/// <summary>
/// Constructor for XDG solvers
/// </summary>
public OpAnalysisBase(LevelSetTracker LsTrk, BlockMsrMatrix Mtx, double[] RHS, UnsetteledCoordinateMapping Mapping, MultiphaseCellAgglomerator CurrentAgglomeration, BlockMsrMatrix _mass, IEnumerable <MultigridOperator.ChangeOfBasisConfig[]> OpConfig, ISpatialOperator abstractOperator)
{
int RHSlen = Mapping.TotalLength;
m_map = Mapping; // mapping
VarGroup = Mapping.BasisS.Count.ForLoop(i => i); //default: all dependent variables are included in operator matrix
m_LsTrk = LsTrk;
m_OpMtx = Mtx.CloneAs();
localRHS = RHS.CloneAs();
// create the Dummy XDG aggregation basis
var baseGrid = Mapping.GridDat;
var mgSeq = Foundation.Grid.Aggregation.CoarseningAlgorithms.CreateSequence(baseGrid, 1);
AggregationGridBasis[][] XAggB = AggregationGridBasis.CreateSequence(mgSeq, Mapping.BasisS);
//
XAggB.UpdateXdgAggregationBasis(CurrentAgglomeration);
// create multigrid operator
m_MultigridOp = new MultigridOperator(XAggB, Mapping,
m_OpMtx,
_mass,
OpConfig,
abstractOperator.DomainVar.Select(varName => abstractOperator.FreeMeanValue[varName]).ToArray());
}
/// <summary>
/// Matrix/Affine assembly in the case of an implicit RK stage.
/// </summary>
protected override void AssembleMatrixCallback(out BlockMsrMatrix System, out double[] Affine, out BlockMsrMatrix PcMassMatrix, DGField[] argCurSt, bool Linearization)
{
if (Linearization == false)
{
throw new NotImplementedException("todo");
}
int Ndof = m_CurrentState.Count;
// copy data from 'argCurSt' to 'CurrentStateMapping', if necessary
// -----------------------------------------------------------
DGField[] locCurSt = CurrentStateMapping.Fields.ToArray();
if (locCurSt.Length != argCurSt.Length)
{
throw new ApplicationException();
}
int NF = locCurSt.Length;
for (int iF = 0; iF < NF; iF++)
{
if (object.ReferenceEquals(locCurSt[iF], argCurSt[iF]))
{
// nothing to do
}
else
{
locCurSt[iF].Clear();
locCurSt[iF].Acc(1.0, argCurSt[iF]);
}
}
// update of level-set
// ----------------------
bool updateAgglom = false;
if (this.Config_LevelSetHandling == LevelSetHandling.Coupled_Once && m_ImplStParams.m_IterationCounter == 0 ||
this.Config_LevelSetHandling == LevelSetHandling.Coupled_Iterative)
{
//MoveLevelSetAndRelatedStuff(locCurSt, m_CurrentPhystime, m_CurrentDt, 1.0);
if (Math.Abs(m_ImplStParams.m_ActualLevSetRelTime - m_ImplStParams.m_RelTime) > 1.0e-14)
{
if (m_ImplStParams.m_IterationCounter <= 0)// only push tracker in the first iter
{
m_LsTrk.PushStacks();
}
MoveLevelSetAndRelatedStuff(locCurSt,
m_ImplStParams.m_CurrentPhystime, m_ImplStParams.m_CurrentDt * m_ImplStParams.m_RelTime, IterUnderrelax,
m_ImplStParams.m_Mass, m_ImplStParams.m_k);
// note that we need to update the agglomeration
updateAgglom = true;
}
}
// update agglomeration
// --------------------
#if DEBUG
if (this.Config_LevelSetHandling == LevelSetHandling.LieSplitting || this.Config_LevelSetHandling == LevelSetHandling.StrangSplitting)
{
Debug.Assert(m_CurrentAgglomeration != null);
Debug.Assert(m_PrecondMassMatrix != null);
// ensure, that, when splitting is used we update the agglomerator in the very first iteration.
}
#endif
if (updateAgglom || m_CurrentAgglomeration == null)
{
this.UpdateAgglom(m_ImplStParams.m_IterationCounter > 0);
// update Multigrid-XDG basis
base.MultigridBasis.UpdateXdgAggregationBasis(m_CurrentAgglomeration);
}
// mass matrix update
// ------------------
if (this.Config_MassMatrixShapeandDependence == MassMatrixShapeandDependence.IsIdentity)
{
// may occur e.g. if one runs the FSI solver as a pure single-phase solver,
// i.e. if the Level-Set is outside the domain.
PcMassMatrix = null;
}
else
{
// checks:
Debug.Assert(this.Config_MassMatrixShapeandDependence == MassMatrixShapeandDependence.IsNonIdentity ||
this.Config_MassMatrixShapeandDependence == MassMatrixShapeandDependence.IsTimeDependent ||
this.Config_MassMatrixShapeandDependence == MassMatrixShapeandDependence.IsTimeAndSolutionDependent,
"Something is not implemented here.");
if (this.Config_MassMatrixShapeandDependence == MassMatrixShapeandDependence.IsNonIdentity &&
Config_LevelSetHandling != LevelSetHandling.None)
{
throw new NotSupportedException("Illegal configuration;");
}
if (this.Config_LevelSetHandling == LevelSetHandling.Coupled_Once || this.Config_LevelSetHandling == LevelSetHandling.Coupled_Iterative)
{
if ((this.Config_MassMatrixShapeandDependence == MassMatrixShapeandDependence.IsNonIdentity && m_PrecondMassMatrix == null) || // compute mass matrix (only once in application lifetime)
(this.Config_MassMatrixShapeandDependence == MassMatrixShapeandDependence.IsTimeDependent && m_ImplStParams.m_IterationCounter == 0) || // compute mass matrix once per timestep
(this.Config_MassMatrixShapeandDependence == MassMatrixShapeandDependence.IsTimeAndSolutionDependent) // re-compute mass matrix in every iteration
)
{
BlockMsrMatrix PM, SM;
UpdateMassMatrix(out PM, out SM, m_ImplStParams.m_CurrentPhystime + m_ImplStParams.m_CurrentDt * m_ImplStParams.m_RelTime);
m_ImplStParams.m_Mass[1] = SM;
m_PrecondMassMatrix = PM;
}
}
PcMassMatrix = m_PrecondMassMatrix;
}
// operator matrix update
// ----------------------
// we perform the extrapolation to have valid parameters if
// - the operator matrix depends on these values
this.m_CurrentAgglomeration.Extrapolate(CurrentStateMapping);
var OpMatrix = new BlockMsrMatrix(CurrentStateMapping);
var OpAffine = new double[Ndof];
this.ComputeOperatorMatrix(OpMatrix, OpAffine, CurrentStateMapping, locCurSt, base.GetAgglomeratedLengthScales(), m_ImplStParams.m_CurrentPhystime + m_ImplStParams.m_CurrentDt * m_ImplStParams.m_RelTime);
// assemble system
// ---------------
double dt = m_ImplStParams.m_CurrentDt;
// select mass matrix (and some checks)
double[] RHS = new double[Ndof];
BlockMsrMatrix MamaRHS, MamaLHS;
if (this.Config_LevelSetHandling == LevelSetHandling.Coupled_Once ||
this.Config_LevelSetHandling == LevelSetHandling.Coupled_Iterative)
{
Debug.Assert(m_ImplStParams.m_Mass.Length == 2);
MamaRHS = m_ImplStParams.m_Mass[0];
MamaLHS = m_ImplStParams.m_Mass[1];
}
else if (this.Config_LevelSetHandling == LevelSetHandling.LieSplitting ||
this.Config_LevelSetHandling == LevelSetHandling.StrangSplitting ||
this.Config_LevelSetHandling == LevelSetHandling.None)
{
Debug.Assert(m_ImplStParams.m_Mass.Length == 1);
MamaRHS = m_ImplStParams.m_Mass[0];
MamaLHS = m_ImplStParams.m_Mass[0];
}
else
{
throw new NotImplementedException();
}
// right-hand-side, resp. affine vector
if (MamaRHS != null)
{
MamaRHS.SpMV(1.0 / dt, m_ImplStParams.m_u0, 0.0, RHS);
}
else
{
Debug.Assert(this.Config_MassMatrixShapeandDependence == MassMatrixShapeandDependence.IsIdentity);
RHS.SetV(m_ImplStParams.m_u0, 1.0 / dt);
}
for (int l = 0; l < m_ImplStParams.m_s; l++)
{
if (m_ImplStParams.m_RK_as[l] != 0.0)
{
RHS.AccV(-m_ImplStParams.m_RK_as[l], m_ImplStParams.m_k[l]);
}
}
Affine = RHS;
Affine.ScaleV(-1.0);
Affine.AccV(m_ImplStParams.m_RK_as[m_ImplStParams.m_s], OpAffine);
// left-hand-side
System = OpMatrix.CloneAs();
System.Scale(m_ImplStParams.m_RK_as[m_ImplStParams.m_s]);
if (MamaLHS != null)
{
System.Acc(1.0 / dt, MamaLHS);
}
else
{
System.AccEyeSp(1.0 / dt);
}
// perform agglomeration
// ---------------------
Debug.Assert(object.ReferenceEquals(m_CurrentAgglomeration.Tracker, m_LsTrk));
m_CurrentAgglomeration.ManipulateMatrixAndRHS(System, Affine, CurrentStateMapping, CurrentStateMapping);
// increase iteration counter
// --------------------------
m_ImplStParams.m_IterationCounter++;
}
/// <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
}
