/// <summary>
/// Sets level-set and solution at time (<paramref name="time"/> + <paramref name="dt"/>).
/// </summary>
double DelUpdateLevelset(DGField[] CurrentState, double time, double dt, double UnderRelax, bool _incremental)
{
// new time
double t = time + dt;
// project new level-set
double s = 1.0;
LevSet.ProjectField((x, y) => - (x - s * t).Pow2() - y.Pow2() + (2.4).Pow2());
LsTrk.UpdateTracker(incremental: _incremental);
// exact solution for new timestep
uEx.GetSpeciesShadowField("A").ProjectField((x, y) => x + alpha_A * t);
uEx.GetSpeciesShadowField("B").ProjectField((x, y) => x + alpha_B * t);
u.Clear();
u.Acc(1.0, uEx);
// markieren, wo ueberhaupt A und B sind
Amarker.Clear();
Bmarker.Clear();
Amarker.AccConstant(+1.0, LsTrk.Regions.GetSpeciesSubGrid("A").VolumeMask);
Bmarker.AccConstant(1.0, LsTrk.Regions.GetSpeciesSubGrid("B").VolumeMask);
// MPI rank
MPICellRank.Clear();
MPICellRank.AccConstant(base.MPIRank);
// return level-set residual
return(0.0);
}
private double SetUpConfiguration()
{
testCase.UpdateLevelSet(levelSet);
levelSetTracker.UpdateTracker(__NearRegionWith: 0, incremental: false, __LevSetAllowedMovement: 2);
XDGField.Clear();
XDGField.GetSpeciesShadowField("A").ProjectField(
1.0, testCase.JumpingFieldSpeciesAInitialValue, default(CellQuadratureScheme));
XDGField.GetSpeciesShadowField("B").ProjectField(
1.0, testCase.JumpingFieldSpeciesBInitialValue, default(CellQuadratureScheme));
SinglePhaseField.Clear();
SinglePhaseField.ProjectField(testCase.ContinuousFieldInitialValue);
double referenceValue = testCase.Solution;
if (testCase is IVolumeTestCase)
{
QuadRule standardRule = Grid.RefElements[0].GetQuadratureRule(2 * XDGField.Basis.Degree + 1);
ScalarFieldQuadrature uncutQuadrature = new ScalarFieldQuadrature(
GridData,
XDGField,
new CellQuadratureScheme(
new FixedRuleFactory <QuadRule>(standardRule),
levelSetTracker.Regions.GetCutCellSubGrid().Complement().VolumeMask),
standardRule.OrderOfPrecision);
uncutQuadrature.Execute();
referenceValue -= uncutQuadrature.Result;
}
return(referenceValue);
}
/// <summary>
/// Sets level-set and solution at time (<paramref name="time"/> + <paramref name="dt"/>).
/// </summary>
double DelUpdateLevelset(DGField[] CurrentState, double time, double dt, double UnderRelax, bool _incremental)
{
// new time
double t = time + dt;
// project new level-set
LevSet.ProjectField(this.Control.LevelSet.Vectorize(t));
LsTrk.UpdateTracker(incremental: _incremental);
// exact solution for new timestep
uEx.GetSpeciesShadowField("A").ProjectField(NonVectorizedScalarFunction.Vectorize(this.Control.uEx_A, t));
uEx.GetSpeciesShadowField("B").ProjectField(NonVectorizedScalarFunction.Vectorize(this.Control.uEx_B, t));
u.Clear();
u.Acc(1.0, uEx);
// markieren, wo ueberhaupt A und B sind
Amarker.Clear();
Bmarker.Clear();
Amarker.AccConstant(+1.0, LsTrk._Regions.GetSpeciesSubGrid("A").VolumeMask);
Bmarker.AccConstant(1.0, LsTrk._Regions.GetSpeciesSubGrid("B").VolumeMask);
// MPI rank
MPICellRank.Clear();
MPICellRank.AccConstant(base.MPIRank);
// return level-set residual
return(0.0);
}
public static void XDG_MatrixPolynomialRestAndPrlgTest_2(
[Values(0, 1, 2, 3)] int p,
[Values(0.0, 0.3)] double AggregationThreshold,
[Values(0, 1)] int TrackerWidth,
[Values(MultigridOperator.Mode.Eye, MultigridOperator.Mode.IdMass)] MultigridOperator.Mode mode)
{
if (AggregationThreshold < 0.1 && p >= 3 && mode == MultigridOperator.Mode.IdMass)
{
// this test combination is not supposed to work:
// without agglomeration, for high p, the mass matrix may be indefinite in small cut-cells
// => Cholesky decomposition on mass matrix fails, i.e. 'mode == IdMass' cannot succseed.
return;
}
XQuadFactoryHelper.MomentFittingVariants variant = XQuadFactoryHelper.MomentFittingVariants.OneStepGaussAndStokes;
var xt = new XDGTestSetup(p, AggregationThreshold, TrackerWidth, mode, variant);
// Restriction & prolongation together with orthonormalization
// -----------------------------------------------------------
for (var mgop = xt.MultigridOp; mgop != null; mgop = mgop.CoarserLevel)
{
var Itself = mgop.Mapping.FromOtherLevelMatrix(mgop.Mapping);
Itself.AccEyeSp(-1.0);
double Itslef_Norm = Itself.InfNorm();
//Console.WriteLine("Level {0}, Restriction onto itself {1}", mgm.LevelIndex, Itslef_Norm);
Assert.LessOrEqual(Itslef_Norm, 1.0e-8);
}
{
// test change of basis on top level
XDGField uTestRnd = new XDGField(xt.XB);
Random rnd = new Random();
for (int i = 0; i < uTestRnd.CoordinateVector.Count; i++)
{
uTestRnd.CoordinateVector[i] = rnd.NextDouble();
}
xt.agg.ClearAgglomerated(uTestRnd.CoordinateVector, uTestRnd.Mapping);
// perform change of basis on top level ...
int Ltop = xt.MultigridOp.Mapping.LocalLength;
double[] uTest_Fine = new double[Ltop];
xt.MultigridOp.TransformSolInto(uTestRnd.CoordinateVector, uTest_Fine);
// .. and back
XDGField uError2 = uTestRnd.CloneAs();
uError2.Clear();
xt.MultigridOp.TransformSolFrom(uError2.CoordinateVector, uTest_Fine);
// compare:
uError2.Acc(-1.0, uTestRnd);
double NORM_uError = uError2.L2Norm();
// output
Console.WriteLine("Top level change of basis error: {0}", NORM_uError);
Assert.LessOrEqual(NORM_uError, 1.0e-8);
}
{
// perform change of basis on top level
int Ltop = xt.MultigridOp.Mapping.LocalLength;
double[] uTest_Fine = new double[Ltop];
xt.MultigridOp.TransformSolInto(xt.uTest.CoordinateVector, uTest_Fine);
// check for each level of the multigrid operator...
for (int iLevel = 0; iLevel < MgSeq.Count() - 1; iLevel++)
{
double[] uTest_Prolonged = new double[Ltop];
XDG_Recursive(0, iLevel, xt.MultigridOp, uTest_Fine, uTest_Prolonged);
XDGField uError = xt.uTest.CloneAs();
uError.Clear();
xt.MultigridOp.TransformSolFrom(uError.CoordinateVector, uTest_Prolonged);
xt.agg.Extrapolate(uError.Mapping);
uError.Acc(-1.0, xt.uTest);
double NORM_uError = uError.L2Norm();
Console.WriteLine("Rest/Prlg error, level {0}: {1}", iLevel, NORM_uError);
Assert.LessOrEqual(NORM_uError, 1.0e-8);
}
}
}
protected override void SetInitial()
{
base.SetInitial();
this.CreateEquationsAndSolvers(null);
if (this.Control.MultiStepInit == true)
{
int CallCount = 0;
if (m_RK_Timestepper != null)
{
throw new NotSupportedException();
}
m_BDF_Timestepper.MultiInit(0.0, 0, this.Control.GetFixedTimestep(),
delegate(int TimestepIndex, double Time, DGField[] St) {
Console.WriteLine("Timestep index {0}, time {1} ", TimestepIndex, Time);
// level-set
// ---------
this.Phi.ProjectField(X => this.Control.Phi(X, Time));
// HMF hacks
if ((this.Control.CircleRadius != null) != (this.Control.CutCellQuadratureType == XQuadFactoryHelper.MomentFittingVariants.ExactCircle))
{
throw new ApplicationException("Illegal HMF configuration.");
}
if (this.Control.CircleRadius != null)
{
ExactCircleLevelSetIntegration.RADIUS = new double[] { this.Control.CircleRadius(Time) };
}
if (CallCount == 0)
{
this.LsTrk.UpdateTracker();
}
else
{
this.LsTrk.UpdateTracker(incremental: true);
}
CallCount++;
// solution
// --------
XDGField _u = (XDGField)St[0];
_u.Clear();
_u.GetSpeciesShadowField("A").ProjectField((X => this.Control.uA_Ex(X, Time)));
_u.GetSpeciesShadowField("B").ProjectField((X => this.Control.uB_Ex(X, Time)));
});
}
else
{
this.Phi.ProjectField(X => this.Control.Phi(X, 0.0));
this.LsTrk.UpdateTracker();
u.Clear();
u.GetSpeciesShadowField("A").ProjectField((X => this.Control.uA_Ex(X, 0.0)));
u.GetSpeciesShadowField("B").ProjectField((X => this.Control.uB_Ex(X, 0.0)));
if (m_BDF_Timestepper != null)
{
m_BDF_Timestepper.SingleInit();
}
}
}
protected override double RunSolverOneStep(int TimestepNo, double phystime, double dt)
{
Console.WriteLine(" Timestep # " + TimestepNo + ", phystime = " + phystime);
//phystime = 1.8;
LsUpdate(phystime);
// operator-matrix assemblieren
MsrMatrix OperatorMatrix = new MsrMatrix(u.Mapping, u.Mapping);
double[] Affine = new double[OperatorMatrix.RowPartitioning.LocalLength];
MultiphaseCellAgglomerator Agg;
MassMatrixFactory Mfact;
// Agglomerator setup
int quadOrder = Op.QuadOrderFunction(new int[] { u.Basis.Degree }, new int[0], new int[] { u.Basis.Degree });
//Agg = new MultiphaseCellAgglomerator(new CutCellMetrics(MomentFittingVariant, quadOrder, LsTrk, ), this.THRESHOLD, false);
Agg = LsTrk.GetAgglomerator(new SpeciesId[] { LsTrk.GetSpeciesId("B") }, quadOrder, this.THRESHOLD);
Console.WriteLine("Inter-Process agglomeration? " + Agg.GetAgglomerator(LsTrk.GetSpeciesId("B")).AggInfo.InterProcessAgglomeration);
if (this.THRESHOLD > 0.01)
{
TestAgglomeration_Extraploation(Agg);
TestAgglomeration_Projection(quadOrder, Agg);
}
// operator matrix assembly
Op.ComputeMatrixEx(LsTrk,
u.Mapping, null, u.Mapping,
OperatorMatrix, Affine, false, 0.0, true,
Agg.CellLengthScales,
LsTrk.GetSpeciesId("B"));
Agg.ManipulateMatrixAndRHS(OperatorMatrix, Affine, u.Mapping, u.Mapping);
// mass matrix factory
Mfact = LsTrk.GetXDGSpaceMetrics(new SpeciesId[] { LsTrk.GetSpeciesId("B") }, quadOrder, 1).MassMatrixFactory;// new MassMatrixFactory(u.Basis, Agg);
// Mass matrix/Inverse Mass matrix
//var MassInv = Mfact.GetMassMatrix(u.Mapping, new double[] { 1.0 }, true, LsTrk.GetSpeciesId("B"));
var Mass = Mfact.GetMassMatrix(u.Mapping, new double[] { 1.0 }, false, LsTrk.GetSpeciesId("B"));
Agg.ManipulateMatrixAndRHS(Mass, default(double[]), u.Mapping, u.Mapping);
var MassInv = Mass.InvertBlocks(OnlyDiagonal: true, Subblocks: true, ignoreEmptyBlocks: true, SymmetricalInversion: false);
// test that operator depends only on B-species values
double DepTest = LsTrk.Regions.GetSpeciesSubGrid("B").TestMatrixDependency(OperatorMatrix, u.Mapping, u.Mapping);
Console.WriteLine("Matrix dependency test: " + DepTest);
Assert.LessOrEqual(DepTest, 0.0);
// diagnostic output
Console.WriteLine("Number of Agglomerations (all species): " + Agg.TotalNumberOfAgglomerations);
Console.WriteLine("Number of Agglomerations (species 'B'): " + Agg.GetAgglomerator(LsTrk.GetSpeciesId("B")).AggInfo.SourceCells.NoOfItemsLocally.MPISum());
// operator auswerten:
double[] x = new double[Affine.Length];
BLAS.daxpy(x.Length, 1.0, Affine, 1, x, 1);
OperatorMatrix.SpMVpara(1.0, u.CoordinateVector, 1.0, x);
MassInv.SpMV(1.0, x, 0.0, du_dx.CoordinateVector);
Agg.GetAgglomerator(LsTrk.GetSpeciesId("B")).Extrapolate(du_dx.Mapping);
// markieren, wo ueberhaupt A und B sind
Bmarker.AccConstant(1.0, LsTrk.Regions.GetSpeciesSubGrid("B").VolumeMask);
Amarker.AccConstant(+1.0, LsTrk.Regions.GetSpeciesSubGrid("A").VolumeMask);
Xmarker.AccConstant(+1.0, LsTrk.Regions.GetSpeciesSubGrid("X").VolumeMask);
// compute error
ERR.Clear();
ERR.Acc(1.0, du_dx_Exact, LsTrk.Regions.GetSpeciesSubGrid("B").VolumeMask);
ERR.Acc(-1.0, du_dx, LsTrk.Regions.GetSpeciesSubGrid("B").VolumeMask);
double L2Err = ERR.L2Norm(LsTrk.Regions.GetSpeciesSubGrid("B").VolumeMask);
Console.WriteLine("L2 Error: " + L2Err);
XERR.Clear();
XERR.GetSpeciesShadowField("B").Acc(1.0, ERR, LsTrk.Regions.GetSpeciesSubGrid("B").VolumeMask);
double xL2Err = XERR.L2Norm();
Console.WriteLine("L2 Error (in XDG space): " + xL2Err);
// check error
if (this.THRESHOLD > 0.01)
{
// without agglomeration, the error in very tiny cut-cells may be large over the whole cell
// However, the error in the XDG-space should be small under all circumstances
Assert.LessOrEqual(L2Err, 1.0e-6);
}
Assert.LessOrEqual(xL2Err, 1.0e-6);
bool IsPassed = ((L2Err <= 1.0e-6 || this.THRESHOLD <= 0.01) && xL2Err <= 1.0e-7);
if (IsPassed)
{
Console.WriteLine("Test PASSED");
}
else
{
Console.WriteLine("Test FAILED: check errors.");
}
// return/Ende
base.NoOfTimesteps = 17;
//base.NoOfTimesteps = 2;
dt = 0.3;
return(dt);
}
private void ExperimentalSolver(out double mintime, out double maxtime, out bool Converged, out int NoOfIter, out int DOFs)
{
using (var tr = new FuncTrace()) {
mintime = double.MaxValue;
maxtime = 0;
Converged = false;
NoOfIter = int.MaxValue;
DOFs = 0;
AggregationGridBasis[][] XAggB;
using (new BlockTrace("Aggregation_basis_init", tr)) {
XAggB = AggregationGridBasis.CreateSequence(base.MultigridSequence, u.Mapping.BasisS);
}
XAggB.UpdateXdgAggregationBasis(this.Op_Agglomeration);
var MassMatrix = this.Op_mass.GetMassMatrix(this.u.Mapping, new double[] { 1.0 }, false, this.LsTrk.SpeciesIdS.ToArray());
double[] _RHSvec = this.GetRHS();
Stopwatch stw = new Stopwatch();
stw.Reset();
stw.Start();
Console.WriteLine("Setting up multigrid operator...");
int p = this.u.Basis.Degree;
var MultigridOp = new MultigridOperator(XAggB, this.u.Mapping,
this.Op_Matrix,
this.Op_mass.GetMassMatrix(new UnsetteledCoordinateMapping(this.u.Basis), false),
OpConfig);
Assert.True(MultigridOp != null);
int L = MultigridOp.Mapping.LocalLength;
DOFs = MultigridOp.Mapping.TotalLength;
double[] RHSvec = new double[L];
MultigridOp.TransformRhsInto(_RHSvec, RHSvec);
ISolverSmootherTemplate exsolver;
SolverFactory SF = new SolverFactory(this.Control.NonLinearSolver, this.Control.LinearSolver);
List <Action <int, double[], double[], MultigridOperator> > Callbacks = new List <Action <int, double[], double[], MultigridOperator> >();
Callbacks.Add(CustomItCallback);
SF.GenerateLinear(out exsolver, MultigridSequence, OpConfig, Callbacks);
using (new BlockTrace("Solver_Init", tr)) {
exsolver.Init(MultigridOp);
}
/*
* string filename = "XdgPoisson" + this.Grid.SpatialDimension + "p" + this.u.Basis.Degree + "R" + this.Grid.CellPartitioning.TotalLength;
* MultigridOp.OperatorMatrix.SaveToTextFileSparse(filename + ".txt");
* RHSvec.SaveToTextFile(filename + "_rhs.txt");
*
* var uEx = this.u.CloneAs();
* Op_Agglomeration.ClearAgglomerated(uEx.Mapping);
* var CO = new ConvergenceObserver(MultigridOp, MassMatrix, uEx.CoordinateVector.ToArray());
* uEx = null;
* CO.TecplotOut = "PoissonConvergence";
* //CO.PlotDecomposition(this.u.CoordinateVector.ToArray());
*
* if (exsolver is ISolverWithCallback) {
* ((ISolverWithCallback)exsolver).IterationCallback = CO.IterationCallback;
* }
* //*/
XDGField u2 = u.CloneAs();
using (new BlockTrace("Solver_Run", tr)) {
// use solver (on XDG-field 'u2').
u2.Clear();
MultigridOp.UseSolver(exsolver, u2.CoordinateVector, _RHSvec);
Console.WriteLine("Solver: {0}, converged? {1}, {2} iterations.", exsolver.GetType().Name, exsolver.Converged, exsolver.ThisLevelIterations);
this.Op_Agglomeration.Extrapolate(u2.Mapping);
Assert.IsTrue(exsolver.Converged, "Iterative solver did not converge.");
}
stw.Stop();
mintime = Math.Min(stw.Elapsed.TotalSeconds, mintime);
maxtime = Math.Max(stw.Elapsed.TotalSeconds, maxtime);
Converged = exsolver.Converged;
NoOfIter = exsolver.ThisLevelIterations;
// compute error between reference solution and multigrid solver
XDGField ErrField = u2.CloneAs();
ErrField.Acc(-1.0, u);
double ERR = ErrField.L2Norm();
double RelERR = ERR / u.L2Norm();
Assert.LessOrEqual(RelERR, 1.0e-6, "Result from iterative solver above threshold.");
}
}
protected override double RunSolverOneStep(int TimestepNo, double phystime, double dt)
{
Console.WriteLine(" Timestep # " + TimestepNo + ", phystime = " + phystime);
//phystime = 1.8;
LsUpdate(phystime);
// operator-matrix assemblieren
MsrMatrix OperatorMatrix = new MsrMatrix(u.Mapping, u.Mapping);
double[] Affine = new double[OperatorMatrix.RowPartitioning.LocalLength];
// Agglomerator setup
MultiphaseCellAgglomerator Agg = LsTrk.GetAgglomerator(new SpeciesId[] { LsTrk.GetSpeciesId("B") }, QuadOrder, this.THRESHOLD);
// plausibility of cell length scales
if (SER_PAR_COMPARISON)
{
TestLengthScales(QuadOrder, TimestepNo);
}
Console.WriteLine("Inter-Process agglomeration? " + Agg.GetAgglomerator(LsTrk.GetSpeciesId("B")).AggInfo.InterProcessAgglomeration);
if (this.THRESHOLD > 0.01)
{
TestAgglomeration_Extraploation(Agg);
TestAgglomeration_Projection(QuadOrder, Agg);
}
CheckExchange(true);
CheckExchange(false);
// operator matrix assembly
XSpatialOperatorMk2.XEvaluatorLinear mtxBuilder = Op.GetMatrixBuilder(base.LsTrk, u.Mapping, null, u.Mapping);
mtxBuilder.time = 0.0;
mtxBuilder.ComputeMatrix(OperatorMatrix, Affine);
Agg.ManipulateMatrixAndRHS(OperatorMatrix, Affine, u.Mapping, u.Mapping);
// mass matrix factory
var Mfact = LsTrk.GetXDGSpaceMetrics(new SpeciesId[] { LsTrk.GetSpeciesId("B") }, QuadOrder, 1).MassMatrixFactory;// new MassMatrixFactory(u.Basis, Agg);
// Mass matrix/Inverse Mass matrix
//var MassInv = Mfact.GetMassMatrix(u.Mapping, new double[] { 1.0 }, true, LsTrk.GetSpeciesId("B"));
var Mass = Mfact.GetMassMatrix(u.Mapping, new double[] { 1.0 }, false, LsTrk.GetSpeciesId("B"));
Agg.ManipulateMatrixAndRHS(Mass, default(double[]), u.Mapping, u.Mapping);
var MassInv = Mass.InvertBlocks(OnlyDiagonal: true, Subblocks: true, ignoreEmptyBlocks: true, SymmetricalInversion: false);
// test that operator depends only on B-species values
double DepTest = LsTrk.Regions.GetSpeciesSubGrid("B").TestMatrixDependency(OperatorMatrix, u.Mapping, u.Mapping);
Console.WriteLine("Matrix dependency test: " + DepTest);
Assert.LessOrEqual(DepTest, 0.0);
// diagnostic output
Console.WriteLine("Number of Agglomerations (all species): " + Agg.TotalNumberOfAgglomerations);
Console.WriteLine("Number of Agglomerations (species 'B'): " + Agg.GetAgglomerator(LsTrk.GetSpeciesId("B")).AggInfo.SourceCells.NoOfItemsLocally.MPISum());
// operator auswerten:
double[] x = new double[Affine.Length];
BLAS.daxpy(x.Length, 1.0, Affine, 1, x, 1);
OperatorMatrix.SpMVpara(1.0, u.CoordinateVector, 1.0, x);
MassInv.SpMV(1.0, x, 0.0, du_dx.CoordinateVector);
Agg.GetAgglomerator(LsTrk.GetSpeciesId("B")).Extrapolate(du_dx.Mapping);
// markieren, wo ueberhaupt A und B sind
Bmarker.AccConstant(1.0, LsTrk.Regions.GetSpeciesSubGrid("B").VolumeMask);
Amarker.AccConstant(+1.0, LsTrk.Regions.GetSpeciesSubGrid("A").VolumeMask);
if (usePhi0 && usePhi1)
{
Xmarker.AccConstant(+1.0, LsTrk.Regions.GetSpeciesSubGrid("X").VolumeMask);
}
// compute error
ERR.Clear();
ERR.Acc(1.0, du_dx_Exact, LsTrk.Regions.GetSpeciesSubGrid("B").VolumeMask);
ERR.Acc(-1.0, du_dx, LsTrk.Regions.GetSpeciesSubGrid("B").VolumeMask);
double L2Err = ERR.L2Norm(LsTrk.Regions.GetSpeciesSubGrid("B").VolumeMask);
Console.WriteLine("L2 Error: " + L2Err);
XERR.Clear();
XERR.GetSpeciesShadowField("B").Acc(1.0, ERR, LsTrk.Regions.GetSpeciesSubGrid("B").VolumeMask);
double xL2Err = XERR.L2Norm();
Console.WriteLine("L2 Error (in XDG space): " + xL2Err);
// check error
double ErrorThreshold = 1.0e-1;
if (this.MomentFittingVariant == XQuadFactoryHelper.MomentFittingVariants.OneStepGaussAndStokes)
{
ErrorThreshold = 1.0e-6; // HMF is designed for such integrands and should perform close to machine accuracy; on general integrands, the precision is different.
}
bool IsPassed = ((L2Err <= ErrorThreshold || this.THRESHOLD <= ErrorThreshold) && xL2Err <= ErrorThreshold);
if (IsPassed)
{
Console.WriteLine("Test PASSED");
}
else
{
Console.WriteLine("Test FAILED: check errors.");
//PlotCurrentState(phystime, TimestepNo, 3);
}
if (TimestepNo > 1)
{
if (this.THRESHOLD > ErrorThreshold)
{
// without agglomeration, the error in very tiny cut-cells may be large over the whole cell
// However, the error in the XDG-space should be small under all circumstances
Assert.LessOrEqual(L2Err, ErrorThreshold, "DG L2 error of computing du_dx");
}
Assert.LessOrEqual(xL2Err, ErrorThreshold, "XDG L2 error of computing du_dx");
}
// return/Ende
base.NoOfTimesteps = 17;
//base.NoOfTimesteps = 2;
dt = 0.3;
return(dt);
}
