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);
}
/// <summary>
/// Compares the cell surface and the boundary integral.
/// </summary>
public static void TestSealing(IGridData gdat)
{
int J = gdat.iLogicalCells.NoOfLocalUpdatedCells;
int[,] E2Clog = gdat.iGeomEdges.LogicalCellIndices;
//
// compute cell surface via edge integrals
//
MultidimensionalArray CellSurf1 = MultidimensionalArray.Create(J);
EdgeQuadrature.GetQuadrature(new int[] { 1 },
gdat, new EdgeQuadratureScheme().Compile(gdat, 2),
delegate(int i0, int Length, QuadRule rule, MultidimensionalArray EvalResult) { // evaluate
EvalResult.SetAll(1.0);
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) { // save results
for (int i = 0; i < Length; i++)
{
int iEdge = i + i0;
int jCellIn = E2Clog[iEdge, 0];
int jCellOt = E2Clog[iEdge, 1];
CellSurf1[jCellIn] += ResultsOfIntegration[i, 0];
if (jCellOt >= 0 && jCellOt < J)
{
CellSurf1[jCellOt] += ResultsOfIntegration[i, 0];
}
}
}).Execute();
//
// compute cell surface via cell boundary integrals
//
var cbqs = new CellBoundaryQuadratureScheme(false, null);
foreach (var Kref in gdat.iGeomCells.RefElements)
{
cbqs.AddFactory(new StandardCellBoundaryQuadRuleFactory(Kref));
}
MultidimensionalArray CellSurf2 = MultidimensionalArray.Create(J);
CellBoundaryQuadrature <CellBoundaryQuadRule> .GetQuadrature(new int[] { 1 },
gdat, cbqs.Compile(gdat, 2),
delegate(int i0, int Length, CellBoundaryQuadRule rule, MultidimensionalArray EvalResult) { // evaluate
EvalResult.SetAll(1.0);
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) { // save results
int NoOfFaces = ResultsOfIntegration.GetLength(1);
for (int i = 0; i < Length; i++)
{
int jCell = i + i0;
for (int iFace = 0; iFace < NoOfFaces; iFace++)
{
CellSurf2[jCell] += ResultsOfIntegration[i, iFace, 0];
}
}
}, cs : CoordinateSystem.Physical).Execute();
//
// compare
//
MultidimensionalArray Err = CellSurf1.CloneAs();
Err.Acc(-1.0, CellSurf2);
double ErrNorm = Err.L2Norm();
double TotSurf = CellSurf1.L2Norm();
Console.WriteLine("Area Check " + Err.L2Norm());
Assert.LessOrEqual(ErrNorm / TotSurf, 1.0e-8);
//for (int j = 0; j < J; j++) {
// if (Err[j].Abs() >= 1.0e-6) {
// Console.WriteLine("Mismatch between edge area and cell surface area in cell {0}, GlobalId {1}, No. of neighbors {3}, {2:0.####E-00}", j, gdat.CurrentGlobalIdPermutation.Values[j], Err[j], gdat.Cells.CellNeighbours[j].Length);
// schas.SetMeanValue(j, 1);
// }
//}
}
protected MultidimensionalArray GaußAnsatzRHS(DivergenceFreeBasis TestBasis, CellBoundaryQuadratureScheme cellBndScheme, CellMask _mask, int order)
{
var _Context = this.tracker.GridDat;
int D = this.tracker.GridDat.Grid.SpatialDimension;
int N = TestBasis.Count;
var coordSys = CoordinateSystem.Reference;
var LsTrk = this.tracker;
int Nrhs = _mask.NoOfItemsLocally;
Debug.Assert(N % D == 0);
N /= D;
MultidimensionalArray RHS = MultidimensionalArray.Create(N, Nrhs);
var splx = this.Kref;
int NoOfFaces = splx.NoOfFaces;
//var normals = _Context.GridDat.Normals;
CellBoundaryQuadrature <CellBoundaryQuadRule> qBnd = null;
int jSgrd = 0;
qBnd = CellBoundaryQuadrature <CellBoundaryQuadRule> .GetQuadrature(new int[] { N },
_Context, cellBndScheme.Compile(_Context, order),
delegate(int i0, int Length, CellBoundaryQuadRule QR, MultidimensionalArray EvalResult) { // Evaluate
NodeSet Nodes = QR.Nodes;
MultidimensionalArray BasisValues;
if (coordSys == CoordinateSystem.Physical)
{
//BasisValues = TestBasis.CellEval(Nodes, i0, Length);
throw new NotImplementedException("todo");
}
else if (coordSys == CoordinateSystem.Reference)
{
BasisValues = TestBasis.Values.GetValues(Nodes);
}
else
{
throw new NotImplementedException();
}
for (int i = 0; i < Length; i++) // loop over cells
{
CellBoundaryQuadRule cR = qBnd.CurrentRule;
int[] NodesPerEdge = cR.NumbersOfNodesPerFace;
Debug.Assert(object.ReferenceEquals(splx, cR.RefElement));
int iNode = 0;
Debug.Assert(NoOfFaces == NodesPerEdge.Length);
for (int e = 0; e < NoOfFaces; e++) // loop over the faces of the cell
{
for (int _n = 0; _n < NodesPerEdge[e]; _n++) // loop over nodes in one edge
{
for (int n = 0; n < N; n++) // loop over Test polynomials (the same as the basis polynomials)
{
double acc = 0;
for (int d = 0; d < D; d++) // loop over spatial directions
{
if (coordSys == CoordinateSystem.Physical)
{
throw new NotImplementedException("todo");
//int q = _Context.GridDat.LocalCellIndexToEdges[i+i0, e];
//int iEdge = Math.Abs(q) - 1;
//double Nsign = Math.Sign(q);
//double Nd = normals[iEdge, d];
//EvalResult[i, iNode, n, d] = BasisValues[i, iNode, n]*Nd*Nsign;
}
else
{
Debug.Assert(coordSys == CoordinateSystem.Reference);
double Nd = splx.FaceNormals[e, d];
//Debug.Assert(Nd == normals[iEdge, d]*Nsign);
acc += BasisValues[iNode, n *D + d] * Nd;
}
}
EvalResult[i, iNode, n] = acc;
}
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, jSgrd }, new int[] { N - 1, jSgrd - 1 });
for (int e = 0; e < NoOfFaces; e++)
{
var ip = ResultsOfIntegration.ExtractSubArrayShallow(new int[] { i, e, 0 }, new int[] { i - 1, e - 1, N - 1 });
ResPart.Acc(1.0, ip);
}
jSgrd++;
}
},
cs : coordSys);
qBnd.Execute();
return(RHS);
}
void SpecialProjection(LevelSetTracker LsTrk, int order, DGField[] Uin, VectorField <SinglePhaseField> Uout)
{
var CC = LsTrk.Regions.GetCutCellMask();
var gDat = LsTrk.GridDat;
// get quadrature rules
// ====================
//XQuadSchemeHelper H = new XQuadSchemeHelper(LsTrk, MomentFittingVariant);
var H = LsTrk.GetXDGSpaceMetrics(new[] { LsTrk.GetSpeciesId("A") }, order, 1).XQuadSchemeHelper;
CellQuadratureScheme cqs = H.GetLevelSetquadScheme(0, CC);
ICompositeQuadRule <QuadRule> surfRule = cqs.Compile(gDat, order);
ICompositeQuadRule <CellBoundaryQuadRule> bndyRule = (new CellBoundaryQuadratureScheme(true, CC)).Compile(gDat, order);
// Compute Mass matrix and RHS for the 'strange' projection
// ========================================================
int L = CC.NoOfItemsLocally;
var Q = new QuadratureKernels(Uin, L);
Q.BlockCnt = 0;
CellQuadrature.GetQuadrature(
new int[] { Q.Nnx + Q.D, Q.Nnx },
gDat,
surfRule,
Q.Evaluate, Q.SaveIntegrationResults_surf).Execute();
Debug.Assert(Q.BlockCnt == L);
Q.BlockCnt = 0;
CellBoundaryQuadrature <CellBoundaryQuadRule> .GetQuadrature(
new int[] { Q.Nnx + Q.D, Q.Nnx },
gDat,
bndyRule,
Q.Evaluate, Q.SaveIntegrationResults_bndy).Execute();
Debug.Assert(Q.BlockCnt == L);
// solve the non-diagonal mass matrix systems
// ==========================================
int BlkCnt = 0;
foreach (int jCell in CC.ItemEnum)
{
var MassMatrix = Q.MassMatrix.ExtractSubArrayShallow(BlkCnt, -1, -1);
var RHS = Q.RHS.ExtractSubArrayShallow(BlkCnt, -1, -1);
// Die "Massenmatrix" muss nicht unbedingt invbar sein, daher: Least-Squares solve
MassMatrix.LeastSquareSolve(RHS);
for (int d = 0; d < Q.D; d++)
{
for (int n = 0; n < Q.Nnx; n++)
{
Uout[d].Coordinates[jCell, n] = RHS[n, d];
}
}
BlkCnt++;
}
}