static double JumpNorm(DGField f)
{
GridData grd = (GridData)f.GridDat;
int D = grd.SpatialDimension;
var e2cTrafo = grd.Edges.Edge2CellTrafos;
f.MPIExchange();
double Unorm = 0;
EdgeQuadrature.GetQuadrature(
new int[] { D + 1 }, grd,
(new EdgeQuadratureScheme()).Compile(grd, f.Basis.Degree * 2),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) { // Evaluate
NodeSet NS = QR.Nodes;
EvalResult.Clear();
int NoOfNodes = NS.NoOfNodes;
for (int j = 0; j < Length; j++)
{
int iEdge = j + i0;
int jCell_IN = grd.Edges.CellIndices[iEdge, 0];
int jCell_OT = grd.Edges.CellIndices[iEdge, 1];
var uDiff = EvalResult.ExtractSubArrayShallow(new int[] { j, 0, 0 }, new int[] { j, NoOfNodes - 1, -1 });
if (jCell_OT >= 0)
{
int iTrafo_IN = grd.Edges.Edge2CellTrafoIndex[iEdge, 0];
int iTrafo_OT = grd.Edges.Edge2CellTrafoIndex[iEdge, 1];
MultidimensionalArray uIN = MultidimensionalArray.Create(1, NoOfNodes);
MultidimensionalArray uOT = MultidimensionalArray.Create(1, NoOfNodes);
NodeSet NS_IN = NS.GetVolumeNodeSet(grd, iTrafo_IN);
NodeSet NS_OT = NS.GetVolumeNodeSet(grd, iTrafo_OT);
f.Evaluate(jCell_IN, 1, NS_IN, uIN);
f.Evaluate(jCell_OT, 1, NS_OT, uOT);
uDiff.Acc(+1.0, uIN);
uDiff.Acc(-1.0, uOT);
}
else
{
uDiff.Clear();
}
}
EvalResult.ApplyAll(x => x * x);
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) { // SaveIntegrationResults
Unorm += ResultsOfIntegration.Sum();
}).Execute();
Unorm = Unorm.MPISum();
return(Unorm.Sqrt());
}
/// <summary>
/// Change-of-basis, in cell 0
/// </summary>
/// <param name="jCell"></param>
/// <param name="pl"></param>
public MultidimensionalArray GetChangeofBasisMatrix(int jCell, PolynomialList pl)
{
var m_Context = this.GridDat;
int N = this.Length;
int M = pl.Count;
int J = this.GridDat.iLogicalCells.NoOfLocalUpdatedCells;
if (jCell < 0 || jCell >= J)
{
throw new ArgumentOutOfRangeException("cell index out of range");
}
MultidimensionalArray Mtx = MultidimensionalArray.Create(N, M);
var cellMask = new CellMask(m_Context, new[] { new Chunk()
{
i0 = jCell, Len = 1
} }, MaskType.Geometrical);
// we project the basis function from 'jCell1' onto 'jCell0'
CellQuadrature.GetQuadrature(new int[2] {
N, M
}, m_Context,
(new CellQuadratureScheme(true, cellMask)).Compile(m_Context, this.Degree + pl.MaxAbsoluteDegree), // 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, jCell, 1).ExtractSubArrayShallow(0, -1, -1);
MultidimensionalArray R = MultidimensionalArray.Create(QR.NoOfNodes, pl.Count);
pl.Evaluate(nodes_Cell0, R);
var EvalResult = _EvalResult.ExtractSubArrayShallow(0, -1, -1, -1);
EvalResult.Multiply(1.0, R, phi_0, 0.0, "knm", "km", "kn");
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
Debug.Assert(Length == 1);
var res = ResultsOfIntegration.ExtractSubArrayShallow(0, -1, -1);
Mtx.Clear();
Mtx.Acc(1.0, res);
}).Execute();
return(Mtx);
}
private MultidimensionalArray EdgeQuadrature(ICompositeQuadRule <QuadRule> surfRule)
{
int E = this.GridData.iLogicalEdges.Count;
var ret = MultidimensionalArray.Create(E);
BoSSS.Foundation.Quadrature.EdgeQuadrature.GetQuadrature(
new int[] { 1 }, this.GridData,
surfRule,
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) { // Evaluate
EvalResult.SetAll(1.0);
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) { // SaveIntegrationResults
ret.ExtractSubArrayShallow(new int[] { i0 }, new int[] { i0 + Length - 1 })
.Set(ResultsOfIntegration.ExtractSubArrayShallow(-1, 0));
}).Execute();
return(ret);
}
void OrthonormalityTest()
{
Basis B = f1.Basis;
int N = B.Length;
var Mtx = new FullMatrix(N, N);
double TotErrSum = 0.0;
CellQuadrature.GetQuadrature(new int[] { N, N }, this.GridDat,
(new CellQuadratureScheme(true)).Compile(GridDat, Math.Min(B.Degree * 2, 16)),
delegate(MultidimensionalArray NodesUntransformed, int iKref) {
var ret = new NodeSetController.NodeSetContainer[] {
GridDat.NSC.CreateContainer(NodesUntransformed, iKref)
};
return(ret);
},
delegate(int i0, int Length, int NoOfNodes, MultidimensionalArray EvalResult) { // void Del_Evaluate
var BasisVal = B.CellEval(0, i0, Length);
EvalResult.Multiply(1.0, BasisVal, BasisVal, 0.0, "jknm", "jkn", "jkm");
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) { // SaveIntegrationResults
for (int i = 0; i < Length; i++)
{
var MassMtx = ResultsOfIntegration.ExtractSubArrayShallow(i, -1, -1);
double errsum = 0;
for (int n = 0; n < N; n++)
{
for (int m = 0; m < N; m++)
{
double soll = (n == m) ? 1.0 : 0.0;
errsum += Math.Abs(MassMtx[m, n] - soll);
}
}
TotErrSum += errsum;
}
}).Execute();
Console.WriteLine("orthonormality error sum:" + TotErrSum);
}
private MultidimensionalArray CellQuadrature(ICompositeQuadRule <QuadRule> surfRule)
{
int J = this.GridData.iLogicalCells.NoOfLocalUpdatedCells;
var ret = MultidimensionalArray.Create(J);
BoSSS.Foundation.Quadrature.CellQuadrature.GetQuadrature(
new int[] { 1 }, this.GridData,
surfRule,
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) { // Evaluate
//Integrand.Evaluate(i0, Length, 0, EvalResult.ExtractSubArrayShallow(-1, -1, 0));
EvalResult.SetAll(1.0);
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) { // SaveIntegrationResults
var A = ret.ExtractSubArrayShallow(new int[] { i0 }, new int[] { i0 + Length - 1 });
var B = ResultsOfIntegration.ExtractSubArrayShallow(-1, 0);
A.Set(B);
}).Execute();
return(ret);
}
MultidimensionalArray StokesAnsatzRHS(Basis TestBasis, CellBoundaryQuadratureScheme cellBndSchme, CellMask _mask, int order)
{
var GridDat = this.tracker.GridDat;
CellBoundaryQuadrature <CellBoundaryQuadRule> qBnd = null;
int N = TestBasis.Length;
int D = GridDat.SpatialDimension;
MultidimensionalArray RHS = MultidimensionalArray.Create(D, N, _mask.NoOfItemsLocally);
double[] CellN = new double[D]; // cell normal
double[] SurfN = new double[D]; // level-set normal
double[] OutwardTang = new double[D]; // level-set tangent, outward of cell
if (D != 2)
{
throw new NotSupportedException("Currently only supported for spatial dimension of 2.");
}
//MultidimensionalArray Nudes = null;
int jSgrd = 0;
qBnd = CellBoundaryQuadrature <CellBoundaryQuadRule> .GetQuadrature(new int[] { D, N },
GridDat, cellBndSchme.Compile(GridDat, order),
delegate(int i0, int Length, CellBoundaryQuadRule NS, MultidimensionalArray EvalResult) { // Evaluate
//MultidimensionalArray BasisValues = TestBasis.Evaluate(0); // reference
//var LSNormals = LsTrk.GetLevelSetReferenceNormals(iLevSet, 0, i0, Length); // reference
MultidimensionalArray BasisValues = TestBasis.CellEval(NS.Nodes, i0, Length); // physical
MultidimensionalArray LSNormals = this.LevelSetData.GetLevelSetNormals(NS.Nodes, i0, Length); // physical
for (int i = 0; i < Length; i++) // loop over cells
//if(i0 + i == 1) {
// EvalResult.ExtractSubArrayShallow(i, -1, -1, -1).Clear();
// continue;
//}
{
CellBoundaryQuadRule cR = qBnd.CurrentRule;
int[] NodesPerEdge = cR.NumbersOfNodesPerFace;
var Kref = cR.RefElement;
int NoOfFaces = Kref.NoOfFaces;
int iNode = 0;
Debug.Assert(NoOfFaces == NodesPerEdge.Length);
for (int e = 0; e < NoOfFaces; e++) // loop over the faces of the cell
{
if (NodesPerEdge[e] <= 0)
{
continue;
}
// reference:
//for (int d = 0; d < D; d++) {
// CellN[d] = Kref.FaceNormals[e, d];
//}
// ~~~~
// physical:
var FaceNodes = new NodeSet(Kref, cR.Nodes.ExtractSubArrayShallow(new int[] { iNode, 0 }, new int[] { iNode + NodesPerEdge[e] - 1, D - 1 }));
var FaceNormals = MultidimensionalArray.Create(NodesPerEdge[e], D);
GridDat.Edges.GetNormalsForCell(FaceNodes, i0, e, FaceNormals);
// ~~~~
for (int _n = 0; _n < NodesPerEdge[e]; _n++) // loop over nodes in one edge
{
for (int d = 0; d < D; d++)
{
SurfN[d] = LSNormals[i, iNode, d];
CellN[d] = FaceNormals[_n, d]; // physical
}
tangente(SurfN, CellN, OutwardTang);
for (int n = 0; n < N; n++) // loop over Test polynomials (the same as the basis polynomials)
{
for (int d = 0; d < D; d++) // loop over spatial direction
{
EvalResult[i, iNode, d, n] = BasisValues[i, iNode, n] * OutwardTang[d]; // physical
//EvalResult[i, iNode, d, n] = BasisValues[iNode, n]*OutwardTang[d]; // reference
}
}
iNode++;
}
}
Debug.Assert(iNode == EvalResult.GetLength(1));
}
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) { // SaveIntegrationResults
for (int i = 0; i < Length; i++)
{
var ResPart = RHS.ExtractSubArrayShallow(new int[] { 0, 0, jSgrd }, new int[] { D - 1, N - 1, jSgrd - 1 });
int NoOfFaces = ResultsOfIntegration.GetLength(1);
for (int e = 0; e < NoOfFaces; e++)
{
var ip = ResultsOfIntegration.ExtractSubArrayShallow(new int[] { i, e, 0, 0 }, new int[] { i - 1, e - 1, D - 1, N - 1 });
ResPart.Acc(1.0, ip);
}
jSgrd++;
}
},
cs : CoordinateSystem.Physical);
qBnd.Execute();
var ret = RHS.ResizeShallow(N * D, _mask.NoOfItemsLocally);
return(ret);
}
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);
}
/// <summary>
/// computes derivatives in various ways and compares them against known values.
/// </summary>
protected override double RunSolverOneStep(int TimestepNo, double phystime, double dt)
{
base.EndTime = 0.0;
base.NoOfTimesteps = 0;
int D = this.GridData.SpatialDimension;
int J = this.GridData.iLogicalCells.NoOfLocalUpdatedCells;
Console.WriteLine("DerivativeTest.exe, test case #" + GRID_CASE + " ******************************");
//var Fix = this.GridData.iGeomEdges.FaceIndices;
//for(int iEdge = 0; iEdge < Fix.GetLength(0); iEdge++) {
// Debug.Assert(Fix[iEdge, 0] >= 0);
// Debug.Assert(Fix[iEdge, 1] >= 0);
//}
// sealing test
// =================
if (this.GridData is Foundation.Grid.Classic.GridData)
{
TestSealing(this.GridData);
}
// cell volume and edge area check, if possible
// ===============================================
if (this.CellVolume > 0)
{
double err = 0;
double Treshold = 1.0e-10;
for (int j = 0; j < J; j++)
{
err += Math.Abs(this.GridData.iLogicalCells.GetCellVolume(j) - this.CellVolume);
}
bool passed = (err < Treshold);
m_passed = m_passed && passed;
Console.WriteLine("Cell volume error: " + err + " passed? " + passed);
Console.WriteLine("--------------------------------------------");
}
if (this.EdgeArea > 0)
{
double err = 0;
double Treshold = 1.0e-10;
int E = this.GridData.iLogicalEdges.Count;
for (int e = 0; e < E; e++)
{
err += Math.Abs(this.GridData.iLogicalEdges.GetEdgeArea(e) - this.EdgeArea);
}
bool passed = (err < Treshold);
m_passed = m_passed && passed;
Console.WriteLine("Edge area error: " + err + " passed? " + passed);
Console.WriteLine("--------------------------------------------");
}
// Orthonormality of basis in physical coords
// ==========================================
{
Basis Bs = this.f1.Basis;
int N = Bs.Length;
int degQuad = this.GridData.iLogicalCells.GetInterpolationDegree(0) * D + Bs.Degree + 3;
int[] jG2jL = this.GridData.iGeomCells.GeomCell2LogicalCell;
// mass matrix: should be identity!
MultidimensionalArray MassMatrix = MultidimensionalArray.Create(J, N, N);
// compute mass matrix by quadrature.
var quad = CellQuadrature.GetQuadrature(new int[] { N, N }, base.GridData,
(new CellQuadratureScheme()).Compile(base.GridData, degQuad),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
NodeSet QuadNodes = QR.Nodes;
MultidimensionalArray BasisVals = Bs.CellEval(QuadNodes, i0, Length);
EvalResult.Multiply(1.0, BasisVals, BasisVals, 0.0, "jknm", "jkn", "jkm");
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
if (jG2jL != null)
{
for (int i = 0; i < Length; i++)
{
int jG = i + i0;
MassMatrix.ExtractSubArrayShallow(jG2jL[jG], -1, -1)
.Acc(1.0, ResultsOfIntegration.ExtractSubArrayShallow(i, -1, -1));
}
}
else
{
MassMatrix.SetSubArray(ResultsOfIntegration, new int[] { i0, 0, 0 }, new int[] { i0 + Length - 1, N - 1, N - 1 });
}
},
cs: CoordinateSystem.Physical);
quad.Execute();
// check that mass matrix is Id.
int MaxErrorCell = -1;
double MaxError = -1;
for (int j = 0; j < J; j++)
{
MultidimensionalArray MassMatrix_j = MassMatrix.ExtractSubArrayShallow(j, -1, -1);
MassMatrix_j.AccEye(-1.0);
double Norm_j = MassMatrix_j.InfNorm();
if (Norm_j > MaxError)
{
MaxError = Norm_j;
MaxErrorCell = j;
}
}
bool passed = (MaxError < 1.0e-8);
m_passed = m_passed && passed;
Console.WriteLine("Mass Matrix, maximum error in Cell #" + MaxErrorCell + ", mass matrix error norm: " + MaxError + " passed? " + passed);
}
// Broken Derivatives
// =================
double totalVolume = (new SubGrid(CellMask.GetFullMask(this.GridData))).Volume;
for (int d = 0; d < D; d++)
{
// compute
f1Gradient_Numerical[d].Clear();
f1Gradient_Numerical[d].Derivative(1.0, f1, d);
f2Gradient_Numerical[d].Clear();
f2Gradient_Numerical[d].Derivative(1.0, f2, d);
// subtract analytical
var Errfield1 = f1Gradient_Numerical[d].CloneAs();
Errfield1.Acc(-1, f1Gradient_Analytical[d]);
var Errfield2 = f2Gradient_Numerical[d].CloneAs();
Errfield2.Acc(-1, f2Gradient_Analytical[d]);
Console.WriteLine("Broken Derivatives: ");
double Treshold = 1.0e-10;
if (AltRefSol)
{
Treshold = 1.0e-4; // not exactly polynomial, therefore a higher threshold
}
double err1_dx = Errfield1.L2Norm() / totalVolume;
bool passed = (err1_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df1/dx{0}_Numerical - df1/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err1_dx, passed));
double err2_dx = Errfield2.L2Norm() / totalVolume;
passed = (err2_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df2/dx{0}_Numerical - df2/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err2_dx, passed));
Console.WriteLine("--------------------------------------------");
}
// Flux Derivatives
// =================
for (int d = 0; d < D; d++)
{
// compute
f1Gradient_Numerical[d].Clear();
f1Gradient_Numerical[d].DerivativeByFlux(1.0, f1, d);
f2Gradient_Numerical[d].Clear();
f2Gradient_Numerical[d].DerivativeByFlux(1.0, f2, d);
f1Gradient_Numerical[d].CheckForNanOrInf(true, true, true);
f2Gradient_Numerical[d].CheckForNanOrInf(true, true, true);
// subtract analytical
var Errfield1 = f1Gradient_Numerical[d].CloneAs();
Errfield1.Acc(-1, f1Gradient_Analytical[d]);
var Errfield2 = f2Gradient_Numerical[d].CloneAs();
Errfield2.Acc(-1, f2Gradient_Analytical[d]);
Console.WriteLine("Flux Derivatives: ");
double Treshold = 1.0e-10;
if (AltRefSol)
{
Treshold = 1.0e-4; // not exactly polynomial, therefore a higher threshold
}
double err1_dx = Errfield1.L2Norm() / totalVolume;
bool passed = (err1_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df1/dx{0}_Numerical - df1/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err1_dx, passed));
double err2_dx = Errfield2.L2Norm() / totalVolume;
passed = (err2_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df2/dx{0}_Numerical - df2/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err2_dx, passed));
Console.WriteLine("--------------------------------------------");
}
// Linear flux Derivatives
// =======================
for (int d = 0; d < D; d++)
{
double[] korrekto = f1Gradient_Numerical[d].CoordinateVector.ToArray();
// compute
DerivativeByFluxLinear(f1, f1Gradient_Numerical[d], d, f1);
DerivativeByFluxLinear(f2, f2Gradient_Numerical[d], d, f2);
// subtract analytical
var Errfield1 = f1Gradient_Numerical[d].CloneAs();
Errfield1.Acc(-1, f1Gradient_Analytical[d]);
var Errfield2 = f2Gradient_Numerical[d].CloneAs();
Errfield2.Acc(-1, f2Gradient_Analytical[d]);
Console.WriteLine("Linear Flux Derivatives: ");
double Treshold = 1.0e-10;
if (AltRefSol)
{
Treshold = 1.0e-4; // not exactly polynomial, therefore a higher threshold
}
double err1_dx = Errfield1.L2Norm() / totalVolume;
bool passed = (err1_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df1/dx{0}_Numerical - df1/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err1_dx, passed));
double err2_dx = Errfield2.L2Norm() / totalVolume;
passed = (err2_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df2/dx{0}_Numerical - df2/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err2_dx, passed));
Console.WriteLine("--------------------------------------------");
}
// Laplacian, nonlinear
// ====================
if (!AltRefSol)
{
var Laplace = (new ipLaplace()).Operator(1);
Laplace.Evaluate(new DGField[] { this.f1 }, new DGField[] { this.Laplace_f1_Numerical });
Laplace.Evaluate(new DGField[] { this.f2 }, new DGField[] { this.Laplace_f2_Numerical });
double Treshold = 1.0e-8;
// subtract analytical
var Errfield1 = Laplace_f1_Numerical.CloneAs();
Errfield1.Acc(-1, Laplace_f1_Analytical);
var Errfield2 = Laplace_f2_Numerical.CloneAs();
Errfield2.Acc(-1, Laplace_f2_Analytical);
double err_Lf1 = Errfield1.L2Norm() / totalVolume;
bool passed = (err_Lf1 < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| /\\f1 Numerical - /\\f1 Analytical ||_2 = {0} (nonlinear evaluation), passed? {1}", err_Lf1, passed));
double err_Lf2 = Errfield2.L2Norm() / totalVolume;
passed = (err_Lf2 < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| /\\f2 Numerical - /\\f2 Analytical ||_2 = {0} (nonlinear evaluation), passed? {1}", err_Lf2, passed));
Console.WriteLine("--------------------------------------------");
}
// Laplacian, linear
// ====================
if (!AltRefSol)
{
var Laplace = (new ipLaplace()).Operator(1);
var LaplaceMtx = new BlockMsrMatrix(this.f1.Mapping, this.Laplace_f1_Numerical.Mapping);
var LaplaceAffine = new double[LaplaceMtx.RowPartitioning.LocalLength];
Laplace.ComputeMatrix(this.f1.Mapping, null, this.Laplace_f1_Numerical.Mapping,
LaplaceMtx, LaplaceAffine, false);
this.Laplace_f1_Numerical.CoordinateVector.SetV(LaplaceAffine);
LaplaceMtx.SpMV(1.0, this.f1.CoordinateVector, 1.0, this.Laplace_f1_Numerical.CoordinateVector);
this.Laplace_f2_Numerical.CoordinateVector.SetV(LaplaceAffine);
LaplaceMtx.SpMV(1.0, this.f2.CoordinateVector, 1.0, this.Laplace_f2_Numerical.CoordinateVector);
// subtract analytical
var Errfield1 = Laplace_f1_Numerical.CloneAs();
Errfield1.Acc(-1, Laplace_f1_Analytical);
var Errfield2 = Laplace_f2_Numerical.CloneAs();
Errfield2.Acc(-1, Laplace_f2_Analytical);
double Treshold = 1.0e-8;
double err_Lf1 = Errfield1.L2Norm() / totalVolume;
bool passed = (err_Lf1 < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| /\\f1 Numerical - /\\f1 Analytical ||_2 = {0} (linear evaluation), passed? {1}", err_Lf1, passed));
double err_Lf2 = Errfield2.L2Norm() / totalVolume;
passed = (err_Lf2 < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| /\\f2 Numerical - /\\f2 Analytical ||_2 = {0} (linear evaluation), passed? {1}", err_Lf2, passed));
// comparison of finite difference Jacobian and Operator matrix
if (TestFDJacobian)
{
this.f1.Clear();
var FDJbuilder = Laplace.GetFDJacobianBuilder(this.f1.Mapping.Fields, null, this.f1.Mapping,
delegate(IEnumerable <DGField> U0, IEnumerable <DGField> Params) {
return;
});
var CheckMatrix = new BlockMsrMatrix(FDJbuilder.CodomainMapping, FDJbuilder.DomainMapping);
var CheckAffine = new double[FDJbuilder.CodomainMapping.LocalLength];
FDJbuilder.ComputeMatrix(CheckMatrix, CheckAffine);
var ErrMatrix = LaplaceMtx.CloneAs();
var ErrAffine = LaplaceAffine.CloneAs();
ErrMatrix.Acc(-1.0, CheckMatrix);
ErrAffine.AccV(-1.0, CheckAffine);
double LinfMtx = ErrMatrix.InfNorm();
double L2Aff = ErrAffine.L2NormPow2().MPISum().Sqrt();
bool passed1 = (LinfMtx < 1.0e-3);
bool passed2 = (L2Aff < Treshold);
Console.WriteLine("Finite Difference Jacobian: Matrix/Affine delta norm {0} {1}, passed? {2} {3}", LinfMtx, L2Aff, passed1, passed2);
m_passed = m_passed && passed1;
m_passed = m_passed && passed2;
}
Console.WriteLine("--------------------------------------------");
}
// finally...
// =================
if (m_passed)
{
Console.WriteLine("All tests passed. *****************************");
}
else
{
Console.WriteLine("Some error above threshold. *******************");
}
return(0.0); // return some artificial timestep
}
/// <summary>
/// Compares the cell surface and the boundary integral.
/// </summary>
public static void TestSealing(IGridData gdat)
{
int J = gdat.iLogicalCells.NoOfLocalUpdatedCells;
int[,] E2Clog = gdat.iGeomEdges.LogicalCellIndices;
//
// compute cell surface via edge integrals
//
MultidimensionalArray CellSurf1 = MultidimensionalArray.Create(J);
EdgeQuadrature.GetQuadrature(new int[] { 1 },
gdat, new EdgeQuadratureScheme().Compile(gdat, 2),
delegate(int i0, int Length, QuadRule rule, MultidimensionalArray EvalResult) { // evaluate
EvalResult.SetAll(1.0);
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) { // save results
for (int i = 0; i < Length; i++)
{
int iEdge = i + i0;
int jCellIn = E2Clog[iEdge, 0];
int jCellOt = E2Clog[iEdge, 1];
CellSurf1[jCellIn] += ResultsOfIntegration[i, 0];
if (jCellOt >= 0 && jCellOt < J)
{
CellSurf1[jCellOt] += ResultsOfIntegration[i, 0];
}
}
}).Execute();
//
// compute cell surface via cell boundary integrals
//
var cbqs = new CellBoundaryQuadratureScheme(false, null);
foreach (var Kref in gdat.iGeomCells.RefElements)
{
cbqs.AddFactory(new StandardCellBoundaryQuadRuleFactory(Kref));
}
MultidimensionalArray CellSurf2 = MultidimensionalArray.Create(J);
CellBoundaryQuadrature <CellBoundaryQuadRule> .GetQuadrature(new int[] { 1 },
gdat, cbqs.Compile(gdat, 2),
delegate(int i0, int Length, CellBoundaryQuadRule rule, MultidimensionalArray EvalResult) { // evaluate
EvalResult.SetAll(1.0);
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) { // save results
int NoOfFaces = ResultsOfIntegration.GetLength(1);
for (int i = 0; i < Length; i++)
{
int jCell = i + i0;
for (int iFace = 0; iFace < NoOfFaces; iFace++)
{
CellSurf2[jCell] += ResultsOfIntegration[i, iFace, 0];
}
}
}, cs : CoordinateSystem.Physical).Execute();
//
// compare
//
MultidimensionalArray Err = CellSurf1.CloneAs();
Err.Acc(-1.0, CellSurf2);
double ErrNorm = Err.L2Norm();
double TotSurf = CellSurf1.L2Norm();
Console.WriteLine("Area Check " + Err.L2Norm());
Assert.LessOrEqual(ErrNorm / TotSurf, 1.0e-8);
//for (int j = 0; j < J; j++) {
// if (Err[j].Abs() >= 1.0e-6) {
// Console.WriteLine("Mismatch between edge area and cell surface area in cell {0}, GlobalId {1}, No. of neighbors {3}, {2:0.####E-00}", j, gdat.CurrentGlobalIdPermutation.Values[j], Err[j], gdat.Cells.CellNeighbours[j].Length);
// schas.SetMeanValue(j, 1);
// }
//}
}
/// <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);
}
}
}
}
static internal void ComputeMassMatrixBlocks(
IEnumerable <SpeciesId> _SpeciesIds,
out Dictionary <SpeciesId, MassMatrixBlockContainer> Result,
Basis b,
XDGSpaceMetrics homie)
{
using (var tracer = new FuncTrace()) {
if (b is XDGBasis)
{
throw new ArgumentException();
}
var ctx = homie.GridDat;
Result = new Dictionary <SpeciesId, MassMatrixBlockContainer>();
var schemeHelper = homie.XQuadSchemeHelper;
int Nnx = b.Length;
int quadorder = homie.CutCellQuadOrder;
// define domains and allocate memory
// ==================================
foreach (var Species in _SpeciesIds) // loop over species...
// interation dom
{
var _IntegrationDomain = homie.LevelSetRegions.GetSpeciesMask(Species).Intersect(homie.LevelSetRegions.GetCutCellMask());
// domain for mass-matrix blocks (include agglomeration targets)
var _BlockDomain = _IntegrationDomain; //.Union(Agg.GetAgglomerator(Species).AggInfo.AllAffectedCells);
// alloc mem for blocks
var _MassMatrixBlocksSpc = MultidimensionalArray.Create(_BlockDomain.NoOfItemsLocally, Nnx, Nnx);
// Subgrid index to cell index
int[] _jSub2jCell = _BlockDomain.ItemEnum.ToArray();
// cell to subgrid index
//Dictionary<int, int> _jCell2jSub;
//if (Agg.GetAgglomerator(Species).AggInfo.AgglomerationPairs.Length > 0) {
// _jCell2jSub = new Dictionary<int, int>();
// for (int i = 0; i < _jSub2jCell.Length; i++) {
// _jCell2jSub.Add(_jSub2jCell[i], i);
// }
//} else {
// _jCell2jSub = null;
//}
Result.Add(Species, new MassMatrixBlockContainer()
{
IntegrationDomain = _IntegrationDomain,
MassMatrixBlocks = _MassMatrixBlocksSpc,
//jCell2jSub = _jCell2jSub,
jSub2jCell = _jSub2jCell
});
}
// compute blocks
// ==============
foreach (var Species in _SpeciesIds)
{
// get quad scheme
CellQuadratureScheme scheme = schemeHelper.GetVolumeQuadScheme(Species, IntegrationDomain: Result[Species].IntegrationDomain);
// result storage
var MassMatrixBlocksSpc = Result[Species].MassMatrixBlocks;
tracer.Info("mass matrix quad order: " + quadorder);
// compute the products of the basis functions:
int BlockCnt = -1;
int[] BlockCell = Result[Species].jSub2jCell;
CellMask speciesCells = homie.LevelSetRegions.GetSpeciesMask(Species);
CellQuadrature.GetQuadrature(
new int[] { Nnx, Nnx },
ctx,
scheme.Compile(ctx, quadorder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
// Del_Evaluate
// ~~~~~~~~~~~~~
var BasisVal = b.CellEval(QR.Nodes, i0, Length);
EvalResult.Multiply(1.0, BasisVal, BasisVal, 0.0, "ikmn", "ikm", "ikn");
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
// Del_SaveIntegrationResults
// ~~~~~~~~~~~~~~~~~~~~~~~~~~
for (int i = 0; i < Length; i++)
{
int jCell = i0 + i;
BlockCnt++;
// insert ID block in agglomeration target cells (if necessary):
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
var Block = MassMatrixBlocksSpc.ExtractSubArrayShallow(BlockCnt, -1, -1);
while (BlockCell[BlockCnt] < jCell)
{
// agglomeration source/target cell that is not cut
// mass matrix is identity (full) or zero (void)
Block.Clear();
if (speciesCells.Contains(BlockCell[BlockCnt]))
{
// cell is full
for (int nn = 0; nn < Nnx; nn++)
{
Block[nn, nn] = 1.0;
}
}
BlockCnt++;
Block = MassMatrixBlocksSpc.ExtractSubArrayShallow(BlockCnt, -1, -1);
}
// store computed block
// - - - - - - - - - - -
Debug.Assert(BlockCell[BlockCnt] == jCell);
MassMatrixBlocksSpc.ExtractSubArrayShallow(BlockCnt, -1, -1)
.Set(ResultsOfIntegration.ExtractSubArrayShallow(i, -1, -1));
#if DEBUG
for (int n = 0; n < Nnx; n++)
{
for (int m = 0; m < Nnx; m++)
{
Debug.Assert(Block[n, m] == Block[m, n]);
}
}
#endif
}
}).Execute();
// ------------------------------------ quadrature end.
BlockCnt++;
while (BlockCnt < MassMatrixBlocksSpc.GetLength(0))
{
// agglomeration source/target cell that is not cut
// mass matrix is identity (full) or zero (void)
var Block = MassMatrixBlocksSpc.ExtractSubArrayShallow(BlockCnt, -1, -1);
Block.Clear();
if (speciesCells.Contains(BlockCell[BlockCnt]))
{
// cell is full
for (int nn = 0; nn < Nnx; nn++)
{
Block[nn, nn] = 1.0;
}
}
BlockCnt++;
}
/*
* // test mass matrix for positive definiteness
* {
* int JSUB = MassMatrixBlocksSpc.GetLength(0);
* SubGrid Idom = null;
*
* int failCount = 0;
* var PosDefiniteTest = new FullMatrix(Nnx, Nnx);
*
* for (int jsub = 0; jsub < JSUB; jsub++) {
* PosDefiniteTest.Clear();
* PosDefiniteTest.Acc(MassMatrixBlocksSpc.ExtractSubArrayShallow(jsub, -1, -1), 1.0);
*
* try {
* PosDefiniteTest.Clear();
* PosDefiniteTest.Acc(MassMatrixBlocksSpc.ExtractSubArrayShallow(jsub, -1, -1), 1.0);
* PosDefiniteTest.InvertSymmetrical();
*
* //PosDefiniteTest.Clear();
* //PosDefiniteTest.AccEye(1.0);
* //PosDefiniteTest.Acc(MassMatrixBlocksSpc.ExtractSubArrayShallow(jsub, -1, -1), -1.0);
* //PosDefiniteTest.InvertSymmetrical();
* } catch (ArithmeticException ae) {
* if (Idom == null)
* Idom = new SubGrid(scheme.Domain);
*
* int jCell = Idom.SubgridIndex2LocalCellIndex[jsub];
* long Gid = Tracker.GridDat.Cells.GetCell(jCell).GlobalID;
*
*
* double volFrac = Tracker.GetSpeciesVolume(jCell, Species)/ctx.Cells.GetCellVolume(jCell);
*
* var errString = string.Format("Indefinite mass matrix in cell: globalId = {0}, local index = {1}, species {2}; \n cell volume fraction: {3};\n [{4}]", Gid, jCell, Tracker.GetSpeciesName(Species), volFrac, ae.Message);
* tracer.Logger.Error(errString);
* //Console.WriteLine(errString);
* failCount++;
* }
* }
*
* if (failCount > 0) {
* var errString = string.Format("Indefinite mass matrix in {0} of {1} cut cells", failCount, JSUB);
* tracer.Logger.Error(errString);
* Console.WriteLine(errString);
* } else {
* Console.WriteLine("No indefinite mass matrix blocks");
* }
*
* }
* // */
// backup before agglomeration (required if we wanna treat e.g. velocity in DG and pressure in XDG)
//MultidimensionalArray[] massMatrixBlocksB4Agglom = new MultidimensionalArray[Result[Species].jSub2jCell.Length];
//Result[Species].MassMatrixBlocks_B4Agglom = massMatrixBlocksB4Agglom;
//var _jCell2jSub = Result[Species].jCell2jSub;
//int J = ctx.Cells.NoOfLocalUpdatedCells;
//foreach (var pair in Agg.GetAgglomerator(Species).AggInfo.AgglomerationPairs) {
// foreach (int jCell in new int[] { pair.jCellSource, pair.jCellTarget }) { // create a backup of source and target cell
// if (jCell >= J)
// continue;
// int jSub = _jCell2jSub[jCell];
// if (massMatrixBlocksB4Agglom[jSub] == null) {
// massMatrixBlocksB4Agglom[jSub] = MassMatrixBlocksSpc.ExtractSubArrayShallow(jSub, -1, -1).CloneAs();
// }
// }
//}
// agglomeration
//Agg.GetAgglomerator(Species).ManipulateMassMatrixBlocks(MassMatrixBlocksSpc, b, Result[Species].jSub2jCell, Result[Species].jCell2jSub);
//throw new NotImplementedException("todo");
}
}
}
