//|| System.Environment.MachineName.ToLowerInvariant().Contains("jenkins")
)
{
// This is Florians Laptop;
// he is to poor to afford MATLAB, so he uses OCTAVE
BatchmodeConnector.Flav = BatchmodeConnector.Flavor.Octave;
BatchmodeConnector.MatlabExecuteable = "C:\\cygwin64\\bin\\bash.exe";
}
var R = new SipControl();
R.ProjectName = "SipPoisson-Voronoi";
R.SessionName = "testrun";
R.savetodb = false;
R.FieldOptions.Add("T", new FieldOpts()
{
Degree = deg, SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Tex", new FieldOpts()
{
Degree = deg * 2
});
R.InitialValues_Evaluators.Add("RHS", X => 1.0);
R.InitialValues_Evaluators.Add("Tex", X => 0.0);
R.ExactSolution_provided = false;
R.NoOfMultigridLevels = int.MaxValue;
R.solver_name = solver_name;
//R.TargetBlockSize = 100;
bool IsIn(params double[] X)
{
Debug.Assert(X.Length == 2);
double xi = X[0];
double yi = X[1];
//for(int l = 0; l < bndys.Length; l++) {
// Debug.Assert(bndys[l].Normal.Length == 2);
// if (bndys[l].PointDistance(xi, yi) > 0.0)
// return false;
//}
if (xi > 1.0)
{
return(false);
}
if (yi > 1.0)
{
return(false);
}
if (xi < 0 && yi < 0)
{
return(false);
}
if (xi < -1)
{
return(false);
}
if (yi < -1)
{
return(false);
}
return(true);
}
int Mirror(ref double[] _x, ref double[] _y, AffineManifold[] bndys)
{
if (_x.Length != _y.Length)
{
throw new ArgumentException();
}
var x = _x.ToList();
var y = _y.ToList();
int N = _x.Length;
// filter all points that are outside of the domain
for (int n = 0; n < N; n++)
{
if (!IsIn(x[n], y[n]))
{
x.RemoveAt(n);
y.RemoveAt(n);
N--;
n--;
}
}
Debug.Assert(x.Count == N);
Debug.Assert(y.Count == N);
for (int n = 0; n < N; n++)
{
Debug.Assert(IsIn(x[n], y[n]));
}
// mirror each point
for (int n = 0; n < N; n++)
{
double xn = x[n];
double yn = y[n];
for (int l = 0; l < bndys.Length; l++)
{
var bndy_l = bndys[l];
double dist = bndy_l.PointDistance(xn, yn);
if (dist < 0)
{
double xMirr = xn - bndy_l.Normal[0] * dist * 2;
double yMirr = yn - bndy_l.Normal[1] * dist * 2;
Debug.Assert(bndy_l.PointDistance(xMirr, yMirr) > 0);
if (!IsIn(xMirr, yMirr))
{
x.Add(xMirr);
y.Add(yMirr);
}
}
}
}
// return
_x = x.ToArray();
_y = y.ToArray();
return(N);
}
GridCommons GridFunc()
{
GridCommons grd = null;
var Matlab = new BatchmodeConnector();
// boundaries for L-domain
AffineManifold[] Boundaries = new AffineManifold[6];
Boundaries[0] = new AffineManifold(new[] { 0.0, 1.0 }, new[] { 0.0, 1.0 });
Boundaries[1] = new AffineManifold(new[] { 1.0, 0.0 }, new[] { 1.0, 0.0 });
Boundaries[2] = new AffineManifold(new[] { -1.0, 0.0 }, new[] { -1.0, 0.0 });
Boundaries[3] = new AffineManifold(new[] { -1.0, 0.0 }, new[] { 0.0, 0.0 });
Boundaries[4] = new AffineManifold(new[] { 0.0, -1.0 }, new[] { 0.0, -1.0 });
Boundaries[5] = new AffineManifold(new[] { 0.0, -1.0 }, new[] { 0.0, 0.0 });
// generate Delaunay vertices
Random rnd = new Random(0);
double[] xNodes = Res.ForLoop(idx => rnd.NextDouble() * 2 - 1);
double[] yNodes = Res.ForLoop(idx => rnd.NextDouble() * 2 - 1);
int ResFix = Mirror(ref xNodes, ref yNodes, Boundaries);
var Nodes = MultidimensionalArray.Create(xNodes.Length, 2);
Nodes.SetColumn(0, xNodes);
Nodes.SetColumn(1, yNodes);
Matlab.PutMatrix(Nodes, "Nodes");
// compute Voronoi diagramm
Matlab.Cmd("[V, C] = voronoin(Nodes);");
// output (export from matlab)
int[][] OutputVertexIndex = new int[Nodes.NoOfRows][];
Matlab.GetStaggeredIntArray(OutputVertexIndex, "C");
Matlab.GetMatrix(null, "V");
// run matlab
Matlab.Execute(false);
// import here
MultidimensionalArray VertexCoordinates = (MultidimensionalArray)(Matlab.OutputObjects["V"]);
// correct indices (1-based index to 0-based index)
foreach (int[] cell in OutputVertexIndex)
{
int K = cell.Length;
for (int k = 0; k < K; k++)
{
cell[k]--;
}
}
// tessellation
List <Cell> cells = new List <Cell>();
List <int[]> aggregation = new List <int[]>();
for (int jV = 0; jV < ResFix; jV++) // loop over Voronoi Cells
{
Debug.Assert(IsIn(Nodes.GetRow(jV)));
int[] iVtxS = OutputVertexIndex[jV];
int NV = iVtxS.Length;
List <int> Agg2Pt = new List <int>();
for (int iTri = 0; iTri < NV - 2; iTri++) // loop over triangles of voronoi cell
{
int iV0 = iVtxS[0];
int iV1 = iVtxS[iTri + 1];
int iV2 = iVtxS[iTri + 2];
double[] V0 = VertexCoordinates.GetRow(iV0);
double[] V1 = VertexCoordinates.GetRow(iV1);
double[] V2 = VertexCoordinates.GetRow(iV2);
double[] D1 = V1.Minus(V0);
double[] D2 = V2.Minus(V0);
Debug.Assert(D1.CrossProduct2D(D2).Abs() > 1.0e-8);
if (D1.CrossProduct2D(D2) < 0)
{
double[] T = V2;
int t = iV2;
V2 = V1;
iV2 = iV1;
V1 = T;
iV1 = t;
}
double[] Center = V0.Plus(V1).Plus(V2).Mul(1.0 / 3.0);
//Debug.Assert(IsIn(Center[0], Center[1]));
Cell Cj = new Cell();
Cj.GlobalID = cells.Count;
Cj.Type = CellType.Triangle_3;
Cj.TransformationParams = MultidimensionalArray.Create(3, 2);
Cj.NodeIndices = new int[] { iV0, iV1, iV2 };
Cj.TransformationParams.SetRow(0, V0);
Cj.TransformationParams.SetRow(1, V1);
Cj.TransformationParams.SetRow(2, V2);
Agg2Pt.Add(cells.Count);
cells.Add(Cj);
}
aggregation.Add(Agg2Pt.ToArray());
}
// return grid
grd = new Grid2D(Triangle.Instance);
grd.Cells = cells.ToArray();
grd.EdgeTagNames.Add(1, BoundaryType.Dirichlet.ToString());
grd.DefineEdgeTags(X => (byte)1);
//grd.Plot2DGrid();
// create aggregation grid
//var agrd = new AggregationGrid(grd, aggregation.ToArray());
return(grd);
};
R.GridFunc = GridFunc;
R.AddBoundaryValue(BoundaryType.Dirichlet.ToString(), "T",
delegate(double[] X) {
//double x = X[0], y = X[1];
return(0.0);
//if(Math.Abs(X[0] - (0.0)) < 1.0e-8)
// return 0.0;
//
//throw new ArgumentOutOfRangeException();
});
return(R);
}
/*
*
* /// <summary>
* /// Test on a 2D Voronoi mesh
* /// </summary>
* /// <param name="Res">
* /// number of randomly chosen Delaunay vertices
* /// </param>
* /// <param name="deg">
* /// polynomial degree
* /// </param>
* /// <param name="solver_name">
* /// Name of solver to use.
* /// </param>
* public static SipControl TestVoronoiOld(int Res, SolverCodes solver_name = SolverCodes.classic_pardiso, int deg = 3) {
*
* if (System.Environment.MachineName.ToLowerInvariant().EndsWith("rennmaschin")
* //|| System.Environment.MachineName.ToLowerInvariant().Contains("jenkins")
* ) {
* // This is Florians Laptop;
* // he is to poor to afford MATLAB, so he uses OCTAVE
* BatchmodeConnector.Flav = BatchmodeConnector.Flavor.Octave;
* BatchmodeConnector.MatlabExecuteable = "C:\\cygwin64\\bin\\bash.exe";
* }
*
*
* var R = new SipControl();
* R.ProjectName = "SipPoisson-Voronoi";
* R.SessionName = "testrun";
* R.savetodb = false;
*
* R.FieldOptions.Add("T", new FieldOpts() { Degree = deg, SaveToDB = FieldOpts.SaveToDBOpt.TRUE });
* R.FieldOptions.Add("Tex", new FieldOpts() { Degree = deg*2 });
* R.InitialValues_Evaluators.Add("RHS", X => 1.0);
* R.InitialValues_Evaluators.Add("Tex", X => 0.0);
* R.ExactSolution_provided = false;
* R.NoOfMultigridLevels = int.MaxValue;
* R.solver_name = solver_name;
* //R.TargetBlockSize = 100;
*
*
*
*
* bool IsIn(double xi, double yi) {
*
* //for(int l = 0; l < bndys.Length; l++) {
* // Debug.Assert(bndys[l].Normal.Length == 2);
* // if (bndys[l].PointDistance(xi, yi) > 0.0)
* // return false;
* //}
* if (xi > 1.0)
* return false;
* if (yi > 1.0)
* return false;
* if (xi < 0 && yi < 0)
* return false;
* if (xi < -1)
* return false;
* if (yi < -1)
* return false;
*
* return true;
* }
*
* bool IsInV(Vector X) {
* Debug.Assert(X.Dim == 2);
* return IsIn(X.x, X.y);
* }
*
* int Mirror(ref double[] _x, ref double[] _y, AffineManifold[] bndys) {
* if (_x.Length != _y.Length)
* throw new ArgumentException();
* var x = _x.ToList();
* var y = _y.ToList();
* int N = _x.Length;
*
*
*
* // filter all points that are outside of the domain
* for (int n = 0; n < N; n++) {
* if (!IsIn(x[n], y[n])) {
* x.RemoveAt(n);
* y.RemoveAt(n);
* N--;
* n--;
* }
* }
* Debug.Assert(x.Count == N);
* Debug.Assert(y.Count == N);
* for (int n = 0; n < N; n++) {
* Debug.Assert(IsIn(x[n], y[n]));
* }
*
* // mirror each point
* for(int n = 0; n < N; n++) {
* double xn = x[n];
* double yn = y[n];
* for(int l = 0; l < bndys.Length; l++) {
* var bndy_l = bndys[l];
*
* double dist = bndy_l.PointDistance(xn, yn);
*
* if(dist < 0) {
* double xMirr = xn - bndy_l.Normal[0] * dist*2;
* double yMirr = yn - bndy_l.Normal[1] * dist*2;
*
* Debug.Assert(bndy_l.PointDistance(xMirr, yMirr) > 0);
*
* if(!IsIn(xMirr, yMirr)) {
* x.Add(xMirr);
* y.Add(yMirr);
* }
* }
* }
* }
*
* // return
* _x = x.ToArray();
* _y = y.ToArray();
* return N;
* }
*
*
* IGrid GridFunc() {
* GridCommons grd = null;
*
* var Matlab = new BatchmodeConnector();
*
* // boundaries for L-domain
* AffineManifold[] Boundaries = new AffineManifold[6];
* Boundaries[0] = new AffineManifold(new[] { 0.0, 1.0 }, new[] { 0.0, 1.0 });
* Boundaries[1] = new AffineManifold(new[] { 1.0, 0.0 }, new[] { 1.0, 0.0 });
* Boundaries[2] = new AffineManifold(new[] { -1.0, 0.0 }, new[] { -1.0, 0.0 });
* Boundaries[3] = new AffineManifold(new[] { -1.0, 0.0 }, new[] { 0.0, 0.0 });
* Boundaries[4] = new AffineManifold(new[] { 0.0, -1.0 }, new[] { 0.0, -1.0 });
* Boundaries[5] = new AffineManifold(new[] { 0.0, -1.0 }, new[] { 0.0, 0.0 });
*
*
* // generate Delaunay vertices
* Random rnd = new Random(0);
* double[] xNodes = Res.ForLoop(idx => rnd.NextDouble()*2 - 1);
* double[] yNodes = Res.ForLoop(idx => rnd.NextDouble()*2 - 1);
* int ResFix = Mirror(ref xNodes, ref yNodes, Boundaries);
*
*
* var Nodes = MultidimensionalArray.Create(xNodes.Length, 2);
* Nodes.SetColumn(0, xNodes);
* Nodes.SetColumn(1, yNodes);
*
* Matlab.PutMatrix(Nodes, "Nodes");
*
* // compute Voronoi diagramm
* Matlab.Cmd("[V, C] = voronoin(Nodes);");
*
* // output (export from matlab)
* int[][] OutputVertexIndex = new int[Nodes.NoOfRows][];
* Matlab.GetStaggeredIntArray(OutputVertexIndex, "C");
* Matlab.GetMatrix(null, "V");
*
* // run matlab
* Matlab.Execute(false);
*
* // import here
* MultidimensionalArray VertexCoordinates = (MultidimensionalArray)(Matlab.OutputObjects["V"]);
*
* // correct indices (1-based index to 0-based index)
* foreach(int[] cell in OutputVertexIndex) {
* int K = cell.Length;
* for (int k = 0; k < K; k++) {
* cell[k]--;
* }
* }
*
* // tessellation
* List<Cell> cells = new List<Cell>();
* List<int[]> aggregation = new List<int[]>();
* for(int jV = 0; jV < ResFix; jV++) { // loop over Voronoi Cells
* Debug.Assert(IsInV(Nodes.GetRowPt(jV)));
*
* int[] iVtxS = OutputVertexIndex[jV];
* int NV = iVtxS.Length;
*
* List<int> Agg2Pt = new List<int>();
*
* for(int iTri = 0; iTri < NV - 2; iTri++) { // loop over triangles of voronoi cell
* int iV0 = iVtxS[0];
* int iV1 = iVtxS[iTri + 1];
* int iV2 = iVtxS[iTri + 2];
*
* Vector V0 = VertexCoordinates.GetRowPt(iV0);
* Vector V1 = VertexCoordinates.GetRowPt(iV1);
* Vector V2 = VertexCoordinates.GetRowPt(iV2);
*
* double[] D1 = V1 - V0;
* double[] D2 = V2 - V0;
* Debug.Assert(D1.CrossProduct2D(D2).Abs() > 1.0e-8);
* if(D1.CrossProduct2D(D2) < 0) {
* Vector T = V2;
* int t = iV2;
* V2 = V1;
* iV2 = iV1;
* V1 = T;
* iV1 = t;
* }
*
* //double[] Center = V0.Plus(V1).Plus(V2).Mul(1.0 / 3.0);
* //Debug.Assert(IsIn(Center[0], Center[1]));
*
* Cell Cj = new Cell();
* Cj.GlobalID = cells.Count;
* Cj.Type = CellType.Triangle_3;
* Cj.TransformationParams = MultidimensionalArray.Create(3, 2);
* Cj.NodeIndices = new int[] { iV0, iV1, iV2 };
* Cj.TransformationParams.SetRowPt(0, V0);
* Cj.TransformationParams.SetRowPt(1, V1);
* Cj.TransformationParams.SetRowPt(2, V2);
*
* Agg2Pt.Add(cells.Count);
*
* cells.Add(Cj);
* }
*
* aggregation.Add(Agg2Pt.ToArray());
* }
*
* // return grid
* grd = new Grid2D(Triangle.Instance);
* grd.Cells = cells.ToArray();
* grd.EdgeTagNames.Add(1, BoundaryType.Dirichlet.ToString());
* grd.DefineEdgeTags(X => (byte)1);
*
* //grd.Plot2DGrid();
*
* // create aggregation grid
* var agrd = new AggregationGrid(grd, aggregation.ToArray());
* return agrd;
*
* };
* R.GridFunc = GridFunc;
*
* R.AddBoundaryValue(BoundaryType.Dirichlet.ToString(), "T",
* delegate (double[] X) {
* //double x = X[0], y = X[1];
*
* return 0.0;
* //if(Math.Abs(X[0] - (0.0)) < 1.0e-8)
* // return 0.0;
* //
* //throw new ArgumentOutOfRangeException();
* });
*
*
*
*
*
* return R;
* }
*
* //*/
/// <summary>
/// Test on a 2D Voronoi mesh
/// </summary>
/// <param name="Res">
/// number of randomly chosen Delaunay vertices
/// </param>
/// <param name="deg">
/// polynomial degree
/// </param>
/// <param name="solver_name">
/// Name of solver to use.
/// </param>
/// <param name="mirror">
/// use vertex mirroring at boundary to make a large fraction of the Voronoi cells conformal
/// </param>
/// <param name="NoOfLlyodsIter">
/// Number of iterations for Llyod's algorithm (aka. Voronoi relaxation)
/// </param>
public static SipControl TestVoronoi(int Res, SolverCodes solver_name = SolverCodes.classic_pardiso, int deg = 1, bool mirror = true, double NoOfLlyodsIter = 0)
{
if (System.Environment.MachineName.ToLowerInvariant().EndsWith("rennmaschin")
//|| System.Environment.MachineName.ToLowerInvariant().Contains("jenkins")
)
{
// This is Florians Laptop;
// he is to poor to afford MATLAB, so he uses OCTAVE
BatchmodeConnector.Flav = BatchmodeConnector.Flavor.Octave;
//BatchmodeConnector.MatlabExecuteable = "C:\\cygwin64\\bin\\bash.exe";
}
var R = new SipControl();
R.ProjectName = "SipPoisson-Voronoi";
R.SessionName = "testrun";
R.savetodb = false;
R.FieldOptions.Add("T", new FieldOpts()
{
Degree = deg, SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Tex", new FieldOpts()
{
Degree = deg * 2
});
R.InitialValues_Evaluators.Add("RHS", X => 0.0);// -1.0 + X[0] * X[0]);
R.InitialValues_Evaluators.Add("Tex", X => X[0]);
R.ExactSolution_provided = false;
R.NoOfMultigridLevels = int.MaxValue;
R.solver_name = solver_name;
R.NoOfMultigridLevels = 1;
//R.TargetBlockSize = 100;
bool IsIn(double xi, double yi)
{
//for(int l = 0; l < bndys.Length; l++) {
// Debug.Assert(bndys[l].Normal.Length == 2);
// if (bndys[l].PointDistance(xi, yi) > 0.0)
// return false;
//}
if (xi > 1.0)
{
return(false);
}
if (yi > 1.0)
{
return(false);
}
if (xi < 0 && yi < 0)
{
return(false);
}
if (xi < -1)
{
return(false);
}
if (yi < -1)
{
return(false);
}
return(true);
}
Vector[] DomainBndyPolygon = new[] {
new Vector(+0, +0),
new Vector(-1, +0),
new Vector(-1, +1),
new Vector(+1, +1),
new Vector(+1, -1),
new Vector(+0, -1)
};
//*/
/*
* bool IsIn(double xi, double yi) {
* double myEps = 0.0;
* if (xi > 1.0 + myEps)
* return false;
* if (yi > 1.0 + myEps)
* return false;
* if (xi < -1 - myEps)
* return false;
* if (yi < -1 - myEps)
* return false;
*
* return true;
* }
*
*
*
* Vector[] DomainBndyPolygon = new[] {
* new Vector(-1,+1),
* new Vector(+1,+1),
* new Vector(+1,-1),
* new Vector(-1,-1)
* };
* //*/
bool IsInV(Vector X)
{
Debug.Assert(X.Dim == 2);
return(IsIn(X.x, X.y));
}
bool Idenity(Vector A, Vector B)
{
bool t2 = (A - B).AbsSquare() < 1.0e-10;
bool t1 = (A - B).AbsSquare() < 1.0e-15;
//Debug.Assert(t1 == t2);
//Voronoi.VoronoiMeshGen.AccuracyFlag = (t1 == t2);
return(t2);
}
IGrid GridFunc()
{
// generate Delaunay vertices
Random rnd = new Random(0);
int RR = Res;
var Node = MultidimensionalArray.Create(RR, 2);
bool useMirror = mirror;
double scl = useMirror ? 2.0 : 4.0;
int cmt = 0;
while (cmt < Res)
{
double nx = rnd.NextDouble() * scl - 0.5 * scl;
double ny = rnd.NextDouble() * scl - 0.5 * scl;
if (IsIn(nx, ny))
{
Node[cmt, 0] = nx;
Node[cmt, 1] = ny;
cmt++;
}
}
// generate mesh
return(Voronoi.VoronoiMeshGen.FromPolygonalDomain(Node, DomainBndyPolygon, useMirror, NoOfLlyodsIter, IsInV, Idenity));
};
R.GridFunc = GridFunc;
R.AddBoundaryValue(BoundaryType.Dirichlet.ToString(), "T",
delegate(double[] X) {
//double x = X[0], y = X[1];
return(X[0]);
//if(Math.Abs(X[0] - (0.0)) < 1.0e-8)
// return 0.0;
//
//throw new ArgumentOutOfRangeException();
});
return(R);
}
public static SipControl ConvergenceTest(int Res = 20, int Dim = 2, LinearSolverCode solver_name = LinearSolverCode.exp_Kcycle_schwarz, int deg = 1)
{
if (Dim != 2 && Dim != 3)
{
throw new ArgumentOutOfRangeException();
}
var R = new SipControl();
R.ProjectName = "ipPoison/cartesian";
R.savetodb = false;
R.FieldOptions.Add("T", new FieldOpts()
{
Degree = deg, SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Tex", new FieldOpts()
{
Degree = deg + 2
});
R.InitialValues_Evaluators.Add("RHS", X => - 1.0); // constant force i.e. gravity
R.ExactSolution_provided = false; //true;
R.LinearSolver.NoOfMultigridLevels = int.MaxValue;
R.LinearSolver.SolverCode = solver_name;
R.LinearSolver.MaxSolverIterations = 200;
R.LinearSolver.TargetBlockSize = 10000;
R.LinearSolver.MaxKrylovDim = 2000;
R.GridFunc = delegate() {
GridCommons grd = null;
if (Dim == 2)
{
double[] xNodes = GenericBlas.Linspace(-10, 10, Res * 5 + 1);
double[] yNodes = GenericBlas.Linspace(-10, 10, Res * 5 + 1);
grd = Grid2D.Cartesian2DGrid(xNodes, yNodes);
}
else
{
throw new NotSupportedException();
}
grd.EdgeTagNames.Add(1, BoundaryType.Dirichlet.ToString());
grd.DefineEdgeTags(delegate(double[] X) {
byte ret;
ret = 1; // all dirichlet
return(ret);
});
return(grd);
};
R.AddBoundaryValue(BoundaryType.Dirichlet.ToString(), "T",
delegate(double[] X) {
double x = X[0], y = X[1];
return(0.0);
});
return(R);
}
/// <summary>
/// Test channel flow around a cylinder (half domain with symmetry condition)
/// </summary>
public static SipControl ConfinedCylinder(int k = 3)
{
var C = new SipControl();
#region other settings
// Miscellaneous Solver Settings
C.ExactSolution_provided = false;
C.savetodb = false;
C.DbPath = @"D:\bosss_db_masterthesis";
C.ProjectName = "ConfinedCylinderipPoisson";
C.SessionName = "Confined Cylinder MG with ipPoisson";
//C.WriteMeSomeAnalyse = @"C:\Users\Matth\Desktop";
#endregion
#region grid instantiation
// GUID's to confined cylinder grids (half)
List <string> grids = new List <string>();
grids.Add("a8370a9b-86b6-4dda-8147-b30f897b2320");
grids.Add("462f3f2e-8cd9-4563-a62f-191629ffd155");
grids.Add("6270aeda-0ae8-4197-939b-4018cd9500fe");
grids.Add("f97ff88f-8980-4760-ba54-76bd7071cdbd");
/*grids.Add("0f6132db-a263-4140-b0b4-cca275f3af3c");*/ //half_0
/*grids.Add("282f25a2-bb4e-4549-96c6-e5d8d806a607");*/ //half_1
/*grids.Add("e174a74c-d2fc-40a1-af12-a16356264911");*/ //half_2
/*grids.Add("de43ee58-c3b3-41bd-9df3-7deb883de36b");*/ //half_3
Guid gridGuid;
if (Guid.TryParse(grids[1], out gridGuid))
{
C.GridGuid = gridGuid;
}
else
{
throw new ArgumentException();
}
#endregion
#region dgfields and bc
// Setup DGFields
C.FieldOptions.Add("T", new FieldOpts()
{
Degree = k,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
C.FieldOptions.Add("Tex", new FieldOpts()
{
Degree = k,
SaveToDB = FieldOpts.SaveToDBOpt.FALSE
});
// Boundary Values
C.AddBoundaryValue("Dirichlet_inlet", "T", "X => 0", false);
C.AddBoundaryValue("Dirichlet_top", "T", "X => 0", false);
C.AddBoundaryValue("Dirichlet_outlet", "T", "X => 0", false);
C.AddBoundaryValue("Dirichlet_bottom", "T", "X => 0", false);
C.AddBoundaryValue("Dirichlet_cylinder", "T", "X => -10", false);
#endregion
#region RHS
//Func<double[], double> exRhs = X => -1;
//C.InitialValues_Evaluators.Add("RHS", exRhs);
#endregion
#region linear solver config
// Linear Solver Settings
C.LinearSolver.MaxKrylovDim = 5000;
C.LinearSolver.MaxSolverIterations = 50;
C.LinearSolver.NoOfMultigridLevels = 5;
C.LinearSolver.SolverCode = LinearSolverCode.exp_Kcycle_schwarz;
C.LinearSolver.TargetBlockSize = 10000;
C.LinearSolver.SolverMode = LinearSolverMode.Solve;
C.SuperSampling = 2;
C.LinearSolver.ConvergenceCriterion = 1E-8;
//C.LinearSolver.SolverMode = LinearSolverMode.SpectralAnalysis;
#endregion
return(C);
}
/// <summary>
/// Test on a Cartesian grid, with a sinusodial solution.
/// </summary>
/// <param name="Res">
/// Grid resolution
/// </param>
/// <param name="Dim">
/// spatial dimension
/// </param>
/// <param name="deg">
/// polynomial degree
/// </param>
/// <param name="solver_name">
/// Name of solver to use.
/// </param>
public static SipControl TestCartesian2(int Res, int Dim, LinearSolverConfig.Code solver_name = LinearSolverConfig.Code.exp_softpcg_schwarz_directcoarse, int deg = 3)
{
if (Dim != 2 && Dim != 3)
{
throw new ArgumentOutOfRangeException();
}
var R = new SipControl();
R.ProjectName = "ipPoison/cartesian";
R.savetodb = false;
R.FieldOptions.Add("T", new FieldOpts()
{
Degree = deg, SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Tex", new FieldOpts()
{
Degree = deg * 2
});
R.InitialValues_Evaluators.Add("RHS", X => - Math.Sin(X[0]));
R.InitialValues_Evaluators.Add("Tex", X => Math.Sin(X[0]));
R.ExactSolution_provided = true;
R.LinearSolver.NoOfMultigridLevels = int.MaxValue;
R.LinearSolver.SolverCode = solver_name;
//R.TargetBlockSize = 100;
R.GridFunc = delegate()
{
GridCommons grd = null;
if (Dim == 2)
{
double[] xNodes = GenericBlas.Linspace(0, 10, Res * 5 + 1);
double[] yNodes = GenericBlas.SinLinSpacing(-1, +1, 0.6, Res + 1);
grd = Grid2D.Cartesian2DGrid(xNodes, yNodes);
}
else if (Dim == 3)
{
double[] xNodes = GenericBlas.Linspace(0, 10, Res * 5 + 1);
double[] yNodes = GenericBlas.SinLinSpacing(-1, +1, 0.6, Res + 1);
double[] zNodes = GenericBlas.SinLinSpacing(-1, +1, 0.6, Res + 1);
grd = Grid3D.Cartesian3DGrid(xNodes, yNodes, zNodes);
}
else
{
throw new NotSupportedException();
}
grd.EdgeTagNames.Add(1, BoundaryType.Dirichlet.ToString());
grd.EdgeTagNames.Add(2, BoundaryType.Neumann.ToString());
grd.DefineEdgeTags(delegate(double[] X)
{
byte ret;
if (Math.Abs(X[0] - 0.0) <= 1.0e-6)
{
ret = 1;
}
else
{
ret = 2;
}
return(ret);
});
return(grd);
};
R.AddBoundaryValue(BoundaryType.Dirichlet.ToString(), "T",
delegate(double[] X)
{
double x = X[0], y = X[1];
if (Math.Abs(X[0] - (0.0)) < 1.0e-8)
{
return(0.0);
}
throw new ArgumentOutOfRangeException();
});
R.AddBoundaryValue(BoundaryType.Neumann.ToString(), "T",
delegate(double[] X)
{
if (Math.Abs(X[1] - 1.0) < 1.0e-8 || Math.Abs(X[1] + 1.0) < 1.0e-8) // y = -1, y = +1
{
return(0);
}
if (X.Length > 2 && (Math.Abs(X[2] - 1.0) < 1.0e-8 || Math.Abs(X[2] + 1.0) < 1.0e-8)) // z = -1, z = +1
{
return(0);
}
if (Math.Abs(X[0] - (+10.0)) < 1.0e-8)
{
return(Math.Cos(10.0));
}
throw new ArgumentOutOfRangeException();
});
return(R);
}
/// <summary>
/// Adaptive mesh refinement on a manufactured solution
/// </summary>
public static SipControl RefinementManufactured(int xRes = 2, int yRes = 2, int deg = 3)
{
double RHS(double[] X)
{
double x = X[0];
double y = X[1];
return(0.001 * Math.Pow(y, 2) * Math.Pow(y - 1, 2) * Math.Exp(10 * Math.Pow(x, 2) + 10 * y) * (200 * Math.Pow(x, 6)
- 400 * Math.Pow(x, 5) + 290 * Math.Pow(x, 4) - 140 * Math.Pow(x, 3) + 56 * Math.Pow(x, 2) - 6 * x + 1)
+ 0.001 * Math.Pow(x, 2) * Math.Pow(x - 1, 2) * Math.Exp(10 * Math.Pow(x, 2) + 10 * y) * (50 * Math.Pow(y, 4)
- 60 * Math.Pow(y, 3)
- 4 * Math.Pow(y, 2) + 14 * y + 1));
}
double Tex(double[] X)
{
double x = X[0];
double y = X[1];
return(0.0005 * Math.Pow(x, 2) * Math.Pow(x - 1, 2) * Math.Pow(y, 2) * Math.Pow(y - 1, 2) * Math.Exp(10 * Math.Pow(x, 2)
+ 10 * y));
}
Func <double[], double> exSol = Tex;
Func <double[], double> exRhs = RHS;
var R = new SipControl();
R.ProjectName = "ipPoison/hRefinementManufactured";
R.savetodb = false;
//R.DbPath = "D:\\BoSSS-db";
R.FieldOptions.Add("T", new FieldOpts()
{
Degree = deg, SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Tex", new FieldOpts()
{
Degree = deg + 1
});
R.InitialValues_Evaluators.Add("RHS", exRhs);
R.InitialValues_Evaluators.Add("Tex", exSol);
R.ExactSolution_provided = true;
//R.LinearSolver.NoOfMultigridLevels = 2;
//R.LinearSolver.SolverCode = LinearSolverConfig.Code.exp_softpcg_mg;
R.LinearSolver.SolverCode = LinearSolverConfig.Code.classic_pardiso;
R.SuppressExceptionPrompt = true;
//R.LinearSolver.SolverCode = LinearSolverConfig.Code.classic_mumps;
R.GridFunc = delegate()
{
double[] xNodes = GenericBlas.Linspace(0, 1, xRes + 1);
double[] yNodes = GenericBlas.Linspace(0, 1, yRes + 1);
var grd = Grid2D.Cartesian2DGrid(xNodes, yNodes);
grd.EdgeTagNames.Add(1, BoundaryType.Dirichlet.ToString());
grd.DefineEdgeTags(delegate(double[] X)
{
byte ret = 1;
return(ret);
});
return(grd);
};
R.AddBoundaryValue(BoundaryType.Dirichlet.ToString(), "T", exSol);
R.NoOfSolverRuns = 1;
R.AdaptiveMeshRefinement = true;
R.NoOfTimesteps = 100;
return(R);
}
/// <summary>
/// Test on a Cartesian grid, with a sinusodial solution.
/// </summary>
/// <param name="Res">
/// Grid resolution
/// </param>
/// <param name="Dim">
/// spatial dimension
/// </param>
/// <param name="deg">
/// polynomial degree
/// </param>
/// <param name="solver_name">
/// Name of solver to use.
/// </param>
public static SipControl TestCartesian2(int Res, int Dim, LinearSolverCode solver_name = LinearSolverCode.exp_Kcycle_schwarz, int deg = 5)
{
//BoSSS.Application.SipPoisson.SipHardcodedControl.TestCartesian2(8,3,deg:2)
if (Dim != 2 && Dim != 3)
{
throw new ArgumentOutOfRangeException();
}
var R = new SipControl();
R.ProjectName = "ipPoison/cartesian";
R.savetodb = false;
R.FieldOptions.Add("T", new FieldOpts()
{
Degree = deg, SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Tex", new FieldOpts()
{
Degree = deg + 2
});
R.InitialValues_Evaluators.Add("RHS", X => - Math.Sin(X[0]));
R.InitialValues_Evaluators.Add("Tex", X => Math.Sin(X[0]));
R.ExactSolution_provided = true;
R.LinearSolver.NoOfMultigridLevels = int.MaxValue;
R.LinearSolver.SolverCode = solver_name;
// exp_Kcycle_schwarz
// exp_gmres_levelpmg
#if DEBUG
// For testing in DEBUG mode, this setting enforces the use
// of many multigrid-levels. In 2D, the examples are so small that
R.LinearSolver.TargetBlockSize = 100;
#endif
R.GridFunc = delegate() {
GridCommons grd = null;
if (Dim == 2)
{
double[] xNodes = GenericBlas.Linspace(0, 10, Res * 5 + 1);
double[] yNodes = GenericBlas.SinLinSpacing(-1, +1, 0.6, Res + 1);
grd = Grid2D.Cartesian2DGrid(xNodes, yNodes);
}
else if (Dim == 3)
{
double[] xNodes = GenericBlas.Linspace(0, 10, Res * 5 + 1);
//double[] yNodes = GenericBlas.SinLinSpacing(-1, +1, 0.6, Res + 1);
//double[] zNodes = GenericBlas.SinLinSpacing(-1, +1, 0.6, Res + 1);
double[] yNodes = GenericBlas.Linspace(-1, +1, Res + 1);
double[] zNodes = GenericBlas.Linspace(-1, +1, Res + 1);
grd = Grid3D.Cartesian3DGrid(xNodes, yNodes, zNodes);
}
else
{
throw new NotSupportedException();
}
grd.EdgeTagNames.Add(1, BoundaryType.Dirichlet.ToString());
grd.EdgeTagNames.Add(2, BoundaryType.Neumann.ToString());
grd.DefineEdgeTags(delegate(double[] X) {
byte ret;
double x = X[0];
if (Math.Abs(x - 0.0) <= 1.0e-8)
{
ret = 1; // Dirichlet
}
else
{
ret = 2; // Neumann
}
return(ret);
});
return(grd);
};
R.AddBoundaryValue(BoundaryType.Dirichlet.ToString(), "T",
delegate(double[] X) {
double x = X[0], y = X[1];
return(Math.Sin(x));
//if (Math.Abs(X[0] - (0.0)) < 1.0e-8)
// return 0.0;
//throw new ArgumentOutOfRangeException();
});
R.AddBoundaryValue(BoundaryType.Neumann.ToString(), "T",
delegate(double[] X) {
double x = X[0], y = X[1], z = X.Length > 2 ? X[2] : 0.0;
if (Math.Abs(y - 1.0) < 1.0e-8 || Math.Abs(y + 1.0) < 1.0e-8) // y = -1, y = +1
{
return(0);
}
if (X.Length > 2 && (Math.Abs(z - 1.0) < 1.0e-8 || Math.Abs(z + 1.0) < 1.0e-8)) // z = -1, z = +1
{
return(0);
}
//if (Math.Abs(X[0] - (+10.0)) < 1.0e-8)
return(Math.Cos(x));
//throw new ArgumentOutOfRangeException();
});
return(R);
}