private void AssembleMatrix(double MU_A, double MU_B, out BlockMsrMatrix M, out double[] b, out MultiphaseCellAgglomerator agg, out MassMatrixFactory massFact)
{
using (var tr = new FuncTrace()) {
// create operator
// ===============
if (this.Control.SetDefaultDiriBndCnd)
{
this.Control.xLaplaceBCs.g_Diri = ((CommonParamsBnd inp) => 0.0);
this.Control.xLaplaceBCs.IsDirichlet = (inp => true);
}
double D = this.GridData.SpatialDimension;
int p = u.Basis.Degree;
double penalty_base = (p + 1) * (p + D) / D;
double penalty_multiplyer = base.Control.penalty_multiplyer;
XQuadFactoryHelper.MomentFittingVariants momentFittingVariant;
if (D == 3)
{
momentFittingVariant = XQuadFactoryHelper.MomentFittingVariants.Classic;
}
momentFittingVariant = this.Control.CutCellQuadratureType;
int order = this.u.Basis.Degree * 2;
XSpatialOperator Op = new XSpatialOperator(1, 1, (A, B, C) => order, "u", "c1");
var lengthScales = ((BoSSS.Foundation.Grid.Classic.GridData)GridData).Cells.PenaltyLengthScales;
var lap = new XLaplace_Bulk(this.LsTrk, penalty_multiplyer * penalty_base, "u", this.Control.xLaplaceBCs, 1.0, MU_A, MU_B, lengthScales, this.Control.ViscosityMode);
Op.EquationComponents["c1"].Add(lap); // Bulk form
Op.EquationComponents["c1"].Add(new XLaplace_Interface(this.LsTrk, MU_A, MU_B, penalty_base * 2, this.Control.ViscosityMode)); // coupling form
Op.Commit();
// create agglomeration
// ====================
var map = new UnsetteledCoordinateMapping(u.Basis);
//agg = new MultiphaseCellAgglomerator(
// new CutCellMetrics(momentFittingVariant,
// QuadOrderFunc.SumOfMaxDegrees(RoundUp: true)(map.BasisS.Select(bs => bs.Degree).ToArray(), new int[0], map.BasisS.Select(bs => bs.Degree).ToArray()),
// //this.HMFDegree,
// LsTrk, this.LsTrk.SpeciesIdS.ToArray()),
// this.Control.AgglomerationThreshold, false);
agg = LsTrk.GetAgglomerator(this.LsTrk.SpeciesIdS.ToArray(), order, this.Control.AgglomerationThreshold);
// compute matrix
// =============
using (new BlockTrace("XdgMatrixAssembly", tr)) {
M = new BlockMsrMatrix(map, map);
b = new double[M.RowPartitioning.LocalLength];
Op.ComputeMatrixEx(LsTrk,
map, null, map,
M, b, false, 0.0, true,
agg.CellLengthScales, null, null, //out massFact,
this.LsTrk.SpeciesIdS.ToArray());
}
// compare with linear evaluation
// ==============================
DGField[] testDomainFieldS = map.BasisS.Select(bb => new XDGField(bb as XDGBasis)).ToArray();
CoordinateVector test = new CoordinateVector(testDomainFieldS);
DGField[] errFieldS = map.BasisS.Select(bb => new XDGField(bb as XDGBasis)).ToArray();
CoordinateVector Err = new CoordinateVector(errFieldS);
var eval = Op.GetEvaluatorEx(LsTrk,
testDomainFieldS, null, map);
foreach (var s in this.LsTrk.SpeciesIdS)
{
eval.SpeciesOperatorCoefficients[s].CellLengthScales = agg.CellLengthScales[s];
}
eval.time = 0.0;
int L = test.Count;
Random r = new Random();
for (int i = 0; i < L; i++)
{
test[i] = r.NextDouble();
}
double[] R1 = new double[L];
double[] R2 = new double[L];
eval.Evaluate(1.0, 1.0, R1);
R2.AccV(1.0, b);
M.SpMV(1.0, test, 1.0, R2);
Err.AccV(+1.0, R1);
Err.AccV(-1.0, R2);
double ErrDist = GenericBlas.L2DistPow2(R1, R2).MPISum().Sqrt();
double Ref = test.L2NormPow2().MPISum().Sqrt();
Assert.LessOrEqual(ErrDist, Ref * 1.0e-5, "Mismatch between explicit evaluation of XDG operator and matrix.");
// agglomeration wahnsinn
// ======================
agg.ManipulateMatrixAndRHS(M, b, map, map);
foreach (var S in this.LsTrk.SpeciesNames)
{
Console.WriteLine(" Species {0}: no of agglomerated cells: {1}",
S, agg.GetAgglomerator(this.LsTrk.GetSpeciesId(S)).AggInfo.SourceCells.NoOfItemsLocally);
}
// mass matrix factory
// ===================
Basis maxB = map.BasisS.ElementAtMax(bss => bss.Degree);
//massFact = new MassMatrixFactory(maxB, agg);
massFact = LsTrk.GetXDGSpaceMetrics(this.LsTrk.SpeciesIdS.ToArray(), order).MassMatrixFactory;
}
}
void TestAgglomeration_Projection(int quadOrder, MultiphaseCellAgglomerator Agg)
{
var Bmask = LsTrk.Regions.GetSpeciesMask("B");
var BbitMask = Bmask.GetBitMask();
var XDGmetrics = LsTrk.GetXDGSpaceMetrics(new SpeciesId[] { LsTrk.GetSpeciesId("B") }, quadOrder, 1);
int degree = Math.Max(0, this.u.Basis.Degree - 1);
_2D SomePolynomial;
if (degree == 0)
{
SomePolynomial = (x, y) => 3.2;
}
else if (degree == 1)
{
SomePolynomial = (x, y) => 3.2 + x - 2.4 * y;
}
else
{
SomePolynomial = (x, y) => x * x + y * y;
}
// ------------------------------------------------
// project the polynomial onto a single-phase field
// ------------------------------------------------
SinglePhaseField NonAgglom = new SinglePhaseField(new Basis(this.GridData, degree), "NonAgglom");
NonAgglom.ProjectField(1.0,
SomePolynomial.Vectorize(),
new CellQuadratureScheme(true, Bmask));
// ------------------------------------------------
// project the polynomial onto the aggomerated XDG-field
// ------------------------------------------------
var qsh = XDGmetrics.XQuadSchemeHelper;
// Compute the inner product of 'SomePolynomial' with the cut-cell-basis, ...
SinglePhaseField xt = new SinglePhaseField(NonAgglom.Basis, "test");
xt.ProjectField(1.0,
SomePolynomial.Vectorize(),
qsh.GetVolumeQuadScheme(this.LsTrk.GetSpeciesId("B")).Compile(this.GridData, Agg.CutCellQuadratureOrder));
CoordinateMapping map = xt.Mapping;
// ... change to the cut-cell-basis, ...
double[] xVec = xt.CoordinateVector.ToArray();
Agg.ManipulateMatrixAndRHS(default(MsrMatrix), xVec, map, null);
{
double[] xVec2 = xVec.CloneAs();
Agg.ClearAgglomerated(xVec2, map); // clearing should have no effect now.
double Err3 = GenericBlas.L2DistPow2(xVec, xVec2).MPISum().Sqrt();
Assert.LessOrEqual(Err3, 0.0);
}
// ... multiply with the inverse mass-matrix, ...
var Mfact = XDGmetrics.MassMatrixFactory;
BlockMsrMatrix MassMtx = Mfact.GetMassMatrix(map, false);
Agg.ManipulateMatrixAndRHS(MassMtx, default(double[]), map, map);
var InvMassMtx = MassMtx.InvertBlocks(OnlyDiagonal: true, Subblocks: true, ignoreEmptyBlocks: true, SymmetricalInversion: true);
double[] xAggVec = new double[xVec.Length];
InvMassMtx.SpMV(1.0, xVec, 0.0, xAggVec);
// ... and extrapolate.
// Since we projected a polynomial, the projection is exact and after extrapolation, must be equal
// to the polynomial.
xt.CoordinateVector.SetV(xAggVec);
Agg.Extrapolate(xt.Mapping);
// ------------------------------------------------
// check the error
// ------------------------------------------------
//double Err2 = xt.L2Error(SomePolynomial.Vectorize(), new CellQuadratureScheme(domain: Bmask));
double Err2 = NonAgglom.L2Error(xt);
Console.WriteLine("Agglom: projection and extrapolation error: " + Err2);
Assert.LessOrEqual(Err2, 1.0e-10);
}
protected override double RunSolverOneStep(int TimestepNo, double phystime, double dt)
{
Console.WriteLine(" Timestep # " + TimestepNo + ", phystime = " + phystime);
//phystime = 1.8;
LsUpdate(phystime);
// operator-matrix assemblieren
MsrMatrix OperatorMatrix = new MsrMatrix(u.Mapping, u.Mapping);
double[] Affine = new double[OperatorMatrix.RowPartitioning.LocalLength];
// Agglomerator setup
MultiphaseCellAgglomerator Agg = LsTrk.GetAgglomerator(new SpeciesId[] { LsTrk.GetSpeciesId("B") }, QuadOrder, this.THRESHOLD);
// plausibility of cell length scales
if (SER_PAR_COMPARISON)
{
TestLengthScales(QuadOrder, TimestepNo);
}
Console.WriteLine("Inter-Process agglomeration? " + Agg.GetAgglomerator(LsTrk.GetSpeciesId("B")).AggInfo.InterProcessAgglomeration);
if (this.THRESHOLD > 0.01)
{
TestAgglomeration_Extraploation(Agg);
TestAgglomeration_Projection(QuadOrder, Agg);
}
CheckExchange(true);
CheckExchange(false);
// operator matrix assembly
XSpatialOperatorMk2.XEvaluatorLinear mtxBuilder = Op.GetMatrixBuilder(base.LsTrk, u.Mapping, null, u.Mapping);
mtxBuilder.time = 0.0;
mtxBuilder.ComputeMatrix(OperatorMatrix, Affine);
Agg.ManipulateMatrixAndRHS(OperatorMatrix, Affine, u.Mapping, u.Mapping);
// mass matrix factory
var Mfact = LsTrk.GetXDGSpaceMetrics(new SpeciesId[] { LsTrk.GetSpeciesId("B") }, QuadOrder, 1).MassMatrixFactory;// new MassMatrixFactory(u.Basis, Agg);
// Mass matrix/Inverse Mass matrix
//var MassInv = Mfact.GetMassMatrix(u.Mapping, new double[] { 1.0 }, true, LsTrk.GetSpeciesId("B"));
var Mass = Mfact.GetMassMatrix(u.Mapping, new double[] { 1.0 }, false, LsTrk.GetSpeciesId("B"));
Agg.ManipulateMatrixAndRHS(Mass, default(double[]), u.Mapping, u.Mapping);
var MassInv = Mass.InvertBlocks(OnlyDiagonal: true, Subblocks: true, ignoreEmptyBlocks: true, SymmetricalInversion: false);
// test that operator depends only on B-species values
double DepTest = LsTrk.Regions.GetSpeciesSubGrid("B").TestMatrixDependency(OperatorMatrix, u.Mapping, u.Mapping);
Console.WriteLine("Matrix dependency test: " + DepTest);
Assert.LessOrEqual(DepTest, 0.0);
// diagnostic output
Console.WriteLine("Number of Agglomerations (all species): " + Agg.TotalNumberOfAgglomerations);
Console.WriteLine("Number of Agglomerations (species 'B'): " + Agg.GetAgglomerator(LsTrk.GetSpeciesId("B")).AggInfo.SourceCells.NoOfItemsLocally.MPISum());
// operator auswerten:
double[] x = new double[Affine.Length];
BLAS.daxpy(x.Length, 1.0, Affine, 1, x, 1);
OperatorMatrix.SpMVpara(1.0, u.CoordinateVector, 1.0, x);
MassInv.SpMV(1.0, x, 0.0, du_dx.CoordinateVector);
Agg.GetAgglomerator(LsTrk.GetSpeciesId("B")).Extrapolate(du_dx.Mapping);
// markieren, wo ueberhaupt A und B sind
Bmarker.AccConstant(1.0, LsTrk.Regions.GetSpeciesSubGrid("B").VolumeMask);
Amarker.AccConstant(+1.0, LsTrk.Regions.GetSpeciesSubGrid("A").VolumeMask);
if (usePhi0 && usePhi1)
{
Xmarker.AccConstant(+1.0, LsTrk.Regions.GetSpeciesSubGrid("X").VolumeMask);
}
// compute error
ERR.Clear();
ERR.Acc(1.0, du_dx_Exact, LsTrk.Regions.GetSpeciesSubGrid("B").VolumeMask);
ERR.Acc(-1.0, du_dx, LsTrk.Regions.GetSpeciesSubGrid("B").VolumeMask);
double L2Err = ERR.L2Norm(LsTrk.Regions.GetSpeciesSubGrid("B").VolumeMask);
Console.WriteLine("L2 Error: " + L2Err);
XERR.Clear();
XERR.GetSpeciesShadowField("B").Acc(1.0, ERR, LsTrk.Regions.GetSpeciesSubGrid("B").VolumeMask);
double xL2Err = XERR.L2Norm();
Console.WriteLine("L2 Error (in XDG space): " + xL2Err);
// check error
double ErrorThreshold = 1.0e-1;
if (this.MomentFittingVariant == XQuadFactoryHelper.MomentFittingVariants.OneStepGaussAndStokes)
{
ErrorThreshold = 1.0e-6; // HMF is designed for such integrands and should perform close to machine accuracy; on general integrands, the precision is different.
}
bool IsPassed = ((L2Err <= ErrorThreshold || this.THRESHOLD <= ErrorThreshold) && xL2Err <= ErrorThreshold);
if (IsPassed)
{
Console.WriteLine("Test PASSED");
}
else
{
Console.WriteLine("Test FAILED: check errors.");
//PlotCurrentState(phystime, TimestepNo, 3);
}
if (TimestepNo > 1)
{
if (this.THRESHOLD > ErrorThreshold)
{
// without agglomeration, the error in very tiny cut-cells may be large over the whole cell
// However, the error in the XDG-space should be small under all circumstances
Assert.LessOrEqual(L2Err, ErrorThreshold, "DG L2 error of computing du_dx");
}
Assert.LessOrEqual(xL2Err, ErrorThreshold, "XDG L2 error of computing du_dx");
}
// return/Ende
base.NoOfTimesteps = 17;
//base.NoOfTimesteps = 2;
dt = 0.3;
return(dt);
}
