/// <summary>
///
/// </summary>
/// <returns></returns>
protected override MsrMatrix ComputeMatrix()
{
MsrMatrix CorrectorMatrix = new MsrMatrix(m_VelocityDivergence[0].LocalLength);
for (int comp = 0; comp < m_VelocityDivergence.Length; comp++)
{
MsrMatrix prod1 = MsrMatrix.Multiply(m_PredictorApproxInv[comp].AssemblyMatrix, m_PressureGradient[comp].OperatorMatrix);
MsrMatrix prod2 = MsrMatrix.Multiply(m_VelocityDivergence[comp].OperatorMatrix, prod1);
CorrectorMatrix.Acc(1.0, prod2);
}
//CorrectorMatrix.AssumeSymmetric = false;
return(CorrectorMatrix);
}
/// <summary>
///
/// </summary>
/// <returns></returns>
protected override MsrMatrix ComputeMatrix()
{
MsrMatrix CorrectorMatrix = new MsrMatrix(m_DivergenceConti[0].LocalLength);
for (int comp = 0; comp < m_DivergenceConti.Length; comp++)
{
MsrMatrix prod1 = MsrMatrix.Multiply(m_PredictorApproxInv.AssemblyMatrix, m_PressureGradient[comp].OperatorMatrix);
MsrMatrix prod2 = MsrMatrix.Multiply(m_DivergenceConti[comp].OperatorMatrix, prod1);
CorrectorMatrix.Acc(1.0, prod2);
}
if (m_PressureStabilization != null)
{
CorrectorMatrix.Acc(-1.0, m_PressureStabilization.OperatorMatrix);
}
//CorrectorMatrix.AssumeSymmetric = true;
return(CorrectorMatrix);
}
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);
}
/// <summary>
/// Computes a potential solution (i.e. neglects convective/diffusive part) to the current residual
/// </summary>
/// <param name="X">input/output: solution guess</param>
/// <param name="RHS">RHS of the saddle point problem</param>
public void Solve <U, V>(U X, V RHS)
where U : IList <double>
where V : IList <double> //
{
double[] RESI = RHS.ToArray();
this.m_MgOp.OperatorMatrix.SpMV(-1.0, X, 1.0, RESI);
var MM = this.m_MgOp.MassMatrix.CloneAs();
MM.AccEyeSp(-1.0);
double nrm = MM.InfNorm();
double[] R1 = new double[USubMatrixIdx_Row.Length];
double[] R2 = new double[PSubMatrixIdx_Row.Length];
RESI.GetSubVector(R1, USubMatrixIdx_Row, default(int[]));
RESI.GetSubVector(R2, PSubMatrixIdx_Row, default(int[]));
double gamma;
if (double.IsInfinity(this.m_SIMPLEOptions.dt))
{
gamma = 1.0;
}
else
{
gamma = (1.0 + this.m_SIMPLEOptions.dt) / this.m_SIMPLEOptions.dt;
}
// RHS of Poisson equation
double[] Poisson_RHS;
{
Poisson_RHS = R2;
if (this.invMM != null)
{
double[] tmp = new double[R1.Length];
this.invMM.SpMVpara(1.0, R1, 0.0, tmp);
this.VelocityDiv.SpMVpara(1.0, tmp, -gamma, Poisson_RHS);
}
else
{
this.VelocityDiv.SpMVpara(1.0, R1, -gamma, Poisson_RHS);
}
}
// LHS of Poisson equation
if (m_PressureSolver == null)
{
m_PressureSolver = m_SIMPLEOptions.PressureSolver;
if (m_PressureSolver is PARDISOSolver)
{
((PARDISOSolver)m_PressureSolver).CacheFactorization = true;
}
MsrMatrix MXCorrector;
if (invMM != null)
{
MXCorrector = MsrMatrix.Multiply(this.VelocityDiv, MsrMatrix.Multiply(this.invMM, this.PressureGrad));
}
else
{
MXCorrector = MsrMatrix.Multiply(this.VelocityDiv, this.PressureGrad);
}
MXCorrector.Acc(-1.0, Stab);
m_PressureSolver.DefineMatrix(MXCorrector);
}
// solve Poisson equation
double[] PressureCorr = new double[R2.Length];
m_PressureSolver.Solve(PressureCorr, Poisson_RHS);
//// compute velocity correction
//double[] VelocityCorr = R1;
//this.PressureGrad.SpMV(-1.0 / gamma, PressureCorr, 1.0, VelocityCorr);
// apply corrections & return
//X.AccV(1.0, VelocityCorr, USubMatrixIdx_Row, default(int[])); // the velocity correction is crap; better not to add it.
X.AccV(1.0, PressureCorr, PSubMatrixIdx_Row, default(int[]));
NoOfIterations++;
}
public void Init(MultigridOperator op)
{
int D = op.GridData.SpatialDimension;
CodName = (new string[] { "mom0", "mom1" });
Params = ArrayTools.Cat(
VariableNames.Velocity0Vector(D));
DomName = ArrayTools.Cat(VariableNames.VelocityVector(D));
LocalOp = new SpatialOperator(DomName, Params, CodName, (A, B, C) => 4);
for (int d = 0; d < D; d++)
{
LocalOp.EquationComponents["mom" + d].Add(new LocalDiffusiveFlux()
{
m_component = d, dt = m_dt, muA = m_muA
});
}
LocalOp.Commit();
//LocalMatrix = op.MassMatrix.CloneAs().ToMsrMatrix();
//LocalMatrix.Clear();
//var U0 = new VectorField<SinglePhaseField>(op.BaseGridProblemMapping Take(D).Select(F => (SinglePhaseField)F).ToArray());
UnsetteledCoordinateMapping test = new UnsetteledCoordinateMapping(op.BaseGridProblemMapping.BasisS.GetSubVector(0, D));
var U0 = ((BoSSS.Foundation.CoordinateMapping)op.Mapping.ProblemMapping).Fields.GetSubVector(0, 2);
var empty = new SinglePhaseField[D];
LocalMatrix = LocalOp.ComputeMatrix(test, empty, test, time: m_dt);
Uidx = op.Mapping.ProblemMapping.GetSubvectorIndices(true, D.ForLoop(i => i));
Pidx = op.Mapping.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 VelocityMass = new MsrMatrix(Upart, Upart, 1, 1);
var leftChangeBasesVel = new MsrMatrix(Upart, Upart, 1, 1);
var rightChangeBasesVel = new MsrMatrix(Upart, Upart, 1, 1);
op.MassMatrix.AccSubMatrixTo(1.0, VelocityMass, Uidx, default(int[]), Uidx, default(int[]), default(int[]), default(int[]));
op.LeftChangeOfBasis.AccSubMatrixTo(1.0, leftChangeBasesVel, Uidx, default(int[]), Uidx, default(int[]), default(int[]), default(int[]));
op.RightChangeOfBasis.AccSubMatrixTo(1.0, rightChangeBasesVel, Uidx, default(int[]), Uidx, default(int[]), default(int[]), default(int[]));
var temp = MsrMatrix.Multiply(leftChangeBasesVel, LocalMatrix);
LocalMatrix = MsrMatrix.Multiply(temp, rightChangeBasesVel);
var M = op.OperatorMatrix;
M.AccSubMatrixTo(1.0, ConvDiff, Uidx, default(int[]), Uidx, default(int[]), default(int[]), default(int[]));
M.AccSubMatrixTo(1.0, pGrad, Uidx, default(int[]), Pidx, default(int[]), default(int[]), default(int[]));
M.AccSubMatrixTo(1.0, divVel, Pidx, default(int[]), Uidx, default(int[]), default(int[]), default(int[]));
LocalMatrix.SaveToTextFileSparse("LocalConvDiffMatrix");
ConvDiff.SaveToTextFileSparse("ConvDiff");
op.MassMatrix.SaveToTextFileSparse("MassMatrix");
VelocityMass.SaveToTextFileSparse("VelocityMass");
}