/// <summary> /// Constructs a quad rule factory using the given subdivision /// strategy. /// </summary> /// <param name="subdivisionStrategy"> /// <see cref="SubdivisionStrategy"/> /// </param> /// <param name="leafDivisions"> /// The additional number of subdivisions for the quadrature rule to be /// used in cut leaves (see <see cref="SubdivisionNode.IsCut"/>). /// </param> public CutCellQuadRuleFactory(ISubdivisionStrategy subdivisionStrategy, int leafDivisions) { SubdivisionStrategy = subdivisionStrategy; if (leafDivisions >= 0) { cutNodeRule = RefElement.GetBruteForceQuadRule(leafDivisions, 1); } }
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); } } }