protected MultidimensionalArray GaußAnsatzMatrix(DivergenceFreeBasis TestBasis, NodeSet SurfQrNodes, int jCell)
{
int N = TestBasis.Count;
int D = this.tracker.GridDat.Grid.SpatialDimension;
Debug.Assert(N % D == 0);
N /= D;
int ksurf = SurfQrNodes.GetLength(0);
Debug.Assert(SurfQrNodes.Dimension == 2);
Debug.Assert(SurfQrNodes.GetLength(1) == D);
int iKref = this.tracker.GridDat.Cells.GetRefElementIndex(jCell);
MultidimensionalArray EdgMatrix = MultidimensionalArray.Create(N, ksurf);
// evaluate Basis and Gradient of Basis
var Phi = TestBasis.Values.GetValues(SurfQrNodes); // test function, n
var LevelSetNormals = this.LevelSetData.GetLevelSetReferenceNormals(SurfQrNodes, jCell, 1).ExtractSubArrayShallow(0, -1, -1);
//metrics = tracker.GetLevelSetNormalReferenceToPhysicalMetrics(this.LevelSetIndex, 0, jCell, 1);
// multiply
for (int k = 0; k < ksurf; k++) // loop over nodes...
{
for (int n = 0; n < N; n++) // loop over basis polynomials...
{
double acc = 0.0;
for (int d = 0; d < D; d++) // loop over spatial dimension...
{
acc += Phi[k, n *D + d] * LevelSetNormals[k, d];
}
EdgMatrix[n, k] = acc;
}
}
// resize and return:
return(EdgMatrix);
}
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 GetQuadRuleSet_Internal(int order)
{
using (new FuncTrace()) {
int original_order = order;
stpwGetQuadRuleSet.Start();
order = Math.Max(order, 2); // Ansatz won't work below 2!
int D = this.tracker.GridDat.SpatialDimension;;
// check arguments, init
// =====================
CellMask _mask = this.MaxGrid;
// subgrid on which the volume rule should be constructed
// ======================================================
CellBoundaryQuadratureScheme cellBndSchme = new CellBoundaryQuadratureScheme(this.cellFaceFactory, _mask);
CellBoundaryQuadratureScheme cellBndLineSchme = null;
if (this.UseStokes)
{
cellBndLineSchme = new CellBoundaryQuadratureScheme(this.LevelSetBoundaryLineFactory, _mask);
}
// set up
// ======
int NoOfEqTotal, NoOfStokesEq, NoOfGaußEq;
DivergenceFreeBasis DivFreeBasis = this.UseGauß ? new DivergenceFreeBasis(tracker.GridDat, this.Kref, order + 1) : null;
Basis ScalarBasis = this.UseStokes ? new Basis(this.tracker.GridDat, order + 1) : null; // we loose a order of 1 for the volume rule due to the divergence operator
NoOfGaußEq = DivFreeBasis != null ? (DivFreeBasis.Count / D) : 0;
NoOfStokesEq = (ScalarBasis != null ? ScalarBasis.Length : 0) * D;
NoOfEqTotal = NoOfGaußEq + NoOfStokesEq;
// define Nodes
// ============
NodeSet NodeSet = null;
{
if (this.Kref.GetType() == typeof(Square))
{
int K = (int)Math.Ceiling(Math.Sqrt(NoOfEqTotal * 1.7)) + 1;
var Nodes1D = GenericBlas.Linspace(-1, 1, K);
var _NodeSet = MultidimensionalArray.Create(K * K, 2);
int n = 0;
for (int i = 0; i < K /*&& n <= NoOfEq*1.1*/; i++)
{
for (int j = 0; j < K /*&& n <= NoOfEq*1.1*/; j++)
{
_NodeSet[n, 0] = Nodes1D[i];
_NodeSet[n, 1] = Nodes1D[j];
n++;
}
}
NodeSet = new NodeSet(this.Kref, _NodeSet);
}
else
{
for (int o = 1; o < 1000000; o++)
{
var qr = Kref.GetBruteForceQuadRule(o, 0);
if (qr.NoOfNodes >= (NoOfEqTotal * 1.1))
{
NodeSet = qr.Nodes;
break;
}
}
}
}
int NoOfNodes = NodeSet.GetLength(0);
// find RHS integrals
// ==================
MultidimensionalArray RHS_Gauß = null;
if (this.UseGauß)
{
stpwGetQuadRuleSet_GaussRHS.Start();
RHS_Gauß = this.GaußAnsatzRHS(DivFreeBasis, cellBndSchme, _mask, order);
stpwGetQuadRuleSet_GaussRHS.Stop();
Debug.Assert(RHS_Gauß.Dimension == 2);
Debug.Assert(RHS_Gauß.GetLength(0) == NoOfGaußEq);
Debug.Assert(RHS_Gauß.GetLength(1) == _mask.NoOfItemsLocally);
}
MultidimensionalArray RHS_Stokes = null;
if (this.UseStokes)
{
stpwGetQuadRuleSet_StokesRHS.Start();
RHS_Stokes = this.StokesAnsatzRHS(ScalarBasis, cellBndLineSchme, _mask, order);
stpwGetQuadRuleSet_StokesRHS.Stop();
Debug.Assert(RHS_Stokes.Dimension == 2);
Debug.Assert(RHS_Stokes.GetLength(0) == NoOfStokesEq);
Debug.Assert(RHS_Stokes.GetLength(1) == _mask.NoOfItemsLocally);
}
// construct da rule!
// ==================
ChunkRulePair <QuadRule>[] SurfaceRule;
{
SurfaceRule = new ChunkRulePair <QuadRule> [_mask.NoOfItemsLocally];
var grddat = this.tracker.GridDat;
// loop over cells in subgrid...
int jSub = 0;
foreach (int jCell in _mask.ItemEnum) // loop over cells in the mask
// setup System
// ============
{
NodeSet surfNodes;
if (this.SurfaceNodesOnZeroLevset)
{
surfNodes = ProjectOntoLevset(jCell, NodeSet);
}
else
{
surfNodes = NodeSet;
}
MultidimensionalArray metrics;
{
int iKref = grddat.Cells.GetRefElementIndex(jCell);
metrics = LevelSetData.GetLevelSetNormalReferenceToPhysicalMetrics(surfNodes, jCell, 1);
}
MultidimensionalArray Mtx_Gauss = null;
if (this.UseGauß)
{
Mtx_Gauss = GaußAnsatzMatrix(DivFreeBasis, surfNodes, jCell);
Debug.Assert(Mtx_Gauss.Dimension == 2);
Debug.Assert(Mtx_Gauss.GetLength(0) == NoOfGaußEq);
Debug.Assert(Mtx_Gauss.GetLength(1) == NoOfNodes);
}
MultidimensionalArray Mtx_Stokes = null;
if (this.UseStokes)
{
Mtx_Stokes = this.StokesAnsatzMatrix(ScalarBasis, surfNodes, jCell);
Debug.Assert(Mtx_Stokes.Dimension == 2);
Debug.Assert(Mtx_Stokes.GetLength(0) == NoOfStokesEq);
Debug.Assert(Mtx_Stokes.GetLength(1) == NoOfNodes);
for (int i = 0; i < NoOfStokesEq; i++)
{
for (int j = 0; j < NoOfNodes; j++)
{
Mtx_Stokes[i, j] /= metrics[0, j];
}
}
}
stpwGetQuadRuleSet_SolveRHS.Start();
// convert to FORTRAN order
MultidimensionalArray _Mtx = MultidimensionalArray.Create(NoOfEqTotal, NoOfNodes);
if (this.UseGauß)
{
_Mtx.ExtractSubArrayShallow(new int[] { 0, 0 }, new int[] { NoOfGaußEq - 1, NoOfNodes - 1 }).Set(Mtx_Gauss);
}
if (this.UseStokes)
{
_Mtx.ExtractSubArrayShallow(new int[] { NoOfGaußEq, 0 }, new int[] { NoOfStokesEq + NoOfGaußEq - 1, NoOfNodes - 1 }).Set(Mtx_Stokes);
}
// convert to FORTRAN order
Debug.Assert(NoOfNodes >= NoOfEqTotal);
MultidimensionalArray _RHS = MultidimensionalArray.Create(NoOfNodes, 1); // this is also output, so it must be larger!
{
for (int i = 0; i < NoOfGaußEq; i++)
{
_RHS[i, 0] = RHS_Gauß[i, jSub];
}
for (int i = 0; i < NoOfStokesEq; i++)
{
_RHS[i + NoOfGaußEq, 0] = RHS_Stokes[i, jSub];
}
}
MultidimensionalArray __RHS = null, __Mtx = null;
if (this.Docheck)
{
// values used for testing:
__RHS = MultidimensionalArray.Create(NoOfEqTotal);
for (int i = 0; i < NoOfEqTotal; i++)
{
__RHS[i] = _RHS[i, 0];
}
__Mtx = MultidimensionalArray.Create(_Mtx.NoOfRows, _Mtx.NoOfCols);
__Mtx.SetMatrix(_Mtx);
}
// solve system
// ============
//int M = _Mtx.NoOfRows;
//int N = _Mtx.NoOfCols;
//LAPACK.F77_LAPACK.DGELSY(M, N, _Mtx.Entries, _RHS.Entries, 1, 1.0e-14);
_Mtx.LeastSquareSolve(_RHS);
if (this.Docheck)
{
// Probe:
MultidimensionalArray X = MultidimensionalArray.Create(NoOfNodes); // weights
X.ResizeShallow(NoOfNodes, 1).SetMatrix(_RHS);
__RHS.Multiply(-1.0, __Mtx, X, 1.0, "j", "jk", "k");
double L2_ERR = __RHS.L2Norm();
if (L2_ERR > 1.0e-7)
{
throw new ApplicationException("Quadrature rule in cell " + jCell + " seems to be not very precise: L2_ERR = " + L2_ERR);
}
//Debug.Assert(L2_ERR < 1.0e-8, "Quadrature rule in cell " + jCell + " seems to be not very precise: L2_ERR = " + L2_ERR);
//if (L2_ERR > 1.0e-9)
// Console.WriteLine("Warning: Quadrature rule in cell " + jCell + ": L2_ERR = " + L2_ERR);
}
stpwGetQuadRuleSet_SolveRHS.Stop();
// return da rule!
// ===============
{
{
// the surface rule
// ----------------
QuadRule qr_l = new QuadRule()
{
OrderOfPrecision = order,
Weights = MultidimensionalArray.Create(NoOfNodes),
Nodes = surfNodes
};
for (int k = 0; k < NoOfNodes; k++)
{
qr_l.Weights[k] = _RHS[k, 0] / metrics[0, k];
}
SurfaceRule[jSub] = new ChunkRulePair <QuadRule>(Chunk.GetSingleElementChunk(jCell), qr_l);
}
}
jSub++;
}
}
stpwGetQuadRuleSet.Stop();
if (!this.m_SurfaceRules.ContainsKey(original_order))
{
this.m_SurfaceRules.Add(original_order, SurfaceRule);
}
}
}
