/// <summary>
/// <see cref="Quadrature{U,V}.CreateNodeSetFamily"/>
/// </summary>
/// <param name="NoOfItems"></param>
/// <param name="rule"></param>
protected override void AllocateBuffers(int NoOfItems, NodeSet rule)
{
base.AllocateBuffers(NoOfItems, rule);
int NoOfNodes = rule.GetLength(0);
int D = m_phi.GridDat.SpatialDimension;
m_gradPhi.Allocate(NoOfItems, NoOfNodes, D);
}
protected override void AllocateBuffers(int NoOfItems, NodeSet rule)
{
base.AllocateBuffers(NoOfItems, rule);
int NoOfNodes = rule.GetLength(0);
if (m_func != null || m_Map != null)
{
m_NodesTransformed.Allocate(new int[] { NoOfItems, NoOfNodes, GridDat.SpatialDimension });
}
}
/// <summary>
/// Evaluates the modified integrand which is
/// \f$
/// \vec{g} = g \frac{\nabla \Phi}{|\nabla \Phi|}
/// \f$
/// where g represents <see cref="m_Field"/>.
/// </summary>
/// <param name="j0">
/// <see cref="LevelSetIntegrator.EvaluateIntegrand"/>
/// </param>
/// <param name="Length">
/// <see cref="LevelSetIntegrator.EvaluateIntegrand"/>
/// </param>
/// <param name="EvalResult">
/// <see cref="LevelSetIntegrator.EvaluateIntegrand"/>
/// </param>
public override void EvaluateIntegrand(NodeSet N, int j0, int Length, MultidimensionalArray EvalResult)
{
using (new FuncTrace()) {
int D = base.m_LevSetTrk.GridDat.SpatialDimension; // spatial dimension
int noOfNodes = EvalResult.GetLength(1); // number of nodes
if (m_LevelSetGradientBuffer.GetLength(0) != Length || m_LevelSetGradientBuffer.GetLength(1) != noOfNodes)
{
m_IntegrandBuffer.Allocate(Length, noOfNodes);
m_LevelSetGradientBuffer.Allocate(Length, noOfNodes, D);
}
m_Field.Evaluate(j0, Length, N, m_IntegrandBuffer, 0.0);
m_levSet.EvaluateGradient(j0, Length, N, m_LevelSetGradientBuffer);
for (int i = 0; i < Length; i++)
{
for (int j = 0; j < noOfNodes; j++)
{
double AbsGradPhi = 0;
for (int d = 0; d < D; d++)
{
double GradPhi_d = m_LevelSetGradientBuffer[i, j, d];
AbsGradPhi += GradPhi_d * GradPhi_d;
}
AbsGradPhi = Math.Sqrt(AbsGradPhi);
double ooAbsGradPhi = 1.0 / AbsGradPhi;
for (int d = 0; d < D; d++)
{
EvalResult[i, j, 0, d] = ooAbsGradPhi * m_LevelSetGradientBuffer[i, j, d] * m_IntegrandBuffer[i, j];
}
}
}
}
}
/// <summary>
/// Ctr
/// </summary>
public PlanarFourierLevSet(FourierLevSetControl Control) : base(Control)
{
setProjectingFourierModes();
// set the material sample points
current_interfaceP = new MultidimensionalArray(2);
current_interfaceP.Allocate(numFp, 2);
for (int sp = 0; sp < numFp; sp++)
{
current_interfaceP[sp, 0] = FourierP[sp];
current_interfaceP[sp, 1] = current_samplP[sp];
}
setInterfaceLength(current_interfaceP);
InterfaceResolution = interfaceLength / numFp;
}
protected override SayeQuadRule BuildSurfaceQuadRule(MultidimensionalArray X, double X_weight, int heightDirection, int cell)
{
double weight = X_weight;
NodeSet node = new NodeSet(RefElement, X.To2DArray());
MultidimensionalArray gradient = lsData.GetLevelSetGradients(node, cell, 1);
gradient = gradient.ExtractSubArrayShallow(new int[] { 0, 0, -1 });
MultidimensionalArray jacobian = grid.Jacobian.GetValue_Cell(node, cell, 1).ExtractSubArrayShallow(0, 0, -1, -1);
//Scale weight
weight *= gradient.L2Norm() / Math.Abs(gradient[heightDirection]);
weight /= jacobian[heightDirection, heightDirection];
MultidimensionalArray weightArr = new MultidimensionalArray(1);
weightArr.Allocate(1);
weightArr[0] = weight;
return(new SayeQuadRule(node, weightArr));
}
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");
}
}
/// <summary>
///
/// </summary>
/// <param name="ctrl"></param>
public PolarFourierLevSet(FourierLevSetControl ctrl) : base(ctrl)
{
this.DomainSize = 2 * Math.PI;
this.center = new MultidimensionalArray(2);
this.center.Allocate(1, 2);
this.center[0, 0] = ctrl.center[0];
this.center[0, 1] = ctrl.center[1];
this.CenterMove = ctrl.centerMove;
this.LevSetForm = ctrl.PLevSetForm;
this.curvComp_extended = ctrl.curvComp_extended;
// set material polar coordinates
interfaceP_polar = new MultidimensionalArray(2);
interfaceP_polar.Allocate(numFp, 2);
for (int sp = 0; sp < numFp; sp++)
{
interfaceP_polar[sp, 0] = FourierP[sp];
interfaceP_polar[sp, 1] = current_samplP[sp];
}
setProjectingFourierModes();
// set the material sample points (cartesian)
current_interfaceP = new MultidimensionalArray(2);
current_interfaceP.Allocate(numFp, 2);
for (int sp = 0; sp < numFp; sp++)
{
current_interfaceP[sp, 0] = center[0, 0] + (interfaceP_polar[sp, 1] * Math.Cos(interfaceP_polar[sp, 0]));
current_interfaceP[sp, 1] = center[0, 1] + (interfaceP_polar[sp, 1] * Math.Sin(interfaceP_polar[sp, 0]));
}
setInterfaceLength(current_interfaceP);
InterfaceResolution = interfaceLength / numFp;
}
void ExtractMatrices()
{
// dispose old solver, if required
// ===============================
if (this.m_PressureSolver != null)
{
this.m_PressureSolver.Dispose();
this.m_PressureSolver = null;
}
// sub-matrices for the Potential Solver
// =====================================
int VelocityLength = this.USubMatrixIdx_Row.Length;
int PressureLength = this.PSubMatrixIdx_Row.Length;
this.PressureGrad = new MsrMatrix(VelocityLength, PressureLength, 1, 1);
this.VelocityDiv = new MsrMatrix(PressureLength, VelocityLength, 1, 1);
this.Stab = new MsrMatrix(PressureLength, PressureLength, 1, 1);
var WholeSystemMatrix = this.m_MgOp.OperatorMatrix;
WholeSystemMatrix.WriteSubMatrixTo(PressureGrad, USubMatrixIdx_Row, default(int[]), PSubMatrixIdx_Row, default(int[]));
WholeSystemMatrix.WriteSubMatrixTo(VelocityDiv, PSubMatrixIdx_Row, default(int[]), USubMatrixIdx_Row, default(int[]));
WholeSystemMatrix.WriteSubMatrixTo(Stab, PSubMatrixIdx_Row, default(int[]), PSubMatrixIdx_Row, default(int[]));
// inverse mass matrix
// ===================
if (this.m_SIMPLEOptions.PotentialSolver_UseMassMatrix)
{
// extract the mass-matrix block for the velocity part
// ---------------------------------------------------
MsrMatrix MM = new MsrMatrix(this.PressureGrad.RowPartitioning, this.VelocityDiv.ColPartition);
this.m_MgOp.MassMatrix.WriteSubMatrixTo(MM, this.USubMatrixIdx_Row, default(int[]), this.USubMatrixIdx_Row, default(int[]));
// invert mass matrix
// ------------------
int D = this.LsTrk.GridDat.SpatialDimension;
this.invMM = new MsrMatrix(MM.RowPartitioning, MM.ColPartition);
MultidimensionalArray Block = new MultidimensionalArray(2);
MultidimensionalArray InvBlock = new MultidimensionalArray(2);
int iRow0 = MM.RowPartitioning.i0;
int JAGG = this.m_MgOp.Mapping.AggGrid.iLogicalCells.NoOfLocalUpdatedCells;
int[] DegreeS = this.m_MgOp.Mapping.DgDegree;
for (int jagg = 0; jagg < JAGG; jagg++) // loop over aggregate cells...
{
for (int d = 0; d < D; d++) // loop over velocity components...
{
int N = this.m_MgOp.Mapping.AggBasis[d].GetLength(jagg, DegreeS[d]);
if (Block.GetLength(0) != N)
{
Block.Allocate(N, N);
InvBlock.Allocate(N, N);
}
for (int n = 0; n < N; n++)
{
CheckMatrix(MM, iRow0, N, iRow0 + n);
for (int m = 0; m < N; m++)
{
Block[n, m] = MM[iRow0 + n, iRow0 + m];
}
}
Block.InvertTo(InvBlock);
for (int n = 0; n < N; n++)
{
for (int m = 0; m < N; m++)
{
this.invMM[iRow0 + n, iRow0 + m] = InvBlock[n, m];
}
}
iRow0 += N;
}
}
Debug.Assert(iRow0 == MM.RowPartitioning.iE);
#if DEBUG
var CheckMX = MM * invMM;
double TRESH = Math.Max(MM.InfNorm(), invMM.InfNorm()) * 1.0e-10;
for (int iRow = CheckMX.RowPartitioning.i0; iRow < CheckMX.RowPartitioning.iE; iRow++)
{
if (Math.Abs(CheckMX.GetDiagonalElement(iRow) - 1.0) > TRESH)
{
throw new ArithmeticException("AapproxInverse is not the Inverse of the Aapprox-Matrix");
}
}
#endif
}
}
/// <summary>
///
/// </summary>
/// <param name="Flds">
/// a list of <em>M</em> DG fields.
/// </param>
/// <param name="Points">
/// 2-dimensional: <br/>
/// - 1st index: point index, from 0 (including) to <em>N</em> (excluding)<br/>
/// - 2nd index: spatial dimension/direction
/// </param>
/// <param name="Result">
/// result of the evaluation of the DG fields <paramref name="Flds"/> at points <paramref name="Points"/>.
/// - 1st index: point index, from 0 (including) to <em>N</em> (excluding)
/// - 2nd index: DG field, from 0 (including) to <em>M</em> (excluding).
/// the result will be accumulated.
/// </param>
/// <param name="UnlocatedPoints">
/// Optional, can be null; otherwise, an array of length <em>N</em>.
/// On exit, in the latter case, true for every point that is not within the grid.
/// </param>
/// <param name="LocalCellIndices">
/// Optional, can be null; otherwise, an array of length <em>N</em>.
/// On exit, in the latter case, the <em>n</em>-th entry contains the local index of the cell
/// where the <em>n</em>-th point is found.
/// </param>
/// <param name="beta">
/// pre-scaling of <paramref name="Result"/> on entry, i.e. before accumulation
/// </param>
/// <param name="alpha">
/// scaling of <paramref name="Flds"/> for evaluation
/// </param>
/// <returns>
/// the number of points that are not within the grid;
/// </returns>
public int Evaluate(double alpha, IEnumerable <DGField> Flds, MultidimensionalArray Points, double beta, MultidimensionalArray Result, BitArray UnlocatedPoints = null, int[] LocalCellIndices = null)
{
// init / check args
// =================
int D = m_Context.Grid.SpatialDimension;
int J = m_Context.Grid.NoOfUpdateCells;
if (Points.Dimension != 2)
{
throw new ArgumentException("must be 2-dimensional", "Points");
}
int N = Points.GetLength(0);
if (Result.Dimension != 2)
{
throw new ArgumentException("must be 2-dimensional", "Result");
}
if (Result.GetLength(0) != N)
{
throw new ArgumentException("mismatch in 1st dimension", "Points,Result");
}
DGField[] Fields = Flds.ToArray();
int M = Fields.Length;
for (int m = 0; m < M; m++)
{
if (!object.ReferenceEquals(this.m_Context, Fields[m].GridDat))
{
throw new ArgumentException($"Mismatch in grid: field #{m} is defined on a different grid.");
}
}
if (Result.GetLength(1) != Fields.Length)
{
throw new ArgumentException("2nd dimension of 'Result' and length of 'Flds' must be equal");
}
if (UnlocatedPoints == null)
{
UnlocatedPoints = new BitArray(N, false);
}
else
{
UnlocatedPoints.SetAll(false);
}
if (LocalCellIndices != null)
{
if (LocalCellIndices.Length != N)
{
throw new ArgumentException("2nd dimension of 'Result' and length of 'LocalCellIndices' must be equal");
}
for (int n = 0; n < N; n++)
{
LocalCellIndices[n] = int.MinValue;
}
}
if (UnlocatedPoints.Length != N)
{
throw new ArgumentException("2nd dimension of 'Result' and length of 'UnlocatedPoints' must be equal");
}
double[] pt = new double[D];
Result.Scale(beta);
// build point localization
// ========================
// filter points that are outside the grid bounding box
int[] Perm2 = new int[N];
{
int cnt = 0;
var bb = CellLoc.GridBB;
for (int n = 0; n < N; n++)
{
for (int d = 0; d < D; d++)
{
pt[d] = Points[n, d];
}
if (!bb.Contains(pt))
{
UnlocatedPoints[n] = true;
}
else
{
Perm2[cnt] = n;
cnt++;
}
}
Array.Resize(ref Perm2, cnt);
}
if (Perm2.Length <= 0)
{
UnlocatedPoints.SetAll(true);
return(N); // we are done
}
int _cnt = 0;
MultidimensionalArray pts = MultidimensionalArray.Create(Perm2.Length, D);
for (int n = 0; n < N; n++)
{
if (!UnlocatedPoints[n])
{
for (int d = 0; d < D; d++)
{
pts[_cnt, d] = Points[n, d];
}
_cnt++;
}
}
int NU = N - Perm2.Length;
UnlocatedPoints.SetAll(true);
N = Perm2.Length;
int[] Perm = new int[N];
int NoOfUnassignedNodes = N;
PointLocalization pl = new PointLocalization(pts, CellLoc.GridBB, Perm);
pts = null; // not required anymore
// localize Points / evaluate at
// =============================
MultidimensionalArray vertGlobalSupect1 = new MultidimensionalArray(2);
MultidimensionalArray vertGlobalSupect = new MultidimensionalArray(2);
MultidimensionalArray vertLocalSuspect = new MultidimensionalArray(3);
NodeSet vertLocal = null;
MultidimensionalArray[] fieldVal = new MultidimensionalArray[M];
for (int m = 0; m < M; m++)
{
fieldVal[m] = new MultidimensionalArray(2);
}
//Console.WriteLine("debgcode akt.");
//int[] bbsfound = new int[Points.GetLength(0)];
BoundingBox CellTreeBB = new BoundingBox(D);
BoundingBox CellBB = new BoundingBox(D);
// loop over cells ...
for (int j = 0; j < J; j++)
{
// code of the cell: all bounding boxes in the tree that
// share a point with the cell
GeomBinTreeBranchCode bbcode; int bbBits;
{
BoundingBoxCode __b = CellLoc.GetCellBoundingBoxCode(j);
bbcode = __b.Branch;
bbBits = (int)__b.SignificantBits;
CellLoc.GridBB.SubBoxFromCode(CellTreeBB, __b);
}
// cell bounding box is smaller than the bounding box in the tree
m_Context.Cells.GetCellBoundingBox(j, CellBB);
if (!CellTreeBB.Contains(CellBB)) // test
{
throw new ApplicationException("internal error: should not happen");
}
CellBB.ExtendByFactor(0.001); // safety factor
// determine all points in cell
int iP0, Len;
pl.GetPointsInBranch(bbcode, bbBits, out iP0, out Len);
if (Len <= 0)
{
// no points in cell j
continue;
}
// transform points to cell-local coordinates
vertGlobalSupect1.Allocate(Len, D);
double[] tempPt = new double[D];
int tempLen = 0;
int[] nPts = new int[Len];
for (int n = 0; n < Len; n++)
{
int nPt = Perm2[Perm[n + iP0]];
if (!UnlocatedPoints[nPt])
{
continue;
}
for (int d = 0; d < D; d++)
{
tempPt[d] = pl.Points[n + iP0, d];
}
if (CellBB.Contains(tempPt))
{
for (int d = 0; d < D; d++)
{
vertGlobalSupect1[tempLen, d] = tempPt[d];
}
nPts[tempLen] = nPt;
tempLen++;
}
}
Len = tempLen;
if (Len <= 0)
{
// no points in cell j
continue;
}
vertGlobalSupect.Allocate(Len, D);
vertGlobalSupect.Set(vertGlobalSupect1.ExtractSubArrayShallow(new int[] { 0, 0 }, new int[] { Len - 1, D - 1 }));
vertLocalSuspect.Allocate(1, Len, D);
CellLoc.GrdDat.TransformGlobal2Local(vertGlobalSupect, vertLocalSuspect, j, 1, 0);
// test
//for (int n = 0; n < Len; n++) {
// for (int d = 0; d < D; d++)
// pt[d] = vertGlobalSupect[n, d];
// if (!CellBB.Contains(pt))
// Console.WriteLine("Huramnet");
//}
var splx = m_Context.Cells.GetRefElement(j);
// test whether the points in the bounding box of cell j
// are also in cell j
bool[] tatsaechlich = new bool[Len];
int Z = 0;
for (int n = 0; n < Len; n++)
{
int nPt = nPts[n];
if (!UnlocatedPoints[nPt])
{
// point was already located in/assigned to another cell
continue;
}
for (int d = 0; d < D; d++)
{
pt[d] = vertGlobalSupect[n, d];
}
if (!CellBB.Contains(pt))
{
continue; // cell bounding box is usually smaller than the bounding box in the tree ('bbcode')
}
for (int d = 0; d < D; d++)
{
pt[d] = vertLocalSuspect[0, n, d];
}
if (splx.IsWithin(pt, 1.0e-8))
{
UnlocatedPoints[nPt] = false;
NoOfUnassignedNodes--;
if (LocalCellIndices != null)
{
LocalCellIndices[nPt] = j;
}
Z++;
tatsaechlich[n] = true;
}
}
if (Z <= 0)
{
// no points in bb
continue;
}
// collect all vertices that are really in cell j
vertLocal = new NodeSet(m_Context.Cells.GetRefElement(j), Z, D);
int z = 0;
for (int n = 0; n < Len; n++)
{
if (!tatsaechlich[n])
{
continue;
}
for (int d = 0; d < D; d++)
{
vertLocal[z, d] = vertLocalSuspect[0, n, d];
}
z++;
}
vertLocal.LockForever();
// evaluate Velocity Field there
for (int m = 0; m < M; m++)
{
fieldVal[m].Allocate(1, Z);
}
for (int m = 0; m < M; m++)
{
Fields[m].Evaluate(j, 1, vertLocal, fieldVal[m]);
}
// store result of evaluation
z = 0;
for (int n = 0; n < Len; n++)
{
//int nPt = Perm2[Perm[n + iP0]];
int nPt = nPts[n];
if (!tatsaechlich[n])
{
continue;
}
for (int m = 0; m < M; m++)
{
Result[nPt, m] += alpha * fieldVal[m][0, z];
}
z++;
}
}
// return
// ======
return(NoOfUnassignedNodes + NU);
}
private void ApproximationMatrix()
{
this.Aapprox = null;
this.AapproxInverse = null;
//MsrMatrix AapproxComp = null;
/*
* switch(m_SIMPLEOptions.Option_Approximation_Predictor) {
* case ApproxPredictor.MassMatrix:
* case ApproxPredictor.LocalizedOperator: { break; }
* default: {
* Aapprox = ConvDiff.CloneAs();
* //switch (m_SIMPLEOptions.Option_Timestepper) {
* // case Timestepper.Steady: break;
* // case Timestepper.ImplicitEuler: {
* // Aapprox.Acc(1.0 / dt, MassMatrix);
* // break;
* // }
* // default: {
* // throw new NotImplementedException("Unknown Timestepper");
* // }
* //}
* AapproxComp = new MsrMatrix(USubMatrixIdx.Length, USubMatrixIdx.Length, MassMatrix.RowPartitioning.BlockSize / (2 * D), MassMatrix.ColPartition.BlockSize / (2 * D));
* Aapprox.WriteSubMatrixTo(AapproxComp, USubMatrixIdx, default(int[]), USubMatrixIdx, default(int[]));
* break;
* }
* }
*/
switch (m_SIMPLEOptions.Option_Approximation_Predictor)
{
case ApproxPredictor.MassMatrix: {
BlockMsrMatrix MM;
if (!double.IsPositiveInfinity(this.m_SIMPLEOptions.dt))
{
// instationary SIMPLE
//MM = this.m_MgOp.MassMatrix.CloneAs();
// hier muss ich mir nochmal was überlegen --
// für einige Präkond.-Optionen
// (genau jene, welche die XDG-Basen für beide Phasen in Cut-Zellen mischen),
// wie etwa
// MultigridOperator.Mode.SymPart_DiagBlockEquilib
// ist eine Block-Skalierung mit rho_A und rho_B
// inkonsistent!
//
throw new NotImplementedException("todo");
}
else
{
MM = this.m_MgOp.MassMatrix;
}
Aapprox = new MsrMatrix(this.ConvDiff.RowPartitioning);
this.m_MgOp.MassMatrix.WriteSubMatrixTo(Aapprox, this.USubMatrixIdx_Row, default(int[]), this.USubMatrixIdx_Row, default(int[]));
//AapproxInverse = MassMatrixInv._ToMsrMatrix();// Aapprox.Invert();
//switch(m_SIMPLEOptions.Option_Timestepper) {
// case Timestepper.Steady: break;
// case Timestepper.ImplicitEuler: {
// Aapprox.Scale(1 + 1.0 / dt);
// AapproxInverse.Scale(1 / (1 + 1.0 / dt));
// /*#if DEBUG
// var CheckMX = AapproxInverse * Aapprox;
// foreach (int i in USubMatrixIdx) {
// if (Math.Abs(CheckMX.GetDiagonalElement(i) - 1.0) > 1e-10) throw new ArithmeticException("AapproxInverse is not the Inverse of the Aapprox-Matrix");
// }
// #endif*/
// break;
// }
// default: {
// throw new NotImplementedException("Unknown Timestepper");
// }
//}
break;
}
case ApproxPredictor.Exact: {
if (this.LsTrk.GridDat.CellPartitioning.MpiSize > 1)
{
throw new NotSupportedException("Not implemented for MPI-parallel runs.");
}
//RowIdx = VelocityMapping.GetSubvectorIndices(this.LsTrk, D.ForLoop(d => d), _SpcIds: this.LsTrk.SpeciesIdS, drk: this.TransportAgglomerator);
//ColIdx = RowIdx;
if (USubMatrixIdx_Row.Length > 4500)
{
Console.WriteLine(string.Format("WARNING: you don't really want to invert a {0}x{0} matrix.", USubMatrixIdx_Row.Length));
}
this.Aapprox = this.ConvDiff;
MultidimensionalArray AapproxFull = Aapprox.ToFullMatrixOnProc0();
MultidimensionalArray AapproxInverseFull = AapproxFull.GetInverse();
this.AapproxInverse = new MsrMatrix(new Partitioning(USubMatrixIdx_Row.Length));
this.AapproxInverse.AccDenseMatrix(1.0, AapproxInverseFull);
break;
}
case ApproxPredictor.Diagonal: {
/*
* Aapprox = new MsrMatrix(ConvDiff.RowPartitioning, ConvDiff.ColPartition);
* AapproxInverse = new MsrMatrix(ConvDiff.RowPartitioning, ConvDiff.ColPartition);
* foreach(int i in USubMatrixIdx) {
* int[] j = new int[] { i };
* double Value = ConvDiff.GetValues(i, j)[0];
* //Value += MassMatrix.GetValues(i, j)[0];
* Aapprox.SetDiagonalElement(i, Value);
* if(Value == 0) {
* AapproxInverse.SetDiagonalElement(i, 0);
* } else {
* AapproxInverse.SetDiagonalElement(i, 1 / Value);
* }
* }
#if DEBUG
* Aapprox.VerifyDataStructure();
* AapproxInverse.VerifyDataStructure();
* var CheckMX = AapproxInverse * Aapprox;
* foreach(int i in USubMatrixIdx) {
* if(Math.Abs(CheckMX.GetDiagonalElement(i) - 1.0) > 1e-13) throw new ArithmeticException("AapproxInverse is not the Inverse of the Operator Matrix");
* }
#endif
* break;
*/
throw new NotImplementedException("todo");
}
case ApproxPredictor.BlockDiagonal: {
/*
* AapproxInverse = new MsrMatrix(Aapprox.RowPartitioning, Aapprox.ColPartition);
* var AapproxCompBD = new BlockDiagonalMatrix(AapproxComp);
* var AapproxCompInvBD = AapproxCompBD.Invert();
* AapproxCompBD._ToMsrMatrix().WriteSubMatrixTo(Aapprox, default(int[]), USubMatrixIdx, default(int[]), USubMatrixIdx);
* AapproxCompInvBD._ToMsrMatrix().WriteSubMatrixTo(AapproxInverse, default(int[]), USubMatrixIdx, default(int[]), USubMatrixIdx);
* //#if DEBUG
* Aapprox.VerifyDataStructure();
* AapproxInverse.VerifyDataStructure();
* var CheckMX = AapproxInverse * Aapprox;
* foreach(int i in USubMatrixIdx) {
* if(Math.Abs(CheckMX.GetDiagonalElement(i) - 1.0) > 1e-12) throw new ArithmeticException("AapproxInverse is not the Inverse of the Operator Matrix");
* }
* //#endif
*
* break;
*/
throw new NotImplementedException("todo");
}
case ApproxPredictor.BlockSum: {
/*
* Console.WriteLine("BlockSum is not properly tested yet and did not work in previous tests");
* int AccdBlockSize = ConvDiff.RowPartitioning.BlockSize / (2 * D);
* var AapproxBD = new BlockDiagonalMatrix(ConvDiff.RowPartitioning);
* var Aapprox = new MsrMatrix(ConvDiff.RowPartitioning);
* int[] indexer = new int[AccdBlockSize];
* for(int i = 0; i < indexer.Length; i++) {
* indexer[i] = i;
* }
* int[] rowindexer = indexer.CloneAs();
*
*
* for(int i = 0; i < ConvDiff.NoOfRows / AccdBlockSize; i++) {
* int[] colindexer = indexer.CloneAs();
* for(int j = 0; j < ConvDiff.NoOfCols / AccdBlockSize; j++) {
* ConvDiff.AccSubMatrixTo(1.0, Aapprox, rowindexer, rowindexer, colindexer, rowindexer);
* for(int r = 0; r < indexer.Length; r++) {
* colindexer[r] += AccdBlockSize;
* }
* }
* for(int r = 0; r < indexer.Length; r++) {
* rowindexer[r] += AccdBlockSize;
* }
* }
* //if (m_SIMPLEOptions.Option_Timestepper == Timestepper.ImplicitEuler) {
* // Aapprox.Acc(1 / dt, MassMatrix);
* //}
* AapproxComp = new MsrMatrix(USubMatrixIdx.Length, USubMatrixIdx.Length, AccdBlockSize, AccdBlockSize);
* Aapprox.WriteSubMatrixTo(AapproxComp, USubMatrixIdx, default(int[]), USubMatrixIdx, default(int[]));
* AapproxInverse = new MsrMatrix(Aapprox.RowPartitioning, Aapprox.ColPartition);
* var AapproxCompBD = new BlockDiagonalMatrix(AapproxComp);
* var AapproxCompInvBD = AapproxCompBD.Invert();
* AapproxCompInvBD._ToMsrMatrix().WriteSubMatrixTo(AapproxInverse, default(int[]), USubMatrixIdx, default(int[]), USubMatrixIdx);
#if DEBUG
* Aapprox.VerifyDataStructure();
* AapproxInverse.VerifyDataStructure();
*
* // Check copying back and forth
* var CheckAapproxComp = new MsrMatrix(Aapprox.RowPartitioning, Aapprox.ColPartition);
* AapproxComp.WriteSubMatrixTo(CheckAapproxComp, default(int[]), USubMatrixIdx, default(int[]), USubMatrixIdx);
* CheckAapproxComp.Acc(-1.0, Aapprox);
* if(CheckAapproxComp.InfNorm() > 1e-14) throw new ArithmeticException("Something went wrong while copying the Aapprox Matrix");
*
* //Check Transformation to BlockdiagonalMatrix
* var CheckAapproxCompBD = new MsrMatrix(Aapprox.RowPartitioning, Aapprox.ColPartition);
* AapproxCompBD._ToMsrMatrix().WriteSubMatrixTo(CheckAapproxCompBD, default(int[]), USubMatrixIdx, default(int[]), USubMatrixIdx);
* CheckAapproxCompBD.Acc(-1.0, Aapprox);
* if(CheckAapproxCompBD.InfNorm() > 1e-14) throw new ArithmeticException("Something went wrong while copying the Aapprox Matrix");
*
* //Check Matrix Inversion
* var CheckMX = AapproxInverse * Aapprox;
* foreach(int i in USubMatrixIdx) {
* if(Math.Abs(CheckMX.GetDiagonalElement(i) - 1.0) > 1e-12) throw new ArithmeticException("AapproxInverse is not the Inverse of the Operator Matrix");
* }
#endif
* break;
*/
throw new NotImplementedException("todo");
}
case ApproxPredictor.Neumann: {
/*
* Console.WriteLine("Neumann did not work in previous Tests, Series does typically not converge");
* int serieslength = 10;
*
* Aapprox = ConvDiff.CloneAs();
* //if (m_SIMPLEOptions.Option_Timestepper != Timestepper.Steady) {
* // Aapprox.Acc(1.0 / dt, MassMatrix);
* //}
* var B = Aapprox.CloneAs();
* double ScalingFactor = Aapprox.InfNorm();
* B.Scale((-1.0 / ScalingFactor.Pow(0))); //Scaling Power up to 4 tried
* B.AccEyeSp(1.0);
* AapproxInverse = B;
* AapproxInverse.AccEyeSp(1.0);
* MsrMatrix OldMoment = B;
* for(int i = 0; i <= serieslength; i++) {
* var NewMoment = OldMoment * B;
* AapproxInverse.Acc(1.0, NewMoment);
* //Debug
* Console.WriteLine("MomentNumber #{0}, InfNormOf Inverse #{1}", i, NewMoment.InfNorm());
* OldMoment = NewMoment;
* }
* AapproxInverse.Scale((1.0 / ScalingFactor.Pow(0))); //Scaling Power up to 4 tried
* break;
*/
throw new NotImplementedException("todo");
}
case ApproxPredictor.LocalizedOperator: {
/*
* Console.WriteLine("Localized Operator did not work in previous Tests");
* double[] LocalizedOpAffine;
* MultiphaseCellAgglomerator LocalizedAgglomerator;
* Aapprox = new MsrMatrix(MassMatrix.RowPartitioning, MassMatrix.ColPartition);
* TransportOpLocalized.AssembleMatrix(
* out Aapprox, out LocalizedOpAffine,
* out LocalizedAgglomerator, out TransportMassFact,
* this.Velocity.Current, null,
* this.LevSet, null, Curv,
* VelocityMapping, VelocityMapping);
* if(Option_Timestepper == Timestepper.ImplicitEuler) {
* Aapprox.Acc(1 / dt, MassMatrix);
* }
*
* var DiagAverage = Aapprox.GetDiagVector().Average();
* foreach(int i in RowIdx) {
* if(Aapprox.GetDiagonalElement(i) == 0.0) {
* //Aapprox.SetDiagonalElement(i, MassMatrix.GetDiagonalElement(i));
* Aapprox.SetDiagonalElement(i, DiagAverage);
* }
* }
* AapproxComp = new MsrMatrix(RowIdx.Length, RowIdx.Length, MassMatrix.RowPartitioning.BlockSize / (2 * D), MassMatrix.ColPartition.BlockSize / (2 * D));
* Aapprox.WriteSubMatrixTo(AapproxComp, RowIdx, default(int[]), ColIdx, default(int[]));
* AapproxInverse = new MsrMatrix(Aapprox.RowPartitioning, Aapprox.ColPartition);
* var AapproxCompBD = new BlockDiagonalMatrix(AapproxComp);
* var AapproxCompInvBD = AapproxCompBD.Invert();
* AapproxCompInvBD._ToMsrMatrix().WriteSubMatrixTo(AapproxInverse, default(int[]), RowIdx, default(int[]), ColIdx);
* //AapproxComp._ToMsrMatrix().WriteSubMatrixTo(Aapprox, default(int[]), RowIdx, default(int[]), ColIdx);
*
*
#if DEBUG
* Aapprox.VerifyDataStructure();
* AapproxInverse.VerifyDataStructure();
* var CheckAapproxCompBD = new MsrMatrix(Aapprox.RowPartitioning, Aapprox.ColPartition);
* AapproxCompBD._ToMsrMatrix().WriteSubMatrixTo(CheckAapproxCompBD, default(int[]), RowIdx, default(int[]), ColIdx);
* CheckAapproxCompBD.Acc(-1.0, Aapprox);
* if(CheckAapproxCompBD.InfNorm() > 1e-14) throw new ArithmeticException("Something went wrong while copying the Aapprox Matrix");
* var CheckMX = AapproxInverse * Aapprox;
* foreach(int i in RowIdx) {
* if(Math.Abs(CheckMX.GetDiagonalElement(i) - 1.0) > 1e-12) throw new ArithmeticException("AapproxInverse is not the Inverse of the Operator Matrix");
* }
#endif
* break;
*/
throw new NotImplementedException("todo");
}
default:
throw new NotImplementedException("todo");
}
if (this.AapproxInverse == null)
{
// block-inversion is required.
// ++++++++++++++++++++++++++++
int D = this.LsTrk.GridDat.SpatialDimension;
this.AapproxInverse = new MsrMatrix(this.Aapprox.RowPartitioning, this.Aapprox.ColPartition);
//int N = this.m_MgOp.Mapping.AggBasis.GetMinimalLength(this.m_MgOp.Mapping.DgDegree[0]);
//Debug.Assert(this.Aapprox.RowPartitioning.LocalLength % N == 0);
MultidimensionalArray Block = new MultidimensionalArray(2);
MultidimensionalArray InvBlock = new MultidimensionalArray(2);
int iRow0 = this.Aapprox.RowPartitioning.i0;
int JAGG = this.m_MgOp.Mapping.AggGrid.iLogicalCells.NoOfLocalUpdatedCells;
int[] DegreeS = this.m_MgOp.Mapping.DgDegree;
for (int jagg = 0; jagg < JAGG; jagg++) // loop over aggregate cells...
{
for (int d = 0; d < D; d++) // loop over velocity components...
{
int N = this.m_MgOp.Mapping.AggBasis[d].GetLength(jagg, DegreeS[d]);
if (Block.GetLength(0) != N)
{
Block.Allocate(N, N);
InvBlock.Allocate(N, N);
}
for (int n = 0; n < N; n++)
{
#if DEBUG
int iRow = iRow0 + n;
{
int[] Cols = null;
double[] Vals = null;
int LR = Aapprox.GetRow(iRow, ref Cols, ref Vals);
int cMin = int.MaxValue;
int cMax = int.MinValue;
for (int lr = 0; lr < LR; lr++)
{
if (Vals[lr] != 0.0)
{
cMin = Math.Min(cMin, Cols[lr]);
cMax = Math.Max(cMax, Cols[lr]);
}
}
Debug.Assert(cMin >= iRow0);
Debug.Assert(cMax < iRow0 + N);
}
#endif
for (int m = 0; m < N; m++)
{
Block[n, m] = this.Aapprox[iRow0 + n, iRow0 + m];
}
}
Block.InvertTo(InvBlock);
for (int n = 0; n < N; n++)
{
for (int m = 0; m < N; m++)
{
this.AapproxInverse[iRow0 + n, iRow0 + m] = InvBlock[n, m];
}
}
iRow0 += N;
}
}
Debug.Assert(iRow0 == this.Aapprox.RowPartitioning.iE);
}
#if DEBUG
var CheckMX = AapproxInverse * Aapprox;
double TRESH = Math.Max(AapproxInverse.InfNorm(), Aapprox.InfNorm()) * 1.0e-10;
for (int iRow = CheckMX.RowPartitioning.i0; iRow < CheckMX.RowPartitioning.iE; iRow++)
{
if (Math.Abs(CheckMX.GetDiagonalElement(iRow) - 1.0) > TRESH)
{
throw new ArithmeticException("AapproxInverse is not the Inverse of the Aapprox-Matrix");
}
}
#endif
}
private double[] ComputeBenchmarkQuantities()
{
int order = 0;
if (CorrectionLsTrk.GetCachedOrders().Count > 0)
{
order = CorrectionLsTrk.GetCachedOrders().Max();
}
else
{
order = 1;
}
var SchemeHelper = CorrectionLsTrk.GetXDGSpaceMetrics(CorrectionLsTrk.SpeciesIdS.ToArray(), order, 1).XQuadSchemeHelper;
// area of bubble
double area = 0.0;
SpeciesId spcId = CorrectionLsTrk.SpeciesIdS[1];
var vqs = SchemeHelper.GetVolumeQuadScheme(spcId);
CellQuadrature.GetQuadrature(new int[] { 1 }, CorrectionLsTrk.GridDat,
vqs.Compile(CorrectionLsTrk.GridDat, order),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
EvalResult.SetAll(1.0);
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
area += ResultsOfIntegration[i, 0];
}
}
).Execute();
area = area.MPISum();
// surface
double surface = 0.0;
//CellQuadratureScheme cqs = SchemeHelper.GetLevelSetquadScheme(0, LsTrk.Regions.GetCutCellMask());
var surfElemVol = SchemeHelper.Get_SurfaceElement_VolumeQuadScheme(spcId);
CellQuadrature.GetQuadrature(new int[] { 1 }, CorrectionLsTrk.GridDat,
surfElemVol.Compile(CorrectionLsTrk.GridDat, this.m_HMForder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
EvalResult.SetAll(1.0);
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
surface += ResultsOfIntegration[i, 0];
}
}
).Execute();
surface = surface.MPISum();
// circularity
double diamtr_c = Math.Sqrt(4 * area / Math.PI);
double perimtr_b = surface;
double circ = Math.PI * diamtr_c / perimtr_b;
// total concentration, careful above values are "old" when CorrectionTracker is not updated, this value is always "new"
double concentration = 0.0;
var tqs = new CellQuadratureScheme();
CellQuadrature.GetQuadrature(new int[] { 1 }, phi.GridDat,
tqs.Compile(phi.GridDat, phi.Basis.Degree * 2 + 2),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
phi.Evaluate(i0, Length, QR.Nodes, EvalResult.ExtractSubArrayShallow(-1, -1, 0));
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
concentration += ResultsOfIntegration[i, 0];
}
}
).Execute();
concentration = concentration.MPISum();
// total mixing energy
double energy = 0.0;
var eqs = new CellQuadratureScheme();
int D = phi.GridDat.SpatialDimension;
SinglePhaseField[] PhiGrad = new SinglePhaseField[D];
for (int d = 0; d < D; d++)
{
PhiGrad[d] = new SinglePhaseField(phi.Basis, string.Format("G_{0}", d));
PhiGrad[d].Derivative(1.0, phi, d);
}
MultidimensionalArray _Phi = new MultidimensionalArray(2);
MultidimensionalArray _GradPhi = new MultidimensionalArray(3);
MultidimensionalArray _NormGrad = new MultidimensionalArray(2);
CellQuadrature.GetQuadrature(new int[] { 1 }, phi.GridDat,
eqs.Compile(phi.GridDat, phi.Basis.Degree * 2 + 2),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
int K = EvalResult.GetLength(1);
// alloc buffers
// -------------
if (_Phi.GetLength(0) != Length || _Phi.GetLength(1) != K)
{
_Phi.Allocate(Length, K);
_GradPhi.Allocate(Length, K, D);
_NormGrad.Allocate(Length, K);
}
else
{
_Phi.Clear();
_GradPhi.Clear();
_NormGrad.Clear();
}
// chemical potential
phi.Evaluate(i0, Length, QR.Nodes, _Phi.ExtractSubArrayShallow(-1, -1));
_Phi.ApplyAll(x => 0.25 / (this.Control.cahn.Pow2()) * (x.Pow2() - 1.0).Pow2());
for (int d = 0; d < D; d++)
{
PhiGrad[d].Evaluate(i0, Length, QR.Nodes, _GradPhi.ExtractSubArrayShallow(-1, -1, d));
}
// free surface energy
for (int d = 0; d < D; d++)
{
var GradPhi_d = _GradPhi.ExtractSubArrayShallow(-1, -1, d);
_NormGrad.Multiply(1.0, GradPhi_d, GradPhi_d, 1.0, "ik", "ik", "ik");
}
_NormGrad.ApplyAll(x => 0.5 * x);
EvalResult.ExtractSubArrayShallow(-1, -1, 0).Acc(1.0, _Phi);
EvalResult.ExtractSubArrayShallow(-1, -1, 0).Acc(1.0, _NormGrad);
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
energy += ResultsOfIntegration[i, 0];
}
}
).Execute();
energy = energy.MPISum();
// replace 1.96 (RB_TC2) with actual surface tension
// see Yue (2004)
double lambda = this.Control.cahn.Pow2() * 1.96 * surface / energy;
return(new double[] { area, surface, circ, concentration, energy, lambda, this.Control.diff });
}
/// <summary>
/// Allocates memory for <see cref="m_WeightBuffer"/>.
/// </summary>
protected override void AllocateBuffers(int NoOfItems, NodeSet ruleNodes)
{
base.AllocateBuffers(NoOfItems, ruleNodes);
m_WeightBuffer.Allocate(NoOfItems, ruleNodes.GetLength(0));
}
/// <summary>
/// for a cloud of points, this method finds the cells which contain the points
/// </summary>
/// <param name="_pts">
/// Input: a cloud of points; 1st index: point index, 2nd index: spatial dimension;
/// </param>
/// <param name="LocalCellIdx">
/// Output: for each point in <paramref name="_pts"/>, the the (local) index of the cell which contains the specific point
/// </param>
/// <param name="NoOfUnassigned">
/// on exit, the number of points which cannot be assigned to one cell
/// </param>
public void LocalizePointsWithinGrid <T>(MultidimensionalArray _pts, T LocalCellIdx, out int NoOfUnassigned) where T : IList <int>
{
using (new FuncTrace()) {
// init and check
// ==============
NoOfUnassigned = 0;
GridData grd = this.GrdDat;
var CellLoc = this;
var splxS = grd.Grid.RefElements;
int D = grd.SpatialDimension;
int N = _pts.GetLength(0);
if (_pts.Dimension != 2)
{
throw new ArgumentException();
}
if (_pts.GetLength(0) != LocalCellIdx.Count)
{
throw new ArgumentException();
}
if (_pts.GetLength(1) != D)
{
throw new ArgumentException();
}
var UnlocatedPoints = new BitArray(N, false);
int J = grd.Cells.NoOfLocalUpdatedCells;
double[] pt = new double[D];
// build point localization
// ========================
// filter points that are outside the grid bounding box
int[] Perm2 = new int[N];
{
int cnt = 0;
var bb = CellLoc.GridBB;
for (int n = 0; n < N; n++)
{
_pts.ExtractVector(pt, 1, 0, D, n, 0);
//for (int d = 0; d < D; d++)
// pt[d] = Points[n, d];
if (!bb.Contains(pt))
{
UnlocatedPoints[n] = true;
NoOfUnassigned++;
}
else
{
Perm2[cnt] = n;
cnt++;
}
}
Array.Resize(ref Perm2, cnt);
}
if (Perm2.Length <= 0)
{
// all points are outside the bounding box of the grid !
LocalCellIdx.SetAll(int.MinValue);
return; // we are done
}
int _cnt = 0;
MultidimensionalArray pts = MultidimensionalArray.Create(Perm2.Length, D);
for (int n = 0; n < N; n++)
{
if (!UnlocatedPoints[n])
{
for (int d = 0; d < D; d++)
{
pts[_cnt, d] = _pts[n, d];
}
_cnt++;
}
}
int NU = N - Perm2.Length;
UnlocatedPoints.SetAll(true);
N = Perm2.Length;
int[] Perm = new int[N];
int NoOfUnassignedNodes = N;
PointLocalization pl = new PointLocalization(pts, CellLoc.GridBB, Perm);
pts = null; // not required anymore
// localize Points / evaluate at
// =============================
MultidimensionalArray vertGlobalSupect = new MultidimensionalArray(2);
MultidimensionalArray vertLocalSuspect = new MultidimensionalArray(3);
BoundingBox CellTreeBB = new BoundingBox(D);
BoundingBox CellBB = new BoundingBox(D);
// loop over cells ...
for (int j = 0; j < J; j++)
{
// code of the cell: all bounding boxes in the tree that
// share a point with the cell
GeomBinTreeBranchCode bbcode; int bbBits;
{
BoundingBoxCode __b = CellLoc.GetCellBoundingBoxCode(j);
bbcode = __b.Branch;
bbBits = (int)__b.SignificantBits;
CellLoc.GridBB.SubBoxFromCode(CellTreeBB, __b);
}
// cell bounding box is smaller than the bounding box in the tree
grd.Cells.GetCellBoundingBox(j, CellBB);
if (!CellTreeBB.Contains(CellBB)) // test
{
throw new ApplicationException("internal error: should not happen");
}
CellBB.ExtendByFactor(0.001); // safety factor
// determine all points in cell
int iP0, Len;
pl.GetPointsInBranch(bbcode, bbBits, out iP0, out Len);
if (Len <= 0)
{
// no points in cell j
continue;
}
// transform points to cell-local coordinates
vertGlobalSupect.Allocate(Len, D);
vertLocalSuspect.Allocate(1, Len, D);
for (int n = 0; n < Len; n++)
{
for (int d = 0; d < D; d++)
{
vertGlobalSupect[n, d] = pl.Points[n + iP0, d];
}
}
CellLoc.GrdDat.TransformGlobal2Local(vertGlobalSupect, vertLocalSuspect, j, 1, 0);
var Kref = grd.Cells.GetRefElement(j);
// test whether the points in the bounding box of cell j
// are also in cell j
for (int n = 0; n < Len; n++)
{
int nPt = Perm2[Perm[n + iP0]];
if (!UnlocatedPoints[nPt])
{
// point was already located in/assigned to another cell
continue;
}
for (int d = 0; d < D; d++)
{
pt[d] = vertGlobalSupect[n, d];
}
if (!CellBB.Contains(pt))
{
continue; // cell bounding box is usually smaller than the bounding box in the tree ('bbcode')
}
for (int d = 0; d < D; d++)
{
pt[d] = vertLocalSuspect[0, n, d];
}
if (Kref.IsWithin(pt))
{
UnlocatedPoints[nPt] = false;
NoOfUnassignedNodes--;
LocalCellIdx[nPt] = j;
}
}
}
// return
NoOfUnassigned += NoOfUnassignedNodes;
}
}
/// <summary>
///
/// </summary>
/// <param name="CellPairs">
/// 1st index: list of cells <br/>
/// 2nd index: in {0, 1}
/// </param>
/// <param name="M">
/// 1st index: corresponds with 1st index of <paramref name="CellPairs"/><br/>
/// 2nd index: matrix row index <br/>
/// 3rd index: matrix column index
/// </param>
/// <param name="Minv">the inverse of <paramref name="M"/></param>
/// <remarks>
/// Let \f$ K_j \f$ and \f$ K_i \f$ be two different cells with a linear-affine
/// transformation to the reference element.
/// Here, \f$ j \f$=<paramref name="CellPairs"/>[a,0] and \f$ i \f$=<paramref name="CellPairs"/>[a,1].
/// The DG-basis in these cells can uniquely be represented as
/// \f[
/// \phi_{j n} (\vec{x}) = p_n (\vec{x}) \vec{1}_{K_j} (\vec{x})
/// \textrm{ and }
/// \phi_{i m} (\vec{x}) = q_m (\vec{x}) \vec{1}_{K_i} (\vec{x})
/// \f]
/// where \f$ \vec{1}_X \f$ denotes the characteristic function for set \f$ X \f$
/// and \f$ p_n\f$ and \f$ p_m\f$ are polynomials.
/// Then, for the output \f$ M \f$ =<paramref name="M"/>[a,-,-] fulfills
/// \f[
/// \phi_{j n} + \sum_{m} M_{m n} \phi_{i m}
/// =
/// p_n \vec{1}_{K_j \cup K_i}
/// \f]
/// </remarks>
public void GetExtrapolationMatrices(int[,] CellPairs, MultidimensionalArray M, MultidimensionalArray Minv = null)
{
var m_Context = this.GridDat;
int N = this.Length;
int Esub = CellPairs.GetLength(0);
int JE = this.GridDat.iLogicalCells.Count;
int J = this.GridDat.iLogicalCells.NoOfLocalUpdatedCells;
if (CellPairs.GetLength(1) != 2)
{
throw new ArgumentOutOfRangeException("second dimension is expected to be 2!");
}
if (M.Dimension != 3)
{
throw new ArgumentException();
}
if (M.GetLength(0) != Esub)
{
throw new ArgumentException();
}
if (M.GetLength(1) != N || M.GetLength(2) != N)
{
throw new ArgumentException();
}
if (Minv != null)
{
if (Minv.GetLength(0) != Esub)
{
throw new ArgumentException();
}
if (Minv.GetLength(1) != N || Minv.GetLength(2) != N)
{
throw new ArgumentException();
}
}
MultidimensionalArray NodesGlobal = new MultidimensionalArray(3);
MultidimensionalArray Minv_tmp = MultidimensionalArray.Create(N, N);
MultidimensionalArray M_tmp = MultidimensionalArray.Create(N, N);
for (int esub = 0; esub < Esub; esub++) // loop over the cell pairs...
{
int jCell0 = CellPairs[esub, 0];
int jCell1 = CellPairs[esub, 1];
if (jCell0 < 0 || jCell0 >= JE)
{
throw new ArgumentOutOfRangeException("Cell index out of range.");
}
if (jCell1 < 0 || jCell1 >= JE)
{
throw new ArgumentOutOfRangeException("Cell index out of range.");
}
bool swap;
if (jCell0 >= J)
{
//if(true) {
swap = true;
int a = jCell0;
jCell0 = jCell1;
jCell1 = a;
}
else
{
swap = false;
}
if (!m_Context.iGeomCells.IsCellAffineLinear(jCell0))
{
throw new NotSupportedException("Currently not supported for curved cells.");
}
if (!m_Context.iGeomCells.IsCellAffineLinear(jCell1))
{
throw new NotSupportedException("Currently not supported for curved cells.");
}
Debug.Assert(jCell0 < J);
var cellMask = new CellMask(m_Context, new[] { new Chunk()
{
i0 = jCell0, Len = 1
} }, MaskType.Geometrical);
// we project the basis function from 'jCell1' onto 'jCell0'
CellQuadrature.GetQuadrature(new int[2] {
N, N
}, m_Context,
(new CellQuadratureScheme(true, cellMask)).Compile(m_Context, this.Degree * 2), // integrate over target cell
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray _EvalResult) {
NodeSet nodes_Cell0 = QR.Nodes;
Debug.Assert(Length == 1);
NodesGlobal.Allocate(1, nodes_Cell0.GetLength(0), nodes_Cell0.GetLength(1));
m_Context.TransformLocal2Global(nodes_Cell0, jCell0, 1, NodesGlobal, 0);
var nodes_Cell1 = new NodeSet(GridDat.iGeomCells.GetRefElement(jCell1), nodes_Cell0.GetLength(0), nodes_Cell0.GetLength(1));
m_Context.TransformGlobal2Local(NodesGlobal.ExtractSubArrayShallow(0, -1, -1), nodes_Cell1, jCell1, null);
nodes_Cell1.LockForever();
var phi_0 = this.CellEval(nodes_Cell0, jCell0, 1).ExtractSubArrayShallow(0, -1, -1);
var phi_1 = this.CellEval(nodes_Cell1, jCell1, 1).ExtractSubArrayShallow(0, -1, -1);
var EvalResult = _EvalResult.ExtractSubArrayShallow(0, -1, -1, -1);
EvalResult.Multiply(1.0, phi_1, phi_0, 0.0, "kmn", "kn", "km");
},
/*_SaveIntegrationResults:*/ delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
Debug.Assert(Length == 1);
var res = ResultsOfIntegration.ExtractSubArrayShallow(0, -1, -1);
Minv_tmp.Clear();
Minv_tmp.Acc(1.0, res);
}).Execute();
// compute the inverse
Minv_tmp.InvertTo(M_tmp);
// store
if (!swap)
{
M.ExtractSubArrayShallow(esub, -1, -1).AccMatrix(1.0, M_tmp);
if (Minv != null)
{
Minv.ExtractSubArrayShallow(esub, -1, -1).AccMatrix(1.0, Minv_tmp);
}
}
else
{
M.ExtractSubArrayShallow(esub, -1, -1).AccMatrix(1.0, Minv_tmp);
if (Minv != null)
{
Minv.ExtractSubArrayShallow(esub, -1, -1).AccMatrix(1.0, M_tmp);
}
}
}
}
/// <summary>
/// Evaluates the divergence of the modified integrand
/// \f$
/// \nabla \cdot \vec{g} = \nabla \cdot (g \frac{\nabla \Phi}{|\nabla \Phi|})
/// \f$
/// which can be expanded to
/// \f$
/// \nabla \cdot \vec{g} = \nabla g \frac{\nabla \Phi}{|\nabla \Phi|} + g (
/// \frac{\Delta \Phi}{|\nabla \Phi|}
/// - \frac{\nabla \Phi}{|\nabla \Phi|} \frac{H(\Phi)}{|\nabla \Phi|} \frac{\nabla \Phi}{|\nabla \Phi|})
/// \f$
/// using the chain rule. HEre, \f$ H(\Phi)\f$
/// denotes the Hessian of the level set (i.e., the second derivatives)
/// </summary>
/// <param name="j0">
/// <see cref="LevelSetIntegrator.EvaluateDivergenceOfIntegrand"/>
/// </param>
/// <param name="Length">
/// <see cref="LevelSetIntegrator.EvaluateDivergenceOfIntegrand"/>
/// </param>
/// <param name="EvalResult">
/// <see cref="LevelSetIntegrator.EvaluateDivergenceOfIntegrand"/>
/// </param>
public override void EvaluateDivergenceOfIntegrand(NodeSet nodes, int j0, int Length, MultidimensionalArray EvalResult)
{
using (new FuncTrace()) {
int D = base.m_LevSetTrk.GridDat.SpatialDimension; // spatial dimension
int noOfNodes = EvalResult.GetLength(1); // number of nodes
if (m_WeighFunctionBuffer.GetLength(0) != Length || m_WeighFunctionBuffer.GetLength(1) != noOfNodes)
{
m_IntegrandBuffer.Allocate(Length, noOfNodes);
m_IntegrandGradientBuffer.Allocate(Length, noOfNodes, D);
m_WeighFunctionBuffer.Allocate(Length, noOfNodes);
m_LevelSetGradientBuffer.Allocate(Length, noOfNodes, D);
m_LevelSetHessianBuffer.Allocate(Length, noOfNodes, D, D);
}
m_Field.Evaluate(j0, Length, nodes, m_IntegrandBuffer);
m_Field.EvaluateGradient(j0, Length, nodes, m_IntegrandGradientBuffer, 0, 0.0);
m_levSet.EvaluateGradient(j0, Length, nodes, m_LevelSetGradientBuffer);
m_levSet.EvaluateHessian(j0, Length, nodes, m_LevelSetHessianBuffer);
EvaluateWeightFunction(nodes, j0, Length, m_WeighFunctionBuffer);
double[] Buf = new double[D];
for (int i = 0; i < Length; i++)
{
for (int j = 0; j < noOfNodes; j++)
{
if (m_WeighFunctionBuffer[i, j] == 0.0)
{
continue;
}
double AbsGradPhi = 0.0;
for (int d = 0; d < D; d++)
{
double GradPhi_d = m_LevelSetGradientBuffer[i, j, d];
AbsGradPhi += GradPhi_d * GradPhi_d;
}
AbsGradPhi = Math.Sqrt(AbsGradPhi);
if (AbsGradPhi < 1e-11)
{
// Assume zero since gradient is nearly zero
continue;
}
double ooAbsGradPhi = 1.0 / AbsGradPhi;
double term1 = 0.0;
for (int d = 0; d < D; d++)
{
term1 += m_IntegrandGradientBuffer[i, j, d] * m_LevelSetGradientBuffer[i, j, d];
}
term1 *= ooAbsGradPhi;
double term2 = 0;
for (int d = 0; d < D; d++)
{
term2 += m_LevelSetHessianBuffer[i, j, d, d];
}
term2 *= ooAbsGradPhi;
double term3 = 0;
{
for (int d1 = 0; d1 < D; d1++)
{
double a = 0;
for (int d2 = 0; d2 < D; d2++)
{
a += m_LevelSetHessianBuffer[i, j, d1, d2] * m_LevelSetGradientBuffer[i, j, d2];
}
Buf[d1] = a;
}
for (int d = 0; d < D; d++)
{
term3 += Buf[d] * m_LevelSetGradientBuffer[i, j, d];
}
term3 *= (ooAbsGradPhi * ooAbsGradPhi * ooAbsGradPhi);
}
EvalResult[i, j, 0] = term1 + m_IntegrandBuffer[i, j] * (term2 - term3);
}
}
}
}
/// <summary>
/// Computation of mean curvature according to Bonnet's formula.
/// </summary>
/// <param name="scale"></param>
/// <param name="Output">
/// output.
/// </param>
/// <param name="quadScheme"></param>
/// <param name="UseCenDiffUpTo">
/// Either 0, 1, or 2:
/// If 0, all derivatives are computed locally (broken derivative);
/// if 1, the first order derivatives are computed by central
/// differences, while the second order ones are computed locally,
/// based on the first order ones;
/// if 2, all derivatives are computed by central differences.
/// </param>
/// <param name="_1stDerivDegree">
/// Relative DG polynomial degree for the 1st order derivatives, i.e.
/// degree is <paramref name="_1stDerivDegree"/>+<em>p</em>, where
/// <em>p</em> is the degree of this field.
/// Only active if <paramref name="UseCenDiffUpTo"/> is greater than 0.
/// </param>
/// <param name="_2ndDerivDegree">
/// Relative DG polynomial degree for the 2nd order derivatives, i.e.
/// degree is <paramref name="_2ndDerivDegree"/>+<em>p</em>, where
/// <em>p</em> is the degree of this field. Only active if
/// <paramref name="UseCenDiffUpTo"/> is greater than 1.
/// </param>
/// <remarks>
/// using central differences causes memory allocation: <em>D</em>
/// fields for <paramref name="UseCenDiffUpTo"/>=1, and
/// <em>D</em>*(<em>D</em>+1) for <paramref name="UseCenDiffUpTo"/>=2,
/// where <em>D</em> notates the spatial dimension.
/// </remarks>
public void ProjectTotalcurvature2(
double scale,
SinglePhaseField Output,
int UseCenDiffUpTo,
int _1stDerivDegree = 0,
int _2ndDerivDegree = 0,
CellQuadratureScheme quadScheme = null)
{
using (new FuncTrace()) {
if (UseCenDiffUpTo < 0 || UseCenDiffUpTo > 2)
{
throw new ArgumentOutOfRangeException();
}
//int M = Output.Basis.Length;
//int N = this.Basis.Length;
int D = this.GridDat.SpatialDimension;
//var NSC = m_context.NSC;
SubGrid sgrd = null;
SpatialOperator.SubGridBoundaryModes bndMode = SpatialOperator.SubGridBoundaryModes.InnerEdge;
if (UseCenDiffUpTo >= 1 && quadScheme != null && quadScheme.Domain != null)
{
sgrd = new SubGrid(quadScheme.Domain);
bndMode = SpatialOperator.SubGridBoundaryModes.OpenBoundary;
}
// compute 1st order derivatives by central differences, if desired
// ================================================================
Basis B2 = new Basis(this.GridDat, this.Basis.Degree + _1stDerivDegree);
SinglePhaseField[] GradientVector = null;
if (UseCenDiffUpTo >= 1)
{
GradientVector = new SinglePhaseField[D];
for (int d = 0; d < D; d++)
{
GradientVector[d] = new SinglePhaseField(B2);
GradientVector[d].DerivativeByFlux(1.0, this, d, sgrd, bndMode);
}
}
// compute 2nd order derivatives by central differences, if desired
// ===============================================================
Basis B3 = new Basis(this.GridDat, this.Basis.Degree + _2ndDerivDegree);
SinglePhaseField[,] HessianTensor = null;
if (UseCenDiffUpTo >= 2)
{
HessianTensor = new SinglePhaseField[D, D];
for (int d1 = 0; d1 < D; d1++)
{
for (int d2 = 0; d2 < D; d2++)
{
HessianTensor[d1, d2] = new SinglePhaseField(B3);
HessianTensor[d1, d2].DerivativeByFlux(1.0, GradientVector[d1], d2, sgrd, bndMode);
}
}
}
// compute and project
// ===================
// buffers:
MultidimensionalArray Phi = new MultidimensionalArray(2);
MultidimensionalArray GradPhi = new MultidimensionalArray(3);
MultidimensionalArray HessPhi = new MultidimensionalArray(4);
MultidimensionalArray ooNormGrad = new MultidimensionalArray(2);
MultidimensionalArray Laplace = new MultidimensionalArray(2);
MultidimensionalArray Q = new MultidimensionalArray(3);
// evaluate/project:
//double Erracc = 0;
Output.ProjectField(scale,
(ScalarFunctionEx) delegate(int j0, int Len, NodeSet NodeSet, MultidimensionalArray result) { // ScalarFunction2
Debug.Assert(result.Dimension == 2);
Debug.Assert(Len == result.GetLength(0));
int K = result.GetLength(1); // number of nodes
// alloc buffers
// -------------
if (Phi.GetLength(0) != Len || Phi.GetLength(1) != K)
{
Phi.Allocate(Len, K);
GradPhi.Allocate(Len, K, D);
HessPhi.Allocate(Len, K, D, D);
ooNormGrad.Allocate(Len, K);
Laplace.Allocate(Len, K);
Q.Allocate(Len, K, D);
}
else
{
Phi.Clear();
GradPhi.Clear();
HessPhi.Clear();
ooNormGrad.Clear();
Laplace.Clear();
Q.Clear();
}
// evaluate Gradient and Hessian
// -----------------------------
if (UseCenDiffUpTo >= 1)
{
for (int d = 0; d < D; d++)
{
GradientVector[d].Evaluate(j0, Len, NodeSet, GradPhi.ExtractSubArrayShallow(-1, -1, d));
}
}
else
{
this.EvaluateGradient(j0, Len, NodeSet, GradPhi);
}
if (UseCenDiffUpTo == 2)
{
for (int d1 = 0; d1 < D; d1++)
{
for (int d2 = 0; d2 < D; d2++)
{
HessianTensor[d1, d2].Evaluate(j0, Len, NodeSet, HessPhi.ExtractSubArrayShallow(-1, -1, d1, d2));
}
}
}
else if (UseCenDiffUpTo == 1)
{
for (int d = 0; d < D; d++)
{
var GradientVector_d = GradientVector[d];
GradientVector_d.EvaluateGradient(j0, Len, NodeSet, HessPhi.ExtractSubArrayShallow(-1, -1, d, -1), 0, 0.0);
}
}
else if (UseCenDiffUpTo == 0)
{
this.EvaluateHessian(j0, Len, NodeSet, HessPhi);
}
else
{
Debug.Assert(false);
}
// compute the monstrous formula
// -----------------------------
// norm of Gradient:
for (int d = 0; d < D; d++)
{
var GradPhi_d = GradPhi.ExtractSubArrayShallow(-1, -1, d);
ooNormGrad.Multiply(1.0, GradPhi_d, GradPhi_d, 1.0, "ik", "ik", "ik");
}
ooNormGrad.ApplyAll(x => 1.0 / Math.Sqrt(x));
// laplacian of phi:
for (int d = 0; d < D; d++)
{
var HessPhi_d_d = HessPhi.ExtractSubArrayShallow(-1, -1, d, d);
Laplace.Acc(1.0, HessPhi_d_d);
}
// result = Laplacian(phi)/|Grad phi|
result.Multiply(1.0, Laplace, ooNormGrad, 0.0, "ik", "ik", "ik");
// result = Grad(1/|Grad(phi)|)
for (int d1 = 0; d1 < D; d1++)
{
var Qd = Q.ExtractSubArrayShallow(-1, -1, d1);
for (int d2 = 0; d2 < D; d2++)
{
var Grad_d2 = GradPhi.ExtractSubArrayShallow(-1, -1, d2);
var Hess_d2_d1 = HessPhi.ExtractSubArrayShallow(-1, -1, d2, d1);
Qd.Multiply(-1.0, Grad_d2, Hess_d2_d1, 1.0, "ik", "ik", "ik");
}
}
ooNormGrad.ApplyAll(x => x * x * x);
result.Multiply(1.0, GradPhi, Q, ooNormGrad, 1.0, "ik", "ikd", "ikd", "ik");
//for (int i = 0; i < Len; i++) {
// for (int k = 0; k < K; k++) {
// double acc = 0;
// for (int d = 0; d < D; d++) {
// acc += GradPhi[i,k,d]*Q[i,k,d]*ooNormGrad[i,k];
// }
// Erracc += (acc - result[i,k]).Abs();
// }
//}
},
quadScheme.SaveCompile(this.GridDat, (Output.Basis.Degree + this.m_Basis.Degree * (this.m_Basis.Degree - 1) * D) * 2)
);
}
}
/// <summary>
/// curvature computation according to Bonnet's formula
/// Copy-Paste from <see cref="LevelSet.EvaluatetotalCurvature"/>, since there is no analytic formula for the curvature of an ellipse
/// </summary>
public void EvaluateTotalCurvature(int j0, int Len, NodeSet NodeSet, MultidimensionalArray result)
{
// (siehe FK, persoenliche Notizen, 08mar13)
// checks
// ------
int K = NodeSet.NoOfNodes;
if (result.Dimension != 2)
{
throw new ArgumentException();
}
if (result.GetLength(0) != Len)
{
throw new ArgumentException();
}
if (result.GetLength(1) != K)
{
throw new ArgumentException();
}
int D = NodeSet.SpatialDimension;
//Debug.Assert(D == this.GridDat.SpatialDimension);
// buffers:
// --------
//MultidimensionalArray Phi = new MultidimensionalArray(2);
MultidimensionalArray GradPhi = new MultidimensionalArray(3);
MultidimensionalArray HessPhi = new MultidimensionalArray(4);
MultidimensionalArray ooNormGrad = new MultidimensionalArray(2);
MultidimensionalArray Laplace = new MultidimensionalArray(2);
MultidimensionalArray Q = new MultidimensionalArray(3);
//Phi.Allocate(Len, K);
GradPhi.Allocate(Len, K, D);
HessPhi.Allocate(Len, K, D, D);
ooNormGrad.Allocate(Len, K);
Laplace.Allocate(Len, K);
Q.Allocate(Len, K, D);
// derivatives
// -----------
// evaluate gradient
this.EvaluateGradient(j0, Len, NodeSet, GradPhi);
// evaluate Hessian
this.EvaluateHessian(j0, Len, NodeSet, HessPhi);
// compute the monstrous formula
// -----------------------------
// norm of Gradient:
for (int d = 0; d < D; d++)
{
var GradPhi_d = GradPhi.ExtractSubArrayShallow(-1, -1, d);
ooNormGrad.Multiply(1.0, GradPhi_d, GradPhi_d, 1.0, "ik", "ik", "ik");
}
ooNormGrad.ApplyAll(x => 1.0 / Math.Sqrt(x));
// laplacian of phi:
for (int d = 0; d < D; d++)
{
var HessPhi_d_d = HessPhi.ExtractSubArrayShallow(-1, -1, d, d);
Laplace.Acc(1.0, HessPhi_d_d);
}
// result = Laplacian(phi)/|Grad phi|
result.Multiply(1.0, Laplace, ooNormGrad, 0.0, "ik", "ik", "ik");
// result += Grad(1/|Grad(phi)|)
for (int d1 = 0; d1 < D; d1++)
{
var Qd = Q.ExtractSubArrayShallow(-1, -1, d1);
for (int d2 = 0; d2 < D; d2++)
{
var Grad_d2 = GradPhi.ExtractSubArrayShallow(-1, -1, d2);
var Hess_d2_d1 = HessPhi.ExtractSubArrayShallow(-1, -1, d2, d1);
Qd.Multiply(-1.0, Grad_d2, Hess_d2_d1, 1.0, "ik", "ik", "ik");
}
}
ooNormGrad.ApplyAll(x => x * x * x);
result.Multiply(1.0, GradPhi, Q, ooNormGrad, 1.0, "ik", "ikd", "ikd", "ik");
}
/// <summary>
/// ctor
/// </summary>
/// <param name="loc"></param>
/// <param name="QuadNodes">
/// quad nodes outside the grid are ignored, i.e. the integrand is assumed to be 0
/// </param>
/// <param name="quadweights">
/// </param>
public Integrator(CellLocalization loc, double[,] QuadNodes, double[] quadweights)
{
int N = QuadNodes.GetLength(0);
if (N != quadweights.Length)
{
throw new ArgumentException("length of 0-th dimension of arrays must match.");
}
int D = QuadNodes.GetLength(1);
if (D != loc.GridBB.D)
{
throw new ArgumentException("mismatch in spatial dimension.");
}
int J = loc.GrdDat.Cells.NoOfLocalUpdatedCells;
GridData gdat = loc.GrdDat;
grdDat = gdat;
// filter quad nodes outside of the bounding box
// =============================================
MultidimensionalArray QuadNodes2;
double[] quadweights2;
int[] orgindex;
{
double[] pt = new double[D];
BitArray inside = new BitArray(N);
int Found = 0;
for (int n = 0; n < N; n++)
{
for (int d = 0; d < D; d++)
{
pt[d] = QuadNodes[n, d];
}
bool ins = loc.GridBB.Contains(pt);
inside[n] = ins;
if (ins)
{
Found++;
}
}
QuadNodes2 = MultidimensionalArray.Create(Found, D);
quadweights2 = new double[Found];
orgindex = new int[Found];
int cnt = 0;
for (int n = 0; n < N; n++)
{
if (inside[n])
{
for (int d = 0; d < D; d++)
{
QuadNodes2[cnt, d] = QuadNodes[n, d];
}
quadweights2[cnt] = quadweights[cnt];
orgindex[cnt] = n;
cnt++;
}
}
QuadNodes = null;
quadweights = null;
N = Found;
}
// build tree of quad nodes
// ========================
int[] Perm = new int[N];
PointLocalization qn = new PointLocalization(QuadNodes2, loc.GridBB, Perm);
double[] quadwegtNew = new double[N];
int[] origindexNew = new int[N];
for (int n = 0; n < N; n++)
{
quadwegtNew[n] = quadweights2[Perm[n]];
origindexNew[n] = orgindex[Perm[n]];
}
quadweights2 = null;
// 1st index: cell index
// 2nd index: quad node index within cell
// 3rd index: spatial coordinate
List <List <double[]> > QuadNodesPerCell = new List <List <double[]> >();
// 1st index: cell index
// 2nd index: quad node index within cell
List <List <double> > QuadWeightsPerCell = new List <List <double> >();
// 1st index: cell index
// 2nd index: quad node index within cell
List <List <int> > OrigIndexPerCell = new List <List <int> >();
for (int j = 0; j < J; j++)
{
QuadNodesPerCell.Add(new List <double[]>());
QuadWeightsPerCell.Add(new List <double>());
OrigIndexPerCell.Add(new List <int>());
}
// try to assign the quad nodes to cells
// =====================================
BitArray PointsLocatedMarker = new BitArray(N); // mark every node, that we assign to a cell with
int NoOfUnassignedNodes = N;
//int[] Cell4Quadnodes = new int[N];
// loop over cells ...
MultidimensionalArray vertGlobal = new MultidimensionalArray(2);
MultidimensionalArray vertLocal = new MultidimensionalArray(3);
for (int j = 0; j < J; j++)
{
//if (loc.CellMaxCode[j] < Locations[0])
// continue; // skip the cell: contains none of the searched points
//if (loc.CellMinCode[j] > Locations[N - 1])
// continue; // skip the cell: contains none of the searched points
GeomBinTreeBranchCode bbcode; int bbBits;
{
BoundingBoxCode __b = loc.GetCellBoundingBoxCode(j);
bbcode = __b.Branch;
bbBits = (int)__b.SignificantBits;
}
int iP0, Len;
qn.GetPointsInBranch(bbcode, bbBits, out iP0, out Len);
if (Len <= 0)
{
continue;
}
vertGlobal.Allocate(Len, D);
vertLocal.Allocate(1, Len, D);
for (int n = 0; n < Len; n++)
{
for (int d = 0; d < D; d++)
{
vertGlobal[n, d] = qn.Points[n + iP0, d];
}
}
gdat.TransformGlobal2Local(vertGlobal, vertLocal, j, 1, 0);
var splx = gdat.Cells.GetRefElement(j);
for (int n = 0; n < Len; n++)
{
int nPt = n + iP0;
if (PointsLocatedMarker[nPt])
{
continue;
}
double[] pt = new double[D];
for (int d = 0; d < D; d++)
{
pt[d] = vertLocal[0, n, d];
}
if (splx.IsWithin(pt))
{
PointsLocatedMarker[nPt] = true;
NoOfUnassignedNodes--;
//Cell4Quadnodes[nPt] = j;
QuadNodesPerCell[j].Add(pt);
QuadWeightsPerCell[j].Add(quadwegtNew[nPt]);
OrigIndexPerCell[j].Add(origindexNew[nPt]);
}
}
}
// record final data structures
// ============================
//m_QuadNodesPerCell = new MultidimensionalArray[J];
m_QuadNodesPerCell = new NodeSet[J];
m_QuadWeightsPerCell = new double[J][];
m_OriginalQuadNodesIndex = new int[J][];
MaxNumberOfNodes = 0;
for (int j = 0; j < J; j++)
{
List <double[]> NodesInCellj = QuadNodesPerCell[j];
m_QuadWeightsPerCell[j] = QuadWeightsPerCell[j].ToArray();
m_OriginalQuadNodesIndex[j] = OrigIndexPerCell[j].ToArray();
int NJ = NodesInCellj.Count;
if (NJ > 0)
{
var _QuadNodesPerCell_j = new NodeSet(grdDat.Cells.GetRefElement(j), NJ, D);
MaxNumberOfNodes = Math.Max(MaxNumberOfNodes, NJ);
for (int nn = 0; nn < NJ; nn++)
{
for (int d = 0; d < D; d++)
{
_QuadNodesPerCell_j[nn, d] = NodesInCellj[nn][d];
}
}
_QuadNodesPerCell_j.LockForever();
m_QuadNodesPerCell[j] = _QuadNodesPerCell_j;
}
else
{
m_QuadNodesPerCell[j] = null;
}
}
}