public EdgeMask GetEdges4RefElement(RefElement Kref)
{
if (m_Edges4RefElement == null)
{
m_Edges4RefElement = new EdgeMask[this.EdgeRefElements.Length];
}
int iKref = this.EdgeRefElements.IndexOf(Kref, (a, b) => object.ReferenceEquals(a, b));
if (m_Edges4RefElement[iKref] == null)
{
EdgeMask parrEdg = m_Owner.ParentGrid.iGeomEdges.GetEdges4RefElement(Kref);
EdgeMask thisAll = EdgeMask.GetFullMask(this.m_Owner, MaskType.Geometrical);
if (parrEdg.MaskType != MaskType.Geometrical)
{
throw new ApplicationException("expecting a geometrical mask");
}
if (thisAll.MaskType != MaskType.Geometrical)
{
throw new ApplicationException("expecting a geometrical mask");
}
BitArray parrBitmask = parrEdg.GetBitMask().CloneAs();
BitArray thisBitMask = thisAll.GetBitMask();
Debug.Assert(parrBitmask.Length == thisBitMask.Length);
BitArray intersect = parrBitmask.And(thisBitMask);
Debug.Assert(object.ReferenceEquals(intersect, parrBitmask));
m_Edges4RefElement[iKref] = new EdgeMask(m_Owner, intersect, MaskType.Geometrical);
}
return(m_Edges4RefElement[iKref]);
}
protected override void CreateEquationsAndSolvers(GridUpdateDataVaultBase L)
{
using (FuncTrace tr = new FuncTrace()) {
// assemble system, create matrix
// ------------------------------
var volQrSch = new CellQuadratureScheme(true, CellMask.GetFullMask(this.GridData));
var edgQrSch = new EdgeQuadratureScheme(true, EdgeMask.GetFullMask(this.GridData));
double D = this.GridData.SpatialDimension;
double penalty_base = (T.Basis.Degree + 1) * (T.Basis.Degree + D) / D;
double penalty_factor = base.Control.penalty_poisson;
{
// equation assembly
// -----------------
tr.Info("creating sparse system...");
Console.WriteLine("creating sparse system for {0} DOF's ...", T.Mapping.Ntotal);
Stopwatch stw = new Stopwatch();
stw.Start();
SpatialOperator LapaceIp = new SpatialOperator(1, 1, QuadOrderFunc.SumOfMaxDegrees(), "T", "T");
var flux = new ipFlux(penalty_base * base.Control.penalty_poisson, this.GridData.Cells.cj, base.Control);
LapaceIp.EquationComponents["T"].Add(flux);
LapaceIp.Commit();
#if DEBUG
var RefLaplaceMtx = new MsrMatrix(T.Mapping);
#endif
LaplaceMtx = new BlockMsrMatrix(T.Mapping);
LaplaceAffine = new double[T.Mapping.LocalLength];
LapaceIp.ComputeMatrixEx(T.Mapping, null, T.Mapping,
LaplaceMtx, LaplaceAffine,
volQuadScheme: volQrSch, edgeQuadScheme: edgQrSch);
#if DEBUG
LaplaceAffine.ClearEntries();
LapaceIp.ComputeMatrixEx(T.Mapping, null, T.Mapping,
RefLaplaceMtx, LaplaceAffine,
volQuadScheme: volQrSch, edgeQuadScheme: edgQrSch);
MsrMatrix ErrMtx = RefLaplaceMtx.CloneAs();
ErrMtx.Acc(-1.0, LaplaceMtx);
double err = ErrMtx.InfNorm();
double infNrm = LaplaceMtx.InfNorm();
Console.WriteLine("Matrix comparison error: " + err + ", matrix norm is: " + infNrm);
Assert.Less(err, infNrm * 1e-10, "MsrMatrix2 comparison failed.");
#endif
//int q = LaplaceMtx._GetTotalNoOfNonZeros();
//tr.Info("finished: Number of non-zeros: " + q);
stw.Stop();
Console.WriteLine("done {0} sec.", stw.Elapsed.TotalSeconds);
//double condNo = LaplaceMtx.condest(BatchmodeConnector.Flavor.Octave);
//Console.WriteLine("condition number: {0:0.####E-00} ",condNo);
}
}
}
/// <summary>
/// computes <see cref="LaplaceMtx"/> and <see cref="LaplaceAffine"/>
/// </summary>
private void UpdateMatrices() {
using (var tr = new FuncTrace()) {
// time measurement for matrix assembly
Stopwatch stw = new Stopwatch();
stw.Start();
// console
Console.WriteLine("creating sparse system for {0} DOF's ...", T.Mapping.Ntotal);
// quadrature domain
var volQrSch = new CellQuadratureScheme(true, CellMask.GetFullMask(this.GridData, MaskType.Geometrical));
var edgQrSch = new EdgeQuadratureScheme(true, EdgeMask.GetFullMask(this.GridData, MaskType.Geometrical));
#if DEBUG
// in DEBUG mode, we compare 'MsrMatrix' (old, reference implementation) and 'BlockMsrMatrix' (new standard)
var RefLaplaceMtx = new MsrMatrix(T.Mapping);
#endif
using (new BlockTrace("SipMatrixAssembly", tr)) {
LaplaceMtx = new BlockMsrMatrix(T.Mapping);
LaplaceAffine = new double[T.Mapping.LocalLength];
LapaceIp.ComputeMatrixEx(T.Mapping, null, T.Mapping,
LaplaceMtx, LaplaceAffine,
volQuadScheme: volQrSch, edgeQuadScheme: edgQrSch);
}
#if DEBUG
LaplaceAffine.ClearEntries();
LapaceIp.ComputeMatrixEx(T.Mapping, null, T.Mapping,
RefLaplaceMtx, LaplaceAffine,
volQuadScheme: volQrSch, edgeQuadScheme: edgQrSch);
MsrMatrix ErrMtx = RefLaplaceMtx.CloneAs();
ErrMtx.Acc(-1.0, LaplaceMtx);
double err = ErrMtx.InfNorm();
double infNrm = LaplaceMtx.InfNorm();
Console.WriteLine("Matrix comparison error: " + err + ", matrix norm is: " + infNrm);
Assert.Less(err, infNrm * 1e-10, "MsrMatrix2 comparison failed.");
#endif
stw.Stop();
Console.WriteLine("done {0} sec.", stw.Elapsed.TotalSeconds);
//var JB = LapaceIp.GetFDJacobianBuilder(T.Mapping.Fields, null, T.Mapping, edgQrSch, volQrSch);
//var JacobiMtx = new BlockMsrMatrix(T.Mapping);
//var JacobiAffine = new double[T.Mapping.LocalLength];
//JB.ComputeMatrix(JacobiMtx, JacobiAffine);
//double L2ErrAffine = GenericBlas.L2Dist(JacobiAffine, LaplaceAffine);
//var ErrMtx2 = LaplaceMtx.CloneAs();
//ErrMtx2.Acc(-1.0, JacobiMtx);
//double LinfErrMtx2 = ErrMtx2.InfNorm();
//JacobiMtx.SaveToTextFileSparse("D:\\tmp\\Jac.txt");
//LaplaceMtx.SaveToTextFileSparse("D:\\tmp\\Lap.txt");
//Console.WriteLine("FD Jacobi Mtx: {0:e14}, Affine: {1:e14}", LinfErrMtx2, L2ErrAffine);
}
}
public static void Plot(IGrid grid)
{
EdgeMask boundaryEdges = EdgeMask.GetFullMask(grid.iGridData, MaskType.Logical);
boundaryEdges.SaveToTextFile(
"edges.txt",
false,
(double[] CoordGlobal, int LogicalItemIndex, int GeomItemIndex) => grid.iGridData.iGeomEdges.EdgeTags[GeomItemIndex]);
Tecplot plt1 = new Tecplot(grid.iGridData, true, false, 0);
Basis b = new Basis(grid.iGridData, 0);
SinglePhaseField field = new SinglePhaseField(b, "u");
plt1.PlotFields("grid", 0, field);
}
/// <summary>
/// checks whether the linear and nonlinear implementation of operator evaluation are mathematically equal
/// </summary>
void LinearNonlinComparisonTest()
{
int L = this.bnd.CoordinateVector.Count();
// need to assure to use the same quadrature oder on both evaluation variants
var volQrSch = (new CellQuadratureScheme(false, CellMask.GetFullMask(this.GridData, MaskType.Geometrical)))
.AddFixedOrderRules(this.GridData, this.PolynomialDegree * 3);
var edgQrSch = new EdgeQuadratureScheme(true, EdgeMask.GetFullMask(this.GridData, MaskType.Geometrical))
.AddFixedOrderRules(this.GridData, this.PolynomialDegree * 3);
//var volQrSch = new CellQuadratureScheme(true, CellMask.GetEmptyMask(this.GridData));
//var edgQrSch = new EdgeQuadratureScheme(true, EdgeMask.GetEmptyMask(this.GridData));
//var edgQrSch = new EdgeQuadratureScheme(true, this.GridData.BoundaryEdges)
// .AddFixedOrderRules(this.GridData, this.PolynomialDegree * 3);
//var edgQrSch = new EdgeQuadratureScheme(true, this.GridData.BoundaryEdges.Complement())
// .AddFixedOrderRules(this.GridData, this.PolynomialDegree * 3);
for (int run = 0; run < 1; run++)
{
// setup a random test vector
Random rnd = new Random();
var TestArgument = this.bnd.CloneAs().CoordinateVector;
for (int i = 0; i < L; i++)
{
TestArgument[i] = rnd.NextDouble();
}
Stopwatch lin = new Stopwatch();
Stopwatch nol = new Stopwatch();
// linear evaluation
CoordinateVector LinResult = this.ViscU_linear.CoordinateVector;
LinResult.Clear();
lin.Start();
{
var map = this.U.Mapping;
var tempOperatorMtx = new MsrMatrix(map, map);
var tempAffine = new double[L];
Operator.ComputeMatrixEx(map, new DGField[] { this.mu }, map,
tempOperatorMtx, tempAffine,
volQuadScheme: volQrSch, edgeQuadScheme: edgQrSch);
tempOperatorMtx.SpMVpara(1.0, TestArgument, 0.0, LinResult);
LinResult.AccV(1.0, tempAffine);
}
lin.Stop();
// nonliner evaluation
CoordinateVector NolResult = this.ViscU_nonlinear.CoordinateVector;
NolResult.Clear();
nol.Start();
{
var evaluator = Operator.GetEvaluatorEx(TestArgument.Mapping, new DGField[] { this.mu }, this.Residual.Mapping,
volQrCtx: volQrSch, edgeQrCtx: edgQrSch);
evaluator.Evaluate(1.0, 0.0, NolResult);
}
nol.Stop();
double L2Dist = GenericBlas.L2DistPow2(LinResult, NolResult).MPISum().Sqrt();
Console.WriteLine("L2 dist of linear/Nonlinear evaluation comparison: {0}", L2Dist);
LinResult.Acc(-1.0, NolResult);
foreach (SinglePhaseField DGfield in LinResult.Mapping.Fields)
{
for (int p = 0; p <= DGfield.Basis.Degree; p++)
{
double L2err_p = DGfield.L2NormPerMode(p);
Console.WriteLine(" ERR{2} {1} \t{0}", L2err_p, DGfield.Identification, p);
}
}
Console.WriteLine("Time linear {0}, time nonlinear: {1}", lin.Elapsed, nol.Elapsed);
Assert.LessOrEqual(L2Dist, 1.0e-4, "L2 distance between linear and nonlinear evaluation of the same flux.");
}
}
/// <summary>
/// computes <see cref="LaplaceMtx"/> and <see cref="LaplaceAffine"/>
/// </summary>
private void UpdateMatrices()
{
using (var tr = new FuncTrace()) {
// time measurement for matrix assembly
Stopwatch stw = new Stopwatch();
stw.Start();
// Stats:
{
int BlkSize = T.Mapping.MaxTotalNoOfCoordinatesPerCell;
int NoOfMtxBlocks = 0;
foreach (int[] Neigs in this.GridData.iLogicalCells.CellNeighbours)
{
NoOfMtxBlocks++; // diagonal block
NoOfMtxBlocks += Neigs.Length; // off-diagonal block
}
NoOfMtxBlocks = NoOfMtxBlocks.MPISum();
int MtxBlockSize = BlkSize * BlkSize;
int MtxSize = MtxBlockSize * NoOfMtxBlocks;
double MtxStorage = MtxSize * (8.0 + 4.0) / (1024 * 1024); // 12 bytes (double+int) per entry
Console.WriteLine(" System size: {0}", T.Mapping.TotalLength);
Console.WriteLine(" No of blocks: {0}", T.Mapping.TotalNoOfBlocks);
Console.WriteLine(" No of blocks in matrix: {0}", NoOfMtxBlocks);
Console.WriteLine(" DG coordinates per cell: {0}", BlkSize);
Console.WriteLine(" Non-zeros per matrix block: {0}", MtxBlockSize);
Console.WriteLine(" Total non-zeros in matrix: {0}", MtxSize);
Console.WriteLine(" Approx. matrix storage (MB): {0}", MtxStorage);
base.QueryHandler.ValueQuery("MtxBlkSz", MtxBlockSize, true);
base.QueryHandler.ValueQuery("NNZMtx", MtxSize, true);
base.QueryHandler.ValueQuery("NNZblk", NoOfMtxBlocks, true);
base.QueryHandler.ValueQuery("MtxMB", MtxStorage, true);
}
Console.WriteLine("creating sparse system for {0} DOF's ...", T.Mapping.Ntotal);
// quadrature domain
var volQrSch = new CellQuadratureScheme(true, CellMask.GetFullMask(this.GridData, MaskType.Geometrical));
var edgQrSch = new EdgeQuadratureScheme(true, EdgeMask.GetFullMask(this.GridData, MaskType.Geometrical));
using (new BlockTrace("SipMatrixAssembly", tr)) {
LaplaceMtx = new BlockMsrMatrix(T.Mapping);
LaplaceAffine = new double[T.Mapping.LocalLength];
LapaceIp.ComputeMatrixEx(T.Mapping, null, T.Mapping,
LaplaceMtx, LaplaceAffine,
volQuadScheme: volQrSch, edgeQuadScheme: edgQrSch);
}
stw.Stop();
//Print process information
Console.WriteLine("done {0} sec.", stw.Elapsed.TotalSeconds);
LaplaceMtx.GetMemoryInfo(out long AllocatedMem, out long UsedMem);
Console.WriteLine(" Used matrix storage (MB): {0}", UsedMem / (1024.0 * 1024));
Console.WriteLine(" Alloc. matrix storage (MB): {0}", AllocatedMem / (1024.0 * 1024));
}
}
public IEnumerable <IChunkRulePair <QuadRule> > GetQuadRuleSet(ExecutionMask mask, int order)
{
if (mask == null)
{
mask = EdgeMask.GetFullMask(tracker.Ctx.GridDat);
}
if (mask is EdgeMask == false)
{
throw new Exception();
}
QuadRule baseRule = lineSimplex.GetQuadratureRule(order);
int D = tracker.Ctx.Grid.GridSimplex.SpatialDimension;
var result = new List <ChunkRulePair <QuadRule> >(mask.NoOfItemsLocally);
foreach (Chunk chunk in mask)
{
for (int i = 0; i < chunk.Len; i++)
{
List <double[]> nodes = new List <double[]>();
List <double> weights = new List <double>();
int[] noOfNodesPerEdge = new int[referenceLineSegments.Length];
int edge = i + chunk.i0;
// Always choose 'left' edge
int cell = tracker.Ctx.GridDat.Edges[edge, 0];
int localEdge = tracker.Ctx.GridDat.EdgeIndices[edge, 0];
LineSegment referenceSegment = referenceLineSegments[localEdge];
double[] roots = referenceSegment.GetRoots(tracker.LevelSets[levSetIndex], cell);
LineSegment[] subSegments = referenceSegment.Split(roots);
for (int k = 0; k < subSegments.Length; k++)
{
for (int m = 0; m < baseRule.NoOfNodes; m++)
{
// Base rule _always_ is a line rule, thus Nodes[*, _0_]
double[] point = subSegments[k].GetPointOnSegment(baseRule.Nodes[m, 0]);
uint lh = tracker.Ctx.NSC.LockNodeSetFamily(
tracker.Ctx.NSC.CreateContainer(
MultidimensionalArray.CreateWrapper(point, 1, D), -1.0));
MultidimensionalArray levelSetValue = tracker.GetLevSetValues(levSetIndex, 0, cell, 1);
tracker.Ctx.NSC.UnlockNodeSetFamily(lh);
// Only positive volume
if (levelSetValue[0, 0] <= 0.0)
{
continue;
}
weights.Add(baseRule.Weights[m] * subSegments[k].Length / referenceSegment.Length);
nodes.Add(point);
}
}
if (weights.Count == 0)
{
continue;
}
MultidimensionalArray localNodes = MultidimensionalArray.Create(nodes.Count, D);
for (int j = 0; j < nodes.Count; j++)
{
for (int d = 0; d < D; d++)
{
localNodes[j, d] = nodes[j][d];
}
}
MultidimensionalArray localEdgeNodes = MultidimensionalArray.Create(nodes.Count, 1);
tracker.Ctx.Grid.GridSimplex.VolumeToEdgeCoordinates(localEdge, localNodes, localEdgeNodes);
QuadRule subdividedRule = new QuadRule()
{
OrderOfPrecision = order,
Weights = MultidimensionalArray.Create(weights.Count),
Nodes = localEdgeNodes.CloneAs()
};
subdividedRule.Weights.SetV(weights, -1);
result.Add(new ChunkRulePair <QuadRule>(
Chunk.GetSingleElementChunk(edge), subdividedRule));
}
}
return(result);
}
protected override void CreateEquationsAndSolvers(GridUpdateDataVaultBase L)
{
using (FuncTrace tr = new FuncTrace()) {
this.BcMap = new IncompressibleBoundaryCondMap(this.GridData, grid.GetBoundaryConfig(), PhysicsMode.Incompressible);
// assemble system, create matrix
// ------------------------------
var volQrSch = new CellQuadratureScheme(true, CellMask.GetFullMask(this.GridData));
var edgQrSch = new EdgeQuadratureScheme(true, EdgeMask.GetFullMask(this.GridData));
//var volQrSch = new CellQuadratureScheme(true, CellMask.GetEmptyMask(this.GridData));
//var edgQrSch = new EdgeQuadratureScheme(true, EdgeMask.GetEmptyMask(this.GridData));
//var edgQrSch = new EdgeQuadratureScheme(true, this.GridDat.BoundaryEdges);
//var edgQrSch = new EdgeQuadratureScheme(true, this.GridDat.BoundaryEdges.Complement());
int D = GridData.SpatialDimension;
double penalty_base = ((double)((U[0].Basis.Degree + 1) * (U[0].Basis.Degree + D))) / ((double)D);
double penalty_factor = 1.2;
// equation assembly
// -----------------
string[] CodNames = D.ForLoop(i => "C" + i);
Operator = new SpatialOperator(VariableNames.VelocityVector(D), new string[] { VariableNames.ViscosityMolecular }, CodNames, QuadOrderFunc.Linear());
for (int d = 0; d < D; d++)
{
if ((this.whichTerms & Terms.T1) != 0)
{
var flx1 = new swipViscosity_Term1(penalty_base * penalty_factor, this.GridData.Cells.cj, d, D, BcMap, this.viscOption, ViscosityOption.VariableViscosity);
flx1.g_Diri_Override = this.solution.U;
flx1.g_Neu_Override = this.solution.dU;
Operator.EquationComponents[CodNames[d]].Add(flx1);
}
if ((this.whichTerms & Terms.T2) != 0)
{
var flx2 = new swipViscosity_Term2(penalty_base * penalty_factor, this.GridData.Cells.cj, d, D, BcMap, this.viscOption, ViscosityOption.VariableViscosity);
flx2.g_Diri_Override = this.solution.U;
flx2.g_Neu_Override = this.solution.dU;
Operator.EquationComponents[CodNames[d]].Add(flx2);
}
if ((this.whichTerms & Terms.T3) != 0)
{
var flx3 = new swipViscosity_Term3(penalty_base * penalty_factor, this.GridData.Cells.cj, d, D, BcMap, this.viscOption, ViscosityOption.VariableViscosity);
flx3.g_Diri_Override = this.solution.U;
flx3.g_Neu_Override = this.solution.dU;
Operator.EquationComponents[CodNames[d]].Add(flx3);
}
} // */
Operator.Commit();
var map = this.U.Mapping;
OperatorMtx = new MsrMatrix(map, map);
Operator.ComputeMatrixEx(map, new DGField[] { this.mu }, map,
OperatorMtx, this.bnd.CoordinateVector,
volQuadScheme: volQrSch, edgeQuadScheme: edgQrSch);
// test for matrix symmetry
// ========================
if (base.MPISize == 1)
{
double MatrixAssymmetry = OperatorMtx.SymmetryDeviation();
Console.WriteLine("Matrix asymmetry: " + MatrixAssymmetry);
Assert.LessOrEqual(Math.Abs(MatrixAssymmetry), 1.0e-10);
}
}
}
/// <summary>
/// Includes assembly of the matrix.
/// </summary>
/// <param name="L"></param>
protected override void CreateEquationsAndSolvers(GridUpdateDataVaultBase L)
{
using (FuncTrace tr = new FuncTrace()) {
// create operator
// ===============
SpatialOperator LapaceIp;
{
double D = this.GridData.SpatialDimension;
double penalty_base = (T.Basis.Degree + 1) * (T.Basis.Degree + D) / D;
double penalty_factor = base.Control.penalty_poisson;
BoundaryCondMap <BoundaryType> PoissonBcMap = new BoundaryCondMap <BoundaryType>(this.GridData, this.Control.BoundaryValues, "T");
LapaceIp = new SpatialOperator(1, 1, QuadOrderFunc.SumOfMaxDegrees(), "T", "T");
var flux = new ipFlux(penalty_base * base.Control.penalty_poisson, this.GridData.Cells.cj, PoissonBcMap);
LapaceIp.EquationComponents["T"].Add(flux);
LapaceIp.Commit();
}
// Create Matrices
// ===============
{
// time measurement for matrix assembly
Stopwatch stw = new Stopwatch();
stw.Start();
// console
Console.WriteLine("creating sparse system for {0} DOF's ...", T.Mapping.Ntotal);
// quadrature domain
var volQrSch = new CellQuadratureScheme(true, CellMask.GetFullMask(this.GridData));
var edgQrSch = new EdgeQuadratureScheme(true, EdgeMask.GetFullMask(this.GridData));
#if DEBUG
// in DEBUG mode, we compare 'MsrMatrix' (old, reference implementation) and 'BlockMsrMatrix' (new standard)
var RefLaplaceMtx = new MsrMatrix(T.Mapping);
#endif
using (new BlockTrace("SipMatrixAssembly", tr)) {
LaplaceMtx = new BlockMsrMatrix(T.Mapping);
LaplaceAffine = new double[T.Mapping.LocalLength];
LapaceIp.ComputeMatrixEx(T.Mapping, null, T.Mapping,
LaplaceMtx, LaplaceAffine,
volQuadScheme: volQrSch, edgeQuadScheme: edgQrSch);
}
#if DEBUG
LaplaceAffine.ClearEntries();
LapaceIp.ComputeMatrixEx(T.Mapping, null, T.Mapping,
RefLaplaceMtx, LaplaceAffine,
volQuadScheme: volQrSch, edgeQuadScheme: edgQrSch);
MsrMatrix ErrMtx = RefLaplaceMtx.CloneAs();
ErrMtx.Acc(-1.0, LaplaceMtx);
double err = ErrMtx.InfNorm();
double infNrm = LaplaceMtx.InfNorm();
Console.WriteLine("Matrix comparison error: " + err + ", matrix norm is: " + infNrm);
Assert.Less(err, infNrm * 1e-10, "MsrMatrix2 comparison failed.");
#endif
stw.Stop();
Console.WriteLine("done {0} sec.", stw.Elapsed.TotalSeconds);
}
//double condNo = LaplaceMtx.condest(BatchmodeConnector.Flavor.Octave);
//Console.WriteLine("condition number: {0:0.####E-00} ",condNo);
}
}