void OrthonormalityTest()
{
Basis B = f1.Basis;
int N = B.Length;
var Mtx = new FullMatrix(N, N);
double TotErrSum = 0.0;
CellQuadrature.GetQuadrature(new int[] { N, N }, this.GridDat,
(new CellQuadratureScheme(true)).Compile(GridDat, Math.Min(B.Degree * 2, 16)),
delegate(MultidimensionalArray NodesUntransformed, int iKref) {
var ret = new NodeSetController.NodeSetContainer[] {
GridDat.NSC.CreateContainer(NodesUntransformed, iKref)
};
return(ret);
},
delegate(int i0, int Length, int NoOfNodes, MultidimensionalArray EvalResult) { // void Del_Evaluate
var BasisVal = B.CellEval(0, i0, Length);
EvalResult.Multiply(1.0, BasisVal, BasisVal, 0.0, "jknm", "jkn", "jkm");
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) { // SaveIntegrationResults
for (int i = 0; i < Length; i++)
{
var MassMtx = ResultsOfIntegration.ExtractSubArrayShallow(i, -1, -1);
double errsum = 0;
for (int n = 0; n < N; n++)
{
for (int m = 0; m < N; m++)
{
double soll = (n == m) ? 1.0 : 0.0;
errsum += Math.Abs(MassMtx[m, n] - soll);
}
}
TotErrSum += errsum;
}
}).Execute();
Console.WriteLine("orthonormality error sum:" + TotErrSum);
}
public void Evaluate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult)
{
// Del_Evaluate
// ~~~~~~~~~~~~~
NodeSet NS = QR.Nodes;
int NoOfNodes = NS.NoOfNodes;
var BasisVal = b.CellEval(NS, i0, Length);
EvalResult.ExtractSubArrayShallow(new int[] { 0, 0, 0, 0 }, new int[] { Length - 1, NoOfNodes - 1, Nnx - 1, Nnx - 1 })
.Multiply(1.0, BasisVal, BasisVal, 0.0, "ikmn", "ikm", "ikn");
if (UevalBuf == null)
{
UevalBuf = MultidimensionalArray.Create(Length, NoOfNodes);
}
if (UevalBuf.GetLength(0) < Length || UevalBuf.GetLength(1) != NoOfNodes)
{
UevalBuf.Allocate(Length, NoOfNodes);
}
MultidimensionalArray _UevalBuf;
if (UevalBuf.GetLength(0) > Length)
{
_UevalBuf = UevalBuf.ExtractSubArrayShallow(new int[] { 0, 0 }, new int[] { Length - 1, NoOfNodes - 1 });
}
else
{
Debug.Assert(UevalBuf.GetLength(0) == Length);
_UevalBuf = UevalBuf;
}
for (int d = 0; d < D; d++)
{
_UevalBuf.Clear();
Uin[d].Evaluate(i0, Length, NS, _UevalBuf);
EvalResult.ExtractSubArrayShallow(new int[] { 0, 0, Nnx + d, 0 }, new int[] { Length - 1, NoOfNodes - 1, Nnx + d - 1, Nnx - 1 })
.Multiply(1.0, BasisVal, _UevalBuf, 0.0, "ikm", "ikm", "ik");
}
}
MultidimensionalArray StokesAnsatzRHS(Basis TestBasis, CellBoundaryQuadratureScheme cellBndSchme, CellMask _mask, int order)
{
var GridDat = this.tracker.GridDat;
CellBoundaryQuadrature <CellBoundaryQuadRule> qBnd = null;
int N = TestBasis.Length;
int D = GridDat.SpatialDimension;
MultidimensionalArray RHS = MultidimensionalArray.Create(D, N, _mask.NoOfItemsLocally);
double[] CellN = new double[D]; // cell normal
double[] SurfN = new double[D]; // level-set normal
double[] OutwardTang = new double[D]; // level-set tangent, outward of cell
if (D != 2)
{
throw new NotSupportedException("Currently only supported for spatial dimension of 2.");
}
//MultidimensionalArray Nudes = null;
int jSgrd = 0;
qBnd = CellBoundaryQuadrature <CellBoundaryQuadRule> .GetQuadrature(new int[] { D, N },
GridDat, cellBndSchme.Compile(GridDat, order),
delegate(int i0, int Length, CellBoundaryQuadRule NS, MultidimensionalArray EvalResult) { // Evaluate
//MultidimensionalArray BasisValues = TestBasis.Evaluate(0); // reference
//var LSNormals = LsTrk.GetLevelSetReferenceNormals(iLevSet, 0, i0, Length); // reference
MultidimensionalArray BasisValues = TestBasis.CellEval(NS.Nodes, i0, Length); // physical
MultidimensionalArray LSNormals = this.LevelSetData.GetLevelSetNormals(NS.Nodes, i0, Length); // physical
for (int i = 0; i < Length; i++) // loop over cells
//if(i0 + i == 1) {
// EvalResult.ExtractSubArrayShallow(i, -1, -1, -1).Clear();
// continue;
//}
{
CellBoundaryQuadRule cR = qBnd.CurrentRule;
int[] NodesPerEdge = cR.NumbersOfNodesPerFace;
var Kref = cR.RefElement;
int NoOfFaces = Kref.NoOfFaces;
int iNode = 0;
Debug.Assert(NoOfFaces == NodesPerEdge.Length);
for (int e = 0; e < NoOfFaces; e++) // loop over the faces of the cell
{
if (NodesPerEdge[e] <= 0)
{
continue;
}
// reference:
//for (int d = 0; d < D; d++) {
// CellN[d] = Kref.FaceNormals[e, d];
//}
// ~~~~
// physical:
var FaceNodes = new NodeSet(Kref, cR.Nodes.ExtractSubArrayShallow(new int[] { iNode, 0 }, new int[] { iNode + NodesPerEdge[e] - 1, D - 1 }));
var FaceNormals = MultidimensionalArray.Create(NodesPerEdge[e], D);
GridDat.Edges.GetNormalsForCell(FaceNodes, i0, e, FaceNormals);
// ~~~~
for (int _n = 0; _n < NodesPerEdge[e]; _n++) // loop over nodes in one edge
{
for (int d = 0; d < D; d++)
{
SurfN[d] = LSNormals[i, iNode, d];
CellN[d] = FaceNormals[_n, d]; // physical
}
tangente(SurfN, CellN, OutwardTang);
for (int n = 0; n < N; n++) // loop over Test polynomials (the same as the basis polynomials)
{
for (int d = 0; d < D; d++) // loop over spatial direction
{
EvalResult[i, iNode, d, n] = BasisValues[i, iNode, n] * OutwardTang[d]; // physical
//EvalResult[i, iNode, d, n] = BasisValues[iNode, n]*OutwardTang[d]; // reference
}
}
iNode++;
}
}
Debug.Assert(iNode == EvalResult.GetLength(1));
}
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) { // SaveIntegrationResults
for (int i = 0; i < Length; i++)
{
var ResPart = RHS.ExtractSubArrayShallow(new int[] { 0, 0, jSgrd }, new int[] { D - 1, N - 1, jSgrd - 1 });
int NoOfFaces = ResultsOfIntegration.GetLength(1);
for (int e = 0; e < NoOfFaces; e++)
{
var ip = ResultsOfIntegration.ExtractSubArrayShallow(new int[] { i, e, 0, 0 }, new int[] { i - 1, e - 1, D - 1, N - 1 });
ResPart.Acc(1.0, ip);
}
jSgrd++;
}
},
cs : CoordinateSystem.Physical);
qBnd.Execute();
var ret = RHS.ResizeShallow(N * D, _mask.NoOfItemsLocally);
return(ret);
}
MultidimensionalArray StokesAnsatzMatrix(Basis TestBasis, NodeSet surfaceNodes, int jCell)
{
int N = TestBasis.Length;
int NoOfNodes = surfaceNodes.GetLength(0);
int D = surfaceNodes.GetLength(1);
var GridDat = this.tracker.GridDat;
Debug.Assert(D == GridDat.SpatialDimension);
int iKref = GridDat.Cells.GetRefElementIndex(jCell);
var scalings = GridDat.Cells.JacobiDet;
int iLevSet = this.LevelSetIndex;
if (!GridDat.Cells.IsCellAffineLinear(jCell))
{
throw new NotSupportedException();
}
//var Phi = TestBasis.Evaluate(0); // reference
//var GradPhi = TestBasis.EvaluateGradient(0); // reference
var Phi = TestBasis.CellEval(surfaceNodes, jCell, 1).ExtractSubArrayShallow(0, -1, -1); // physical
var GradPhi = TestBasis.CellEvalGradient(surfaceNodes, jCell, 1).ExtractSubArrayShallow(0, -1, -1, -1); // physical
//var LevsetNormal = this.LsTrk.GetLevelSetReferenceNormals(iLevSet, 0, jCell, 1); // reference
//var Curvature = this.LsTrk.GetLevelSetReferenceCurvature(iLevSet, 0, jCell, 1); // reference
var LevsetNormal = this.LevelSetData.GetLevelSetNormals(surfaceNodes, jCell, 1).ExtractSubArrayShallow(0, -1, -1); // physical
var Curvature = MultidimensionalArray.Create(1, NoOfNodes); // physical
((LevelSet)(this.tracker.LevelSets[iLevSet])).EvaluateTotalCurvature(jCell, 1, surfaceNodes, Curvature); // physical
var Coeffs = MultidimensionalArray.Create(D, N, NoOfNodes);
if (D == 2)
{
for (int k = 0; k < NoOfNodes; k++) // loop over nodes
{
double Nx = LevsetNormal[k, 0];
double Ny = LevsetNormal[k, 1];
double kappa = Curvature[0, k];
double Prj_11 = 1.0 - Nx * Nx, Prj_12 = -Nx * Ny,
Prj_21 = -Ny * Nx, Prj_22 = 1.0 - Ny * Ny;
for (int n = 0; n < N; n++)
{
double Phi_kn = Phi[k, n];
double dPhi_dx_kn = GradPhi[k, n, 0];
double dPhi_dy_kn = GradPhi[k, n, 1];
Coeffs[0, n, k] = -Phi_kn * kappa * Nx + Prj_11 * dPhi_dx_kn + Prj_12 * dPhi_dy_kn;
Coeffs[1, n, k] = -Phi_kn * kappa * Ny + Prj_21 * dPhi_dx_kn + Prj_22 * dPhi_dy_kn;
}
}
}
else if (D == 3)
{
throw new NotImplementedException("to do.");
}
else
{
throw new NotSupportedException("Unknown spatial dimension.");
}
Coeffs.Scale(scalings[jCell]); // physical
return(Coeffs.ResizeShallow(N * D, NoOfNodes));
}
/// <summary>
/// computes derivatives in various ways and compares them against known values.
/// </summary>
protected override double RunSolverOneStep(int TimestepNo, double phystime, double dt)
{
base.EndTime = 0.0;
base.NoOfTimesteps = 0;
int D = this.GridData.SpatialDimension;
int J = this.GridData.iLogicalCells.NoOfLocalUpdatedCells;
Console.WriteLine("DerivativeTest.exe, test case #" + GRID_CASE + " ******************************");
//var Fix = this.GridData.iGeomEdges.FaceIndices;
//for(int iEdge = 0; iEdge < Fix.GetLength(0); iEdge++) {
// Debug.Assert(Fix[iEdge, 0] >= 0);
// Debug.Assert(Fix[iEdge, 1] >= 0);
//}
// sealing test
// =================
if (this.GridData is Foundation.Grid.Classic.GridData)
{
TestSealing(this.GridData);
}
// cell volume and edge area check, if possible
// ===============================================
if (this.CellVolume > 0)
{
double err = 0;
double Treshold = 1.0e-10;
for (int j = 0; j < J; j++)
{
err += Math.Abs(this.GridData.iLogicalCells.GetCellVolume(j) - this.CellVolume);
}
bool passed = (err < Treshold);
m_passed = m_passed && passed;
Console.WriteLine("Cell volume error: " + err + " passed? " + passed);
Console.WriteLine("--------------------------------------------");
}
if (this.EdgeArea > 0)
{
double err = 0;
double Treshold = 1.0e-10;
int E = this.GridData.iLogicalEdges.Count;
for (int e = 0; e < E; e++)
{
err += Math.Abs(this.GridData.iLogicalEdges.GetEdgeArea(e) - this.EdgeArea);
}
bool passed = (err < Treshold);
m_passed = m_passed && passed;
Console.WriteLine("Edge area error: " + err + " passed? " + passed);
Console.WriteLine("--------------------------------------------");
}
// Orthonormality of basis in physical coords
// ==========================================
{
Basis Bs = this.f1.Basis;
int N = Bs.Length;
int degQuad = this.GridData.iLogicalCells.GetInterpolationDegree(0) * D + Bs.Degree + 3;
int[] jG2jL = this.GridData.iGeomCells.GeomCell2LogicalCell;
// mass matrix: should be identity!
MultidimensionalArray MassMatrix = MultidimensionalArray.Create(J, N, N);
// compute mass matrix by quadrature.
var quad = CellQuadrature.GetQuadrature(new int[] { N, N }, base.GridData,
(new CellQuadratureScheme()).Compile(base.GridData, degQuad),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
NodeSet QuadNodes = QR.Nodes;
MultidimensionalArray BasisVals = Bs.CellEval(QuadNodes, i0, Length);
EvalResult.Multiply(1.0, BasisVals, BasisVals, 0.0, "jknm", "jkn", "jkm");
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
if (jG2jL != null)
{
for (int i = 0; i < Length; i++)
{
int jG = i + i0;
MassMatrix.ExtractSubArrayShallow(jG2jL[jG], -1, -1)
.Acc(1.0, ResultsOfIntegration.ExtractSubArrayShallow(i, -1, -1));
}
}
else
{
MassMatrix.SetSubArray(ResultsOfIntegration, new int[] { i0, 0, 0 }, new int[] { i0 + Length - 1, N - 1, N - 1 });
}
},
cs: CoordinateSystem.Physical);
quad.Execute();
// check that mass matrix is Id.
int MaxErrorCell = -1;
double MaxError = -1;
for (int j = 0; j < J; j++)
{
MultidimensionalArray MassMatrix_j = MassMatrix.ExtractSubArrayShallow(j, -1, -1);
MassMatrix_j.AccEye(-1.0);
double Norm_j = MassMatrix_j.InfNorm();
if (Norm_j > MaxError)
{
MaxError = Norm_j;
MaxErrorCell = j;
}
}
bool passed = (MaxError < 1.0e-8);
m_passed = m_passed && passed;
Console.WriteLine("Mass Matrix, maximum error in Cell #" + MaxErrorCell + ", mass matrix error norm: " + MaxError + " passed? " + passed);
}
// Broken Derivatives
// =================
double totalVolume = (new SubGrid(CellMask.GetFullMask(this.GridData))).Volume;
for (int d = 0; d < D; d++)
{
// compute
f1Gradient_Numerical[d].Clear();
f1Gradient_Numerical[d].Derivative(1.0, f1, d);
f2Gradient_Numerical[d].Clear();
f2Gradient_Numerical[d].Derivative(1.0, f2, d);
// subtract analytical
var Errfield1 = f1Gradient_Numerical[d].CloneAs();
Errfield1.Acc(-1, f1Gradient_Analytical[d]);
var Errfield2 = f2Gradient_Numerical[d].CloneAs();
Errfield2.Acc(-1, f2Gradient_Analytical[d]);
Console.WriteLine("Broken Derivatives: ");
double Treshold = 1.0e-10;
if (AltRefSol)
{
Treshold = 1.0e-4; // not exactly polynomial, therefore a higher threshold
}
double err1_dx = Errfield1.L2Norm() / totalVolume;
bool passed = (err1_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df1/dx{0}_Numerical - df1/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err1_dx, passed));
double err2_dx = Errfield2.L2Norm() / totalVolume;
passed = (err2_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df2/dx{0}_Numerical - df2/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err2_dx, passed));
Console.WriteLine("--------------------------------------------");
}
// Flux Derivatives
// =================
for (int d = 0; d < D; d++)
{
// compute
f1Gradient_Numerical[d].Clear();
f1Gradient_Numerical[d].DerivativeByFlux(1.0, f1, d);
f2Gradient_Numerical[d].Clear();
f2Gradient_Numerical[d].DerivativeByFlux(1.0, f2, d);
f1Gradient_Numerical[d].CheckForNanOrInf(true, true, true);
f2Gradient_Numerical[d].CheckForNanOrInf(true, true, true);
// subtract analytical
var Errfield1 = f1Gradient_Numerical[d].CloneAs();
Errfield1.Acc(-1, f1Gradient_Analytical[d]);
var Errfield2 = f2Gradient_Numerical[d].CloneAs();
Errfield2.Acc(-1, f2Gradient_Analytical[d]);
Console.WriteLine("Flux Derivatives: ");
double Treshold = 1.0e-10;
if (AltRefSol)
{
Treshold = 1.0e-4; // not exactly polynomial, therefore a higher threshold
}
double err1_dx = Errfield1.L2Norm() / totalVolume;
bool passed = (err1_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df1/dx{0}_Numerical - df1/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err1_dx, passed));
double err2_dx = Errfield2.L2Norm() / totalVolume;
passed = (err2_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df2/dx{0}_Numerical - df2/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err2_dx, passed));
Console.WriteLine("--------------------------------------------");
}
// Linear flux Derivatives
// =======================
for (int d = 0; d < D; d++)
{
double[] korrekto = f1Gradient_Numerical[d].CoordinateVector.ToArray();
// compute
DerivativeByFluxLinear(f1, f1Gradient_Numerical[d], d, f1);
DerivativeByFluxLinear(f2, f2Gradient_Numerical[d], d, f2);
// subtract analytical
var Errfield1 = f1Gradient_Numerical[d].CloneAs();
Errfield1.Acc(-1, f1Gradient_Analytical[d]);
var Errfield2 = f2Gradient_Numerical[d].CloneAs();
Errfield2.Acc(-1, f2Gradient_Analytical[d]);
Console.WriteLine("Linear Flux Derivatives: ");
double Treshold = 1.0e-10;
if (AltRefSol)
{
Treshold = 1.0e-4; // not exactly polynomial, therefore a higher threshold
}
double err1_dx = Errfield1.L2Norm() / totalVolume;
bool passed = (err1_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df1/dx{0}_Numerical - df1/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err1_dx, passed));
double err2_dx = Errfield2.L2Norm() / totalVolume;
passed = (err2_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df2/dx{0}_Numerical - df2/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err2_dx, passed));
Console.WriteLine("--------------------------------------------");
}
// Laplacian, nonlinear
// ====================
if (!AltRefSol)
{
var Laplace = (new ipLaplace()).Operator(1);
Laplace.Evaluate(new DGField[] { this.f1 }, new DGField[] { this.Laplace_f1_Numerical });
Laplace.Evaluate(new DGField[] { this.f2 }, new DGField[] { this.Laplace_f2_Numerical });
double Treshold = 1.0e-8;
// subtract analytical
var Errfield1 = Laplace_f1_Numerical.CloneAs();
Errfield1.Acc(-1, Laplace_f1_Analytical);
var Errfield2 = Laplace_f2_Numerical.CloneAs();
Errfield2.Acc(-1, Laplace_f2_Analytical);
double err_Lf1 = Errfield1.L2Norm() / totalVolume;
bool passed = (err_Lf1 < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| /\\f1 Numerical - /\\f1 Analytical ||_2 = {0} (nonlinear evaluation), passed? {1}", err_Lf1, passed));
double err_Lf2 = Errfield2.L2Norm() / totalVolume;
passed = (err_Lf2 < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| /\\f2 Numerical - /\\f2 Analytical ||_2 = {0} (nonlinear evaluation), passed? {1}", err_Lf2, passed));
Console.WriteLine("--------------------------------------------");
}
// Laplacian, linear
// ====================
if (!AltRefSol)
{
var Laplace = (new ipLaplace()).Operator(1);
var LaplaceMtx = new BlockMsrMatrix(this.f1.Mapping, this.Laplace_f1_Numerical.Mapping);
var LaplaceAffine = new double[LaplaceMtx.RowPartitioning.LocalLength];
Laplace.ComputeMatrix(this.f1.Mapping, null, this.Laplace_f1_Numerical.Mapping,
LaplaceMtx, LaplaceAffine, false);
this.Laplace_f1_Numerical.CoordinateVector.SetV(LaplaceAffine);
LaplaceMtx.SpMV(1.0, this.f1.CoordinateVector, 1.0, this.Laplace_f1_Numerical.CoordinateVector);
this.Laplace_f2_Numerical.CoordinateVector.SetV(LaplaceAffine);
LaplaceMtx.SpMV(1.0, this.f2.CoordinateVector, 1.0, this.Laplace_f2_Numerical.CoordinateVector);
// subtract analytical
var Errfield1 = Laplace_f1_Numerical.CloneAs();
Errfield1.Acc(-1, Laplace_f1_Analytical);
var Errfield2 = Laplace_f2_Numerical.CloneAs();
Errfield2.Acc(-1, Laplace_f2_Analytical);
double Treshold = 1.0e-8;
double err_Lf1 = Errfield1.L2Norm() / totalVolume;
bool passed = (err_Lf1 < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| /\\f1 Numerical - /\\f1 Analytical ||_2 = {0} (linear evaluation), passed? {1}", err_Lf1, passed));
double err_Lf2 = Errfield2.L2Norm() / totalVolume;
passed = (err_Lf2 < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| /\\f2 Numerical - /\\f2 Analytical ||_2 = {0} (linear evaluation), passed? {1}", err_Lf2, passed));
// comparison of finite difference Jacobian and Operator matrix
if (TestFDJacobian)
{
this.f1.Clear();
var FDJbuilder = Laplace.GetFDJacobianBuilder(this.f1.Mapping.Fields, null, this.f1.Mapping,
delegate(IEnumerable <DGField> U0, IEnumerable <DGField> Params) {
return;
});
var CheckMatrix = new BlockMsrMatrix(FDJbuilder.CodomainMapping, FDJbuilder.DomainMapping);
var CheckAffine = new double[FDJbuilder.CodomainMapping.LocalLength];
FDJbuilder.ComputeMatrix(CheckMatrix, CheckAffine);
var ErrMatrix = LaplaceMtx.CloneAs();
var ErrAffine = LaplaceAffine.CloneAs();
ErrMatrix.Acc(-1.0, CheckMatrix);
ErrAffine.AccV(-1.0, CheckAffine);
double LinfMtx = ErrMatrix.InfNorm();
double L2Aff = ErrAffine.L2NormPow2().MPISum().Sqrt();
bool passed1 = (LinfMtx < 1.0e-3);
bool passed2 = (L2Aff < Treshold);
Console.WriteLine("Finite Difference Jacobian: Matrix/Affine delta norm {0} {1}, passed? {2} {3}", LinfMtx, L2Aff, passed1, passed2);
m_passed = m_passed && passed1;
m_passed = m_passed && passed2;
}
Console.WriteLine("--------------------------------------------");
}
// finally...
// =================
if (m_passed)
{
Console.WriteLine("All tests passed. *****************************");
}
else
{
Console.WriteLine("Some error above threshold. *******************");
}
return(0.0); // return some artificial timestep
}
static internal void ComputeMassMatrixBlocks(
IEnumerable <SpeciesId> _SpeciesIds,
out Dictionary <SpeciesId, MassMatrixBlockContainer> Result,
Basis b,
XDGSpaceMetrics homie)
{
using (var tracer = new FuncTrace()) {
if (b is XDGBasis)
{
throw new ArgumentException();
}
var ctx = homie.GridDat;
Result = new Dictionary <SpeciesId, MassMatrixBlockContainer>();
var schemeHelper = homie.XQuadSchemeHelper;
int Nnx = b.Length;
int quadorder = homie.CutCellQuadOrder;
// define domains and allocate memory
// ==================================
foreach (var Species in _SpeciesIds) // loop over species...
// interation dom
{
var _IntegrationDomain = homie.LevelSetRegions.GetSpeciesMask(Species).Intersect(homie.LevelSetRegions.GetCutCellMask());
// domain for mass-matrix blocks (include agglomeration targets)
var _BlockDomain = _IntegrationDomain; //.Union(Agg.GetAgglomerator(Species).AggInfo.AllAffectedCells);
// alloc mem for blocks
var _MassMatrixBlocksSpc = MultidimensionalArray.Create(_BlockDomain.NoOfItemsLocally, Nnx, Nnx);
// Subgrid index to cell index
int[] _jSub2jCell = _BlockDomain.ItemEnum.ToArray();
// cell to subgrid index
//Dictionary<int, int> _jCell2jSub;
//if (Agg.GetAgglomerator(Species).AggInfo.AgglomerationPairs.Length > 0) {
// _jCell2jSub = new Dictionary<int, int>();
// for (int i = 0; i < _jSub2jCell.Length; i++) {
// _jCell2jSub.Add(_jSub2jCell[i], i);
// }
//} else {
// _jCell2jSub = null;
//}
Result.Add(Species, new MassMatrixBlockContainer()
{
IntegrationDomain = _IntegrationDomain,
MassMatrixBlocks = _MassMatrixBlocksSpc,
//jCell2jSub = _jCell2jSub,
jSub2jCell = _jSub2jCell
});
}
// compute blocks
// ==============
foreach (var Species in _SpeciesIds)
{
// get quad scheme
CellQuadratureScheme scheme = schemeHelper.GetVolumeQuadScheme(Species, IntegrationDomain: Result[Species].IntegrationDomain);
// result storage
var MassMatrixBlocksSpc = Result[Species].MassMatrixBlocks;
tracer.Info("mass matrix quad order: " + quadorder);
// compute the products of the basis functions:
int BlockCnt = -1;
int[] BlockCell = Result[Species].jSub2jCell;
CellMask speciesCells = homie.LevelSetRegions.GetSpeciesMask(Species);
CellQuadrature.GetQuadrature(
new int[] { Nnx, Nnx },
ctx,
scheme.Compile(ctx, quadorder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
// Del_Evaluate
// ~~~~~~~~~~~~~
var BasisVal = b.CellEval(QR.Nodes, i0, Length);
EvalResult.Multiply(1.0, BasisVal, BasisVal, 0.0, "ikmn", "ikm", "ikn");
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
// Del_SaveIntegrationResults
// ~~~~~~~~~~~~~~~~~~~~~~~~~~
for (int i = 0; i < Length; i++)
{
int jCell = i0 + i;
BlockCnt++;
// insert ID block in agglomeration target cells (if necessary):
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
var Block = MassMatrixBlocksSpc.ExtractSubArrayShallow(BlockCnt, -1, -1);
while (BlockCell[BlockCnt] < jCell)
{
// agglomeration source/target cell that is not cut
// mass matrix is identity (full) or zero (void)
Block.Clear();
if (speciesCells.Contains(BlockCell[BlockCnt]))
{
// cell is full
for (int nn = 0; nn < Nnx; nn++)
{
Block[nn, nn] = 1.0;
}
}
BlockCnt++;
Block = MassMatrixBlocksSpc.ExtractSubArrayShallow(BlockCnt, -1, -1);
}
// store computed block
// - - - - - - - - - - -
Debug.Assert(BlockCell[BlockCnt] == jCell);
MassMatrixBlocksSpc.ExtractSubArrayShallow(BlockCnt, -1, -1)
.Set(ResultsOfIntegration.ExtractSubArrayShallow(i, -1, -1));
#if DEBUG
for (int n = 0; n < Nnx; n++)
{
for (int m = 0; m < Nnx; m++)
{
Debug.Assert(Block[n, m] == Block[m, n]);
}
}
#endif
}
}).Execute();
// ------------------------------------ quadrature end.
BlockCnt++;
while (BlockCnt < MassMatrixBlocksSpc.GetLength(0))
{
// agglomeration source/target cell that is not cut
// mass matrix is identity (full) or zero (void)
var Block = MassMatrixBlocksSpc.ExtractSubArrayShallow(BlockCnt, -1, -1);
Block.Clear();
if (speciesCells.Contains(BlockCell[BlockCnt]))
{
// cell is full
for (int nn = 0; nn < Nnx; nn++)
{
Block[nn, nn] = 1.0;
}
}
BlockCnt++;
}
/*
* // test mass matrix for positive definiteness
* {
* int JSUB = MassMatrixBlocksSpc.GetLength(0);
* SubGrid Idom = null;
*
* int failCount = 0;
* var PosDefiniteTest = new FullMatrix(Nnx, Nnx);
*
* for (int jsub = 0; jsub < JSUB; jsub++) {
* PosDefiniteTest.Clear();
* PosDefiniteTest.Acc(MassMatrixBlocksSpc.ExtractSubArrayShallow(jsub, -1, -1), 1.0);
*
* try {
* PosDefiniteTest.Clear();
* PosDefiniteTest.Acc(MassMatrixBlocksSpc.ExtractSubArrayShallow(jsub, -1, -1), 1.0);
* PosDefiniteTest.InvertSymmetrical();
*
* //PosDefiniteTest.Clear();
* //PosDefiniteTest.AccEye(1.0);
* //PosDefiniteTest.Acc(MassMatrixBlocksSpc.ExtractSubArrayShallow(jsub, -1, -1), -1.0);
* //PosDefiniteTest.InvertSymmetrical();
* } catch (ArithmeticException ae) {
* if (Idom == null)
* Idom = new SubGrid(scheme.Domain);
*
* int jCell = Idom.SubgridIndex2LocalCellIndex[jsub];
* long Gid = Tracker.GridDat.Cells.GetCell(jCell).GlobalID;
*
*
* double volFrac = Tracker.GetSpeciesVolume(jCell, Species)/ctx.Cells.GetCellVolume(jCell);
*
* var errString = string.Format("Indefinite mass matrix in cell: globalId = {0}, local index = {1}, species {2}; \n cell volume fraction: {3};\n [{4}]", Gid, jCell, Tracker.GetSpeciesName(Species), volFrac, ae.Message);
* tracer.Logger.Error(errString);
* //Console.WriteLine(errString);
* failCount++;
* }
* }
*
* if (failCount > 0) {
* var errString = string.Format("Indefinite mass matrix in {0} of {1} cut cells", failCount, JSUB);
* tracer.Logger.Error(errString);
* Console.WriteLine(errString);
* } else {
* Console.WriteLine("No indefinite mass matrix blocks");
* }
*
* }
* // */
// backup before agglomeration (required if we wanna treat e.g. velocity in DG and pressure in XDG)
//MultidimensionalArray[] massMatrixBlocksB4Agglom = new MultidimensionalArray[Result[Species].jSub2jCell.Length];
//Result[Species].MassMatrixBlocks_B4Agglom = massMatrixBlocksB4Agglom;
//var _jCell2jSub = Result[Species].jCell2jSub;
//int J = ctx.Cells.NoOfLocalUpdatedCells;
//foreach (var pair in Agg.GetAgglomerator(Species).AggInfo.AgglomerationPairs) {
// foreach (int jCell in new int[] { pair.jCellSource, pair.jCellTarget }) { // create a backup of source and target cell
// if (jCell >= J)
// continue;
// int jSub = _jCell2jSub[jCell];
// if (massMatrixBlocksB4Agglom[jSub] == null) {
// massMatrixBlocksB4Agglom[jSub] = MassMatrixBlocksSpc.ExtractSubArrayShallow(jSub, -1, -1).CloneAs();
// }
// }
//}
// agglomeration
//Agg.GetAgglomerator(Species).ManipulateMassMatrixBlocks(MassMatrixBlocksSpc, b, Result[Species].jSub2jCell, Result[Species].jCell2jSub);
//throw new NotImplementedException("todo");
}
}
}
