/// <summary>
/// Calculate Extension
/// </summary>
public void ConstructExtension(IList <DGField> InterfaceValue = null, bool nearfield = false)
{
using (new FuncTrace()) {
Extension.Clear(nearfield ? LevelSetTracker.Regions.GetNearFieldMask(1) : null);
ComputeMatrices(InterfaceValue ?? InterfaceParams, nearfield);
//Solve System
double[] RHS = OpAffine.CloneAs();
RHS.ScaleV(-1.0);
ISparseSolver slv = Control.solverFactory();
if (nearfield)
{
SubGrid subGrid = LevelSetTracker.Regions.GetNearFieldSubgrid(1);
int[] SubVecIdx = Extension.Mapping.GetSubvectorIndices(subGrid, true, new int[] { 0 });
int L = SubVecIdx.Length;
MsrMatrix SubMatrix = new MsrMatrix(L);
double[] SubRHS = new double[L];
double[] SubSolution = new double[L];
OpMatrix.AccSubMatrixTo(1.0, SubMatrix, SubVecIdx, default(int[]), SubVecIdx, default(int[]));
SubRHS.Clear();
SubSolution.Clear();
SubRHS.AccV(1.0, RHS, default(int[]), SubVecIdx);
SubSolution.AccV(1.0, Extension.CoordinateVector, default(int[]), SubVecIdx);
slv.DefineMatrix(SubMatrix);
slv.Solve(SubSolution, SubRHS);
Extension.Clear(subGrid.VolumeMask);
Extension.CoordinateVector.AccV(1.0, SubSolution, SubVecIdx, default(int[]));
}
else
{
slv.DefineMatrix(OpMatrix);
slv.Solve(Extension.CoordinateVector, RHS);
}
slv.Dispose();
}
}
public void ImplicitEuler(double dt, SubGrid S, SinglePhaseField inout_Levset)
{
var VolMsk = S.VolumeMask;
var EdgMsk = S.InnerEdgesMask;
UnsetteledCoordinateMapping Map = inout_Levset.Mapping;
if (dt <= 0.0)
{
throw new ArgumentOutOfRangeException("Timestep size must be greater than 0.");
}
MsrMatrix Pmtx = PenaltyMatrix(EdgMsk, inout_Levset.Basis, inout_Levset.Basis);
Pmtx.Scale(-1.0);
int[] SubVecIdx = Map.GetSubvectorIndices(S, true, new int[] { 0 });
int L = SubVecIdx.Length;
MsrMatrix SubMtx = new MsrMatrix(L, L);
Pmtx.AccSubMatrixTo(1.0, SubMtx, SubVecIdx, default(int[]), SubVecIdx, default(int[]));
SubMtx.AccEyeSp(1.0 / dt);
double[] RHS = new double[L];
double[] SOL = new double[L];
RHS.AccV(1.0 / dt, inout_Levset.CoordinateVector, default(int[]), SubVecIdx);
using (var solver = new PARDISOSolver()) {
solver.DefineMatrix(SubMtx);
solver.Solve(SOL, RHS);
}
inout_Levset.CoordinateVector.ClearEntries(SubVecIdx);
inout_Levset.CoordinateVector.AccV(1.0, SOL, SubVecIdx, default(int[]));
}
public void Init(MultigridOperator op)
{
int D = op.Mapping.GridData.SpatialDimension;
var M = op.OperatorMatrix;
var MgMap = op.Mapping;
this.m_mgop = op;
if (!M.RowPartitioning.EqualsPartition(MgMap.Partitioning))
{
throw new ArgumentException("Row partitioning mismatch.");
}
if (!M.ColPartition.EqualsPartition(MgMap.Partitioning))
{
throw new ArgumentException("Column partitioning mismatch.");
}
Uidx = MgMap.ProblemMapping.GetSubvectorIndices(true, D.ForLoop(i => i));
Pidx = MgMap.ProblemMapping.GetSubvectorIndices(true, D);
int Upart = Uidx.Length;
int Ppart = Pidx.Length;
ConvDiff = new MsrMatrix(Upart, Upart, 1, 1);
pGrad = new MsrMatrix(Upart, Ppart, 1, 1);
divVel = new MsrMatrix(Ppart, Upart, 1, 1);
var PxP = new MsrMatrix(Ppart, Ppart, 1, 1);
M.AccSubMatrixTo(1.0, ConvDiff, Uidx, default(int[]), Uidx, default(int[]));
M.AccSubMatrixTo(1.0, pGrad, Uidx, default(int[]), Pidx, default(int[]));
M.AccSubMatrixTo(1.0, divVel, Pidx, default(int[]), Uidx, default(int[]));
M.AccSubMatrixTo(1.0, PxP, Pidx, default(int[]), Pidx, default(int[]));
Mtx = M;
int L = M.RowPartitioning.LocalLength;
int i0 = Mtx.RowPartitioning.i0;
P = new MsrMatrix(Mtx);
P.Clear();
// Debugging output
//ConvDiff.SaveToTextFileSparse("ConvDiff");
//divVel.SaveToTextFileSparse("divVel");
//pGrad.SaveToTextFileSparse("pGrad");
//PxP.SaveToTextFileSparse("PxP");
velMassMatrix = new MsrMatrix(Upart, Upart, 1, 1);
op.MassMatrix.AccSubMatrixTo(1.0, velMassMatrix, Uidx, default(int[]), Uidx, default(int[]));
switch (SchurOpt)
{
case SchurOptions.exact:
{
// Building complete Schur and Approximate Schur
MultidimensionalArray Poisson = MultidimensionalArray.Create(Pidx.Length, Pidx.Length);
MultidimensionalArray SchurConvPart = MultidimensionalArray.Create(Pidx.Length, Pidx.Length);
MultidimensionalArray Schur = MultidimensionalArray.Create(Pidx.Length, Pidx.Length);
using (BatchmodeConnector bmc = new BatchmodeConnector())
{
bmc.PutSparseMatrix(ConvDiff, "ConvDiff");
bmc.PutSparseMatrix(velMassMatrix, "MassMatrix");
bmc.PutSparseMatrix(divVel, "divVel");
bmc.PutSparseMatrix(pGrad, "pGrad");
bmc.Cmd("Qdiag = diag(diag(MassMatrix))");
bmc.Cmd("invT= inv(Qdiag)");
bmc.Cmd("Poisson = full(invT)*pGrad");
bmc.Cmd("ConvPart = ConvDiff*Poisson");
bmc.Cmd("ConvPart= full(invT)*ConvPart");
bmc.Cmd("ConvPart= divVel*ConvPart");
bmc.Cmd("Poisson = divVel*Poisson");
bmc.Cmd("ConvDiffInv = inv(full(ConvDiff))");
bmc.Cmd("Schur = divVel*ConvDiffInv");
bmc.Cmd("Schur = Schur*pGrad");
bmc.GetMatrix(Poisson, "Poisson");
bmc.GetMatrix(SchurConvPart, "ConvPart");
bmc.GetMatrix(Schur, "-Schur");
bmc.Execute(false);
}
PoissonMtx_T = Poisson.ToMsrMatrix();
PoissonMtx_H = Poisson.ToMsrMatrix();
SchurConvMtx = SchurConvPart.ToMsrMatrix();
SchurMtx = Schur.ToMsrMatrix();
SchurMtx.Acc(PxP, 1);
ConvDiff.AccSubMatrixTo(1.0, P, default(int[]), Uidx, default(int[]), Uidx);
pGrad.AccSubMatrixTo(1.0, P, default(int[]), Uidx, default(int[]), Pidx);
SchurMtx.AccSubMatrixTo(1.0, P, default(int[]), Pidx, default(int[]), Pidx);
return;
}
case SchurOptions.decoupledApprox:
{
// Do assembly for approximate Schur inverse
invVelMassMatrix = velMassMatrix.CloneAs();
invVelMassMatrix.Clear();
invVelMassMatrixSqrt = invVelMassMatrix.CloneAs();
for (int i = velMassMatrix.RowPartitioning.i0; i < velMassMatrix.RowPartitioning.iE; i++)
{
if (ApproxScaling)
{
invVelMassMatrix.SetDiagonalElement(i, 1 / (velMassMatrix[i, i]));
invVelMassMatrixSqrt.SetDiagonalElement(i, 1 / (Math.Sqrt(velMassMatrix[i, i])));
}
else
{
invVelMassMatrix.SetDiagonalElement(i, 1);
invVelMassMatrixSqrt.SetDiagonalElement(i, 1);
}
}
//invVelMassMatrix.SaveToTextFileSparse("invVelMassMatrix");
//velMassMatrix.SaveToTextFileSparse("velMassMatrix");
//ConvDiffPoissonMtx = MsrMatrix.Multiply(ConvDiff, pGrad);
//ConvDiffPoissonMtx = MsrMatrix.Multiply(divVel, ConvDiffPoissonMtx);
// Inverse of mass matrix in Matlab
//MultidimensionalArray temp = MultidimensionalArray.Create(Uidx.Length, Uidx.Length);
//using (BatchmodeConnector bmc = new BatchmodeConnector())
//{
// bmc.PutSparseMatrix(velMassMatrix, "velMassMatrix");
// bmc.Cmd("invVelMassMatrix = inv(full(velMassMatrix))");
// bmc.GetMatrix(temp, "invVelMassMatrix");
// bmc.Execute(false);
//}
//invVelMassMatrix = temp.ToMsrMatrix();
//ConvDiffPoissonMtx = MsrMatrix.Multiply(ConvDiffPoissonMtx, PoissonMtx);
//ConvDiffPoissonMtx = MsrMatrix.Multiply(PoissonMtx, ConvDiffPoissonMtx);
//ConvDiff.AccSubMatrixTo(1.0, P, default(int[]), Uidx, default(int[]), Uidx);
//pGrad.AccSubMatrixTo(1.0, P, default(int[]), Uidx, default(int[]), Pidx);
//ConvDiffPoissonMtx.AccSubMatrixTo(1.0, P, default(int[]), Pidx, default(int[]), Pidx);
//op.MassMatrix.SaveToTextFileSparse("MassMatrix");
//velMassMatrix.SaveToTextFileSparse("velMassMatrix2");
// Possion scaled by inverse of the velocity mass matrix
PoissonMtx_T = MsrMatrix.Multiply(invVelMassMatrix, pGrad);
PoissonMtx_T = MsrMatrix.Multiply(divVel, PoissonMtx_T);
////PoissonMtx_T.Acc(PxP, 1); // p.379
// Poisson scaled by sqrt of inverse of velocity mass matrix
PoissonMtx_H = MsrMatrix.Multiply(invVelMassMatrixSqrt, pGrad);
PoissonMtx_H = MsrMatrix.Multiply(divVel, PoissonMtx_H);
//PoissonMtx_H.Acc(PxP, 1); // p.379
return;
}
case SchurOptions.SIMPLE:
{
var invdiag_ConvDiff = ConvDiff.CloneAs();
invdiag_ConvDiff.Clear();
for (int i = ConvDiff.RowPartitioning.i0; i < ConvDiff.RowPartitioning.iE; i++)
{
invdiag_ConvDiff[i, i] = 1 / ConvDiff[i, i];
}
simpleSchur = MsrMatrix.Multiply(invdiag_ConvDiff, pGrad);
simpleSchur = MsrMatrix.Multiply(divVel, simpleSchur);
return;
}
default:
throw new NotImplementedException("SchurOption");
}
//var ConvDiffInvMtx = ConvDiffInv.ToMsrMatrix();
//// x= inv(P)*b !!!!! To be done with approximate Inverse
// P.SpMV(1, B, 0, X);
}
// Local Variables for Iteration
// <summary>
// Counter for Iteration Steps
// </summary>
//double OldResidual = double.MaxValue;
//int divergencecounter = 0;
///// <summary>
///// Checks for Reaching Max. Number of Iterations and Divergence of Algorithm
///// </summary>
///// <param name="Residual">Change Rate of the Algorithm</param>
///// <returns>Reaching Max Iterations, Aborts when diverged</returns>
//public bool CheckAbortCriteria(double Residual, int IterationCounter) {
// if (Residual <= ConvergenceCriterion) {
// Console.WriteLine("EllipticReInit converged after {0} Iterations ", IterationCounter);
// return true;
// }
// if (Residual >= OldResidual) divergencecounter++;
// else divergencecounter = 0;
// if (IterationCounter >= MaxIteration) {
// Console.WriteLine("Elliptic Reinit Max Iterations Reached");
// return true;
// };
// if (divergencecounter > MaxIteration / 2) {
// Console.WriteLine("Elliptic Reinit diverged - Aborting");
// throw new ApplicationException();
// }
// OldResidual = Residual;
// IterationCounter++;
// return false;
//}
//bool PreviouslyOnSubgrid = false;
/// <summary>
/// Updates the Operator Matrix after level-set motion
/// </summary>
/// <param name="Restriction">
/// The subgrid, on which the ReInit is performed
/// </param>
/// <param name="IncludingInterface">
/// !! Not yet functional !!
/// True, if the subgrid contains the interface, this causes all external edges of the subgrid to be treated as boundaries
/// False, for the rest of the domain, thus the flux to the adjacent cells wil be evaluated
/// </param>
public void UpdateOperators(SubGrid Restriction = null, bool IncludingInterface = true)
{
if (!IncludingInterface)
{
throw new NotImplementedException("Untested, not yet functional!");
}
using (new FuncTrace()) {
//using (var slv = new ilPSP.LinSolvers.MUMPS.MUMPSSolver()) {
//using (var slv = new ilPSP.LinSolvers.PARDISO.PARDISOSolver()) {
//using (var slv = new ilPSP.LinSolvers.HYPRE.GMRES()) {
if (Control.Upwinding)
{
OldPhi.Clear();
OldPhi.Acc(1.0, Phi);
//Calculate
LevelSetGradient.Clear();
LevelSetGradient.Gradient(1.0, Phi, Restriction?.VolumeMask);
//LevelSetGradient.Gradient(1.0, Phi);
//LevelSetGradient.GradientByFlux(1.0, Phi);
MeanLevelSetGradient.Clear();
MeanLevelSetGradient.AccLaidBack(1.0, LevelSetGradient, Restriction?.VolumeMask);
//MeanLevelSetGradient.AccLaidBack(1.0, LevelSetGradient);
}
if (slv != null)
{
slv.Dispose();
}
slv = Control.solverFactory();
OpMatrix_interface.Clear();
OpAffine_interface.Clear();
// Build the Quadrature-Scheme for the interface operator
// Note: The HMF-Quadrature over a surface is formally a volume quadrature, since it uses the volume quadrature nodes.
//XSpatialOperatorExtensions.ComputeMatrixEx(Operator_interface,
////Operator_interface.ComputeMatrixEx(
// LevelSetTracker,
// Phi.Mapping,
// null,
// Phi.Mapping,
// OpMatrix_interface,
// OpAffine_interface,
// false,
// 0,
// false,
// subGrid:Restriction,
// whichSpc: LevelSetTracker.GetSpeciesId("A")
// );
XSpatialOperatorMk2.XEvaluatorLinear mtxBuilder = Operator_interface.GetMatrixBuilder(LevelSetTracker, Phi.Mapping, null, Phi.Mapping);
MultiphaseCellAgglomerator dummy = LevelSetTracker.GetAgglomerator(LevelSetTracker.SpeciesIdS.ToArray(), Phi.Basis.Degree * 2 + 2, 0.0);
//mtxBuilder.SpeciesOperatorCoefficients[LevelSetTracker.GetSpeciesId("A")].CellLengthScales = dummy.CellLengthScales[LevelSetTracker.GetSpeciesId("A")];
mtxBuilder.CellLengthScales.Add(LevelSetTracker.GetSpeciesId("A"), dummy.CellLengthScales[LevelSetTracker.GetSpeciesId("A")]);
mtxBuilder.time = 0;
mtxBuilder.MPITtransceive = false;
mtxBuilder.ComputeMatrix(OpMatrix_interface, OpAffine_interface);
// Regenerate OpMatrix for subgrid -> adjacent cells must be trated as boundary
if (Restriction != null)
{
OpMatrix_bulk.Clear();
OpAffine_bulk.Clear();
//Operator_bulk.ComputeMatrix(
// Phi.Mapping,
// parameterFields,
// Phi.Mapping,
// OpMatrix_bulk, OpAffine_bulk,
// OnlyAffine: false, sgrd: Restriction);
EdgeQuadratureScheme edgescheme;
//if (Control.Upwinding) {
// edgescheme = new EdgeQuadratureScheme(true, IncludingInterface ? Restriction.AllEdgesMask : null);
//}
//else {
edgescheme = new EdgeQuadratureScheme(true, IncludingInterface ? Restriction.InnerEdgesMask : null);
//}
Operator_bulk.ComputeMatrixEx(Phi.Mapping,
parameterFields,
Phi.Mapping, OpMatrix_bulk, OpAffine_bulk, false, 0,
edgeQuadScheme: edgescheme,
volQuadScheme: new CellQuadratureScheme(true, IncludingInterface ? Restriction.VolumeMask : null)
);
//PreviouslyOnSubgrid = true;
}
// recalculate full Matrix
//else if (PreviouslyOnSubgrid) {
else
{
OpMatrix_bulk.Clear();
OpAffine_bulk.Clear();
Operator_bulk.ComputeMatrixEx(Phi.Mapping,
parameterFields,
Phi.Mapping, OpMatrix_bulk, OpAffine_bulk, false, 0
);
//PreviouslyOnSubgrid = false;
}
/// Compose the Matrix
/// This is symmetric due to the symmetry of the SIP and the penalty term
OpMatrix.Clear();
OpMatrix.Acc(1.0, OpMatrix_bulk);
OpMatrix.Acc(1.0, OpMatrix_interface);
OpMatrix.AssumeSymmetric = !Control.Upwinding;
//OpMatrix.AssumeSymmetric = false;
/// Compose the RHS of the above operators. (-> Boundary Conditions)
/// This does NOT include the Nonlinear RHS, which will be added later
OpAffine.Clear();
OpAffine.AccV(1.0, OpAffine_bulk);
OpAffine.AccV(1.0, OpAffine_interface);
#if Debug
ilPSP.Connectors.Matlab.BatchmodeConnector matlabConnector;
matlabConnector = new BatchmodeConnector();
#endif
if (Restriction != null)
{
SubVecIdx = Phi.Mapping.GetSubvectorIndices(Restriction, true, new int[] { 0 });
int L = SubVecIdx.Length;
SubMatrix = new MsrMatrix(L);
SubRHS = new double[L];
SubSolution = new double[L];
OpMatrix.AccSubMatrixTo(1.0, SubMatrix, SubVecIdx, default(int[]), SubVecIdx, default(int[]));
slv.DefineMatrix(SubMatrix);
#if Debug
Console.WriteLine("ConditionNumber of ReInit-Matrix is " + SubMatrix.condest().ToString("E"));
#endif
}
else
{
slv.DefineMatrix(OpMatrix);
#if Debug
Console.WriteLine("ConditionNumber of ReInit-Matrix is " + OpMatrix.condest().ToString("E"));
#endif
}
}
}