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>
* /// initialized by the constructor to avoid MPI-deadlocks;
* /// </summary>
* Dictionary<RefElement, EdgeMask> m_Subgrid4Kref_AllEdges = new Dictionary<RefElement, EdgeMask>();
*/
//LevelSetTracker lsTrk {
// get {
// return XDGSpaceMetrics.Tracker;
// }
//}
public EdgeQuadratureScheme Get_SurfaceElement_EdgeQuadScheme(SpeciesId sp)
{
if (!this.SpeciesList.Contains(sp))
{
throw new ArgumentException("Given species (id = " + sp.cntnt + ") is not supported.");
}
//var allRelevantEdges = this.m_SpeciesSubgrid_InnerAndDomainEdges[sp].Intersect(this.m_CutCellSubgrid_InnerEdges);
var innerCutCellEdges = this.XDGSpaceMetrics.LevelSetRegions.GetCutCellSubGrid().InnerEdgesMask;
var boundaryCutCellEdges = ExecutionMask.Intersect(this.XDGSpaceMetrics.LevelSetRegions.GetCutCellSubGrid().BoundaryEdgesMask, this.XDGSpaceMetrics.GridDat.BoundaryEdges);
var allRelevantEdges = this.m_SpeciesSubgrid_InnerAndDomainEdges[sp].Intersect(ExecutionMask.Union(innerCutCellEdges, boundaryCutCellEdges));
//EdgeMask AggEdges = this.CellAgglomeration != null ? this.CellAgglomeration.GetAgglomerator(sp).AggInfo.AgglomerationEdges : null;
//if (AggEdges != null && AggEdges.NoOfItemsLocally > 0)
// allRelevantEdges = allRelevantEdges.Except(AggEdges);
var edgeQrIns = new EdgeQuadratureScheme(false, allRelevantEdges);
foreach (var Kref in XDGSpaceMetrics.GridDat.Grid.RefElements)
{
for (int iLevSet = 0; iLevSet < XDGSpaceMetrics.NoOfLevelSets; iLevSet++) // loop over level sets...
{
EdgeMask cutEdges = this.GetCutEdges(Kref, iLevSet);
var factory = this.XDGSpaceMetrics.XQuadFactoryHelper.GetSurfaceElement_BoundaryRuleFactory(iLevSet, Kref);
edgeQrIns.AddFactory(factory, cutEdges);
}
}
return(edgeQrIns);
}
/// <summary>
/// accumulates the derivative of DG field <paramref name="f"/>
/// (along the <paramref name="d"/>-th axis) times <paramref name="alpha"/>
/// to this field, i.e. <br/>
/// this = this + <paramref name="alpha"/>* \f$ \frac{\partial}{\partial x_d} \f$ <paramref name="f"/>;
/// </summary>
/// <param name="f"></param>
/// <param name="d">
/// 0 for the x-derivative, 1 for the y-derivative, 2 for the z-derivative
/// </param>
/// <param name="alpha">
/// scaling of <paramref name="f"/>;
/// </param>
/// <param name="em">
/// An optional restriction to the domain in which the derivative is computed (it may, e.g.
/// be only required in boundary cells, so a computation over the whole domain
/// would be a waste of computation power. A proper execution mask for this case would be e.g.
/// <see cref="BoSSS.Foundation.Grid.GridData.BoundaryCells"/>.)<br/>
/// if null, the computation is carried out in the whole domain
/// </param>
override public void Derivative(double alpha, DGField f, int d, CellMask em)
{
using (var tr = new FuncTrace()) {
MPICollectiveWatchDog.Watch(csMPI.Raw._COMM.WORLD);
if (this.Basis.Degree < f.Basis.Degree - 1)
{
throw new ArgumentException("cannot compute derivative because of incompatible basis functions.", "f");
}
if (f.Basis.GetType() != this.Basis.GetType())
{
throw new ArgumentException("cannot compute derivative because of incompatible basis functions.", "f");
}
int D = GridDat.SpatialDimension;
if (d < 0 || d >= D)
{
throw new ArgumentException("spatial dimension out of range.", "d");
}
Quadrature.EdgeQuadratureScheme _qInsEdge;
Quadrature.CellQuadratureScheme _qInsVol;
{
_qInsEdge = (new Quadrature.EdgeQuadratureScheme(false, EdgeMask.GetEmptyMask(this.GridDat)));
_qInsVol = (new Quadrature.CellQuadratureScheme(true, em));
}
var op = (new BrokenDerivativeForm(d)).Operator(1, g => _qInsEdge, g => _qInsVol);
op.Evaluate(alpha, 1.0, f.Mapping, null, this.Mapping);
}
}
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]);
}
/// <summary>
///
/// </summary>
/// <param name="spatialOp"></param>
/// <param name="Fieldsmap"></param>
/// <param name="Parameters">
/// optional parameter fields, can be null if
/// <paramref name="spatialOp"/> contains no parameters; must match
/// the parameter field list of <paramref name="spatialOp"/>, see
/// <see cref="BoSSS.Foundation.SpatialOperator.ParameterVar"/>
/// </param>
/// <param name="sgrdBnd">
/// Options for the treatment of edges at the boundary of a SubGrid,
/// <see cref="SubGridBoundaryModes"/></param>
/// <param name="timeStepConstraints">
/// optional list of time step constraints <see cref="TimeStepConstraint"/>
/// </param>
/// <param name="sgrd">
/// optional restriction to computational domain
/// </param>
public ExplicitEuler(SpatialOperator spatialOp, CoordinateMapping Fieldsmap, CoordinateMapping Parameters, SubGridBoundaryModes sgrdBnd, IList <TimeStepConstraint> timeStepConstraints = null, SubGrid sgrd = null)
{
using (new ilPSP.Tracing.FuncTrace()) {
// verify input
// ============
TimeStepperCommon.VerifyInput(spatialOp, Fieldsmap, Parameters);
Mapping = Fieldsmap;
CurrentState = new CoordinateVector(Mapping);
ParameterMapping = Parameters;
IList <DGField> ParameterFields =
(ParameterMapping == null) ? (new DGField[0]) : ParameterMapping.Fields;
this.TimeStepConstraints = timeStepConstraints;
SubGrid = sgrd ?? new SubGrid(CellMask.GetFullMask(Fieldsmap.First().GridDat));
// generate Evaluator
// ==================
CellMask cm = SubGrid.VolumeMask;
EdgeMask em = SubGrid.AllEdgesMask;
Operator = spatialOp;
m_Evaluator = new Lazy <IEvaluatorNonLin>(delegate() {
spatialOp.EdgeQuadraturSchemeProvider = g => new EdgeQuadratureScheme(true, em);
spatialOp.VolumeQuadraturSchemeProvider = g => new CellQuadratureScheme(true, cm);
var op = spatialOp.GetEvaluatorEx(
Fieldsmap, ParameterFields, Fieldsmap);
op.ActivateSubgridBoundary(SubGrid.VolumeMask, sgrdBnd);
return(op);
});
}
}
/// <summary>
/// accumulates the derivative of DG field <paramref name="f"/>
/// (along the <paramref name="d"/>-th axis) times <paramref name="alpha"/>
/// to this field, i.e. <br/>
/// this = this + <paramref name="alpha"/>* \f$ \frac{\partial}{\partial x_d} \f$ <paramref name="f"/>;
/// </summary>
/// <param name="f"></param>
/// <param name="d">
/// 0 for the x-derivative, 1 for the y-derivative, 2 for the
/// z-derivative
/// </param>
/// <param name="alpha">
/// scaling of <paramref name="f"/>;
/// </param>
/// <param name="optionalSubGrid">
/// An optional restriction to the domain in which the derivative is
/// computed (it may, e.g. be only required in boundary cells, so a
/// computation over the whole domain would be a waste of computational
/// power. A proper execution mask would be see e.g.
/// <see cref="GridData.BoundaryCells"/>.)
/// <br/>
/// if null, the computation is carried out in the whole domain.
/// </param>
/// <param name="bndMode">
/// if a sub-grid is provided, this determines how the sub-grid
/// boundary should be treated.
/// </param>
/// <remarks>
/// The derivative is calculated using Riemann flux functions
/// (central difference);<br/>
/// In comparison to
/// <see cref="Derivative(double, DGField, int, CellMask)"/>, this method
/// should be slower, but produce more sane results, especially for
/// fields of low polynomial degree (0 or 1);
/// </remarks>
virtual public void DerivativeByFlux(double alpha, DGField f, int d, SubGrid optionalSubGrid = null, SubGridBoundaryModes bndMode = SubGridBoundaryModes.OpenBoundary)
{
int D = this.Basis.GridDat.SpatialDimension;
if (d < 0 || d >= D)
{
throw new ArgumentException("spatial dimension out of range.", "d");
}
MPICollectiveWatchDog.Watch(csMPI.Raw._COMM.WORLD);
EdgeMask emEdge = (optionalSubGrid != null) ? optionalSubGrid.AllEdgesMask : null;
CellMask emVol = (optionalSubGrid != null) ? optionalSubGrid.VolumeMask : null;
SpatialOperator d_dx = new SpatialOperator(1, 1, QuadOrderFunc.Linear(), "in", "out");
d_dx.EdgeQuadraturSchemeProvider = g => new Quadrature.EdgeQuadratureScheme(true, emEdge);
d_dx.VolumeQuadraturSchemeProvider = g => new Quadrature.CellQuadratureScheme(true, emVol);
var flux = CreateDerivativeFlux(d, f.Identification);
d_dx.EquationComponents["out"].Add(flux);
d_dx.Commit();
var ev = d_dx.GetEvaluatorEx(
new CoordinateMapping(f), null, this.Mapping);
if (optionalSubGrid != null)
{
ev.ActivateSubgridBoundary(optionalSubGrid.VolumeMask, bndMode);
}
ev.Evaluate <CoordinateVector>(alpha, 1.0, this.CoordinateVector);
}
/// <summary>
/// accumulates the projection of some vector field to this field, i.e.
/// \f[
/// this = this + \alpha \cdot \| \vec{vec} \|.
/// \f]
/// </summary>
/// <param name="alpha">factor \f$ \alpha \f$ </param>
/// <param name="vec">vector field \f$ \vec{vec} \f$ </param>
/// <param name="em">
/// An optional restriction to the domain in which the projection is computed (it may, e.g.
/// be only required in boundary cells, so a computation over the whole domain
/// would be a waste of computation power. If null, the computation is carried out in the whole domain;
/// </param>
virtual public void ProjectAbs(double alpha, CellMask em, params DGField[] vec)
{
int K = vec.Length;
string[] args = new string[K];
for (int k = 0; k < K; k++)
{
args[k] = "_" + k;
}
SpatialOperator powOp = new SpatialOperator(args, new string[] { "res" }, QuadOrderFunc.SumOfMaxDegrees());
powOp.EquationComponents["res"].Add(new AbsSource(args));
powOp.Commit();
CoordinateVector coDom = new CoordinateVector(this);
var ev = powOp.GetEvaluatorEx(
new CoordinateMapping(vec),
null,
coDom.Mapping,
edgeQrCtx: new EdgeQuadratureScheme(true, EdgeMask.GetEmptyMask(this.Basis.GridDat)),
volQrCtx: new CellQuadratureScheme(true, em));
ev.Evaluate <CoordinateVector>(alpha, 1.0, coDom); // only sources, no edge integrals required
}
/// <summary>
/// All edges that have to be considered for the integration of species <paramref name="sp"/>.
/// </summary>
/// <param name="sp"></param>
/// <param name="IntegrationDomainRestriction">Optional restriction to the integration domain.</param>
public EdgeMask GetEdgeMask(SpeciesId sp, EdgeMask IntegrationDomainRestriction = null)
{
if (!this.SpeciesList.Contains(sp))
{
throw new ArgumentException("Given species ( id = " + sp.cntnt + ") is not supported.");
}
EdgeMask allRelevantEdges;
if (IntegrationDomainRestriction == null)
{
allRelevantEdges = this.m_SpeciesSubgrid_InnerAndDomainEdges[sp];
}
else
{
// user provides integration domain, intersect with that
allRelevantEdges = this.m_SpeciesSubgrid_InnerAndDomainEdges[sp].Intersect(IntegrationDomainRestriction);
}
//// optionally, exclude edges between agglomerated cells
//EdgeMask AggEdges = (this.CellAgglomeration != null) ? (this.CellAgglomeration.GetAgglomerator(sp).AggInfo.AgglomerationEdges) : (default(EdgeMask));
//if (AggEdges != null && AggEdges.NoOfItemsLocally > 0)
// allRelevantEdges = allRelevantEdges.Except(AggEdges);
return(allRelevantEdges);
}
/// <summary>
///
/// </summary>
/// <param name="spatialOp"></param>
/// <param name="Fieldsmap"></param>
/// <param name="Parameters">
/// optional parameter fields, can be null if
/// <paramref name="spatialOp"/> contains no parameters; must match
/// the parameter field list of <paramref name="spatialOp"/>, see
/// <see cref="BoSSS.Foundation.SpatialOperator.ParameterVar"/>
/// </param>
/// <param name="sgrdBnd">
/// Options for the treatment of edges at the boundary of a SubGrid,
/// <see cref="SpatialOperator.SubGridBoundaryModes"/></param>
/// <param name="timeStepConstraints">
/// optional list of time step constraints <see cref="TimeStepConstraint"/>
/// </param>
/// <param name="sgrd">
/// optional restriction to computational domain
/// </param>
public ExplicitEuler(SpatialOperator spatialOp, CoordinateMapping Fieldsmap, CoordinateMapping Parameters, SpatialOperator.SubGridBoundaryModes sgrdBnd, IList <TimeStepConstraint> timeStepConstraints = null, SubGrid sgrd = null)
{
using (new ilPSP.Tracing.FuncTrace()) {
// verify input
// ============
if (!spatialOp.ContainsNonlinear && !(spatialOp.ContainsLinear()))
{
throw new ArgumentException("spatial differential operator seems to contain no components.", "spatialOp");
}
if (spatialOp.DomainVar.Count != spatialOp.CodomainVar.Count)
{
throw new ArgumentException("spatial differential operator must have the same number of domain and codomain variables.", "spatialOp");
}
if (Fieldsmap.Fields.Count != spatialOp.CodomainVar.Count)
{
throw new ArgumentException("the number of fields in the coordinate mapping must be equal to the number of domain/codomain variables of the spatial differential operator", "fields");
}
if (Parameters == null)
{
if (spatialOp.ParameterVar.Count != 0)
{
throw new ArgumentException("the number of fields in the parameter mapping must be equal to the number of parameter variables of the spatial differential operator", "Parameters");
}
}
else
{
if (Parameters.Fields.Count != spatialOp.ParameterVar.Count)
{
throw new ArgumentException("the number of fields in the parameter mapping must be equal to the number of parameter variables of the spatial differential operator", "Parameters");
}
}
Mapping = Fieldsmap;
DGCoordinates = new CoordinateVector(Mapping);
ParameterMapping = Parameters;
IList <DGField> ParameterFields =
(ParameterMapping == null) ? (new DGField[0]) : ParameterMapping.Fields;
this.TimeStepConstraints = timeStepConstraints;
SubGrid = sgrd ?? new SubGrid(CellMask.GetFullMask(Fieldsmap.First().GridDat));
// generate Evaluator
// ==================
CellMask cm = SubGrid.VolumeMask;
EdgeMask em = SubGrid.AllEdgesMask;
Operator = spatialOp;
m_Evaluator = new Lazy <SpatialOperator.Evaluator>(() => spatialOp.GetEvaluatorEx(
Fieldsmap, ParameterFields, Fieldsmap,
new EdgeQuadratureScheme(true, em),
new CellQuadratureScheme(true, cm),
SubGrid,
sgrdBnd));
}
}
public void Evaluate(EdgeMask em, SinglePhaseField inp_LevSet, SinglePhaseField outp_Result)
{
MsrMatrix Matrix;
Matrix = PenaltyMatrix(em, inp_LevSet.Basis, outp_Result.Basis);
Matrix.SpMV(1.0, inp_LevSet.CoordinateVector, 0.0, outp_Result.CoordinateVector);
}
/// <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);
}
}
/// <summary>
/// the jump-seminorm of DG-field <paramref name="f"/>:
/// <latex mode="display">
///
/// </latex>
/// </summary>
/// <param name="f"></param>
/// <param name="CM"></param>
/// <returns></returns>
public static double JumpSemiNorm(this Field f, EdgeMask CM = null)
{
using (new FuncTrace()) {
var qi = new EdgeQuadratureScheme(CM);
var quad = new JumpSemiNormIntegrator(f, qi);
quad.Execute();
return(Math.Sqrt(quad.overallResult));
}
}
static double JumpNorm(DGField f, EdgeMask em)
{
GridData grd = grid;
int D = grd.SpatialDimension;
var e2cTrafo = grd.Edges.Edge2CellTrafos;
double Unorm = 0;
EdgeQuadrature.GetQuadrature(
new int[] { D + 1 }, grd,
(new EdgeQuadratureScheme(true, em)).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 iTrafo_IN = grd.Edges.Edge2CellTrafoIndex[iEdge, 0];
int jCell_IN = grd.Edges.CellIndices[iEdge, 0];
int iTrafo_OT = grd.Edges.Edge2CellTrafoIndex[iEdge, 1];
int jCell_OT = grd.Edges.CellIndices[iEdge, 1];
MultidimensionalArray uIN = MultidimensionalArray.Create(1, NoOfNodes);
MultidimensionalArray uOT = MultidimensionalArray.Create(1, NoOfNodes);
MultidimensionalArray Grad_uIN = MultidimensionalArray.Create(1, NoOfNodes, D);
MultidimensionalArray Grad_uOT = MultidimensionalArray.Create(1, NoOfNodes, D);
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);
f.EvaluateGradient(jCell_IN, 1, NS_IN, Grad_uIN);
f.EvaluateGradient(jCell_OT, 1, NS_OT, Grad_uOT);
var uDiff = EvalResult.ExtractSubArrayShallow(new int[] { j, 0, 0 }, new int[] { j, NoOfNodes - 1, -1 });
var Grad_uDiff = EvalResult.ExtractSubArrayShallow(new int[] { j, 0, 1 }, new int[] { j, NoOfNodes - 1, D });
uDiff.Acc(+1.0, uIN);
uDiff.Acc(-1.0, uOT);
Grad_uDiff.Acc(+1.0, Grad_uIN);
Grad_uDiff.Acc(-1.0, Grad_uOT);
}
EvalResult.ApplyAll(x => x * x);
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) { // SaveIntegrationResults
Unorm += ResultsOfIntegration.Sum();
}).Execute();
double totNorm = Unorm.MPISum().Sqrt();
return(totNorm);
}
void ConstructorCommon()
{
var Krefs = this.XDGSpaceMetrics.GridDat.Grid.RefElements;
// initialize some mask's and subgrids
// ===================================
// since most methods of this class are non-collective,
// an access to some Subgrid-member may cause an MPI-deadlock.
// (this becomes even more unpredictable due to the on-demand-pattern in which most members of the Subgrid-class are implemented);
//
foreach (var spId in this.SpeciesList)
{
SubGrid spSgrd = this.XDGSpaceMetrics.LevelSetRegions.GetSpeciesSubGrid(spId);
this.m_SpeciesSubgrid_InnerAndDomainEdges.Add(
spId,
spSgrd.InnerEdgesMask.Union(spSgrd.AllEdgesMask.Intersect(XDGSpaceMetrics.GridDat.BoundaryEdges)));
}
// all cut edges
// =============
m_CutCellSubgrid_InnerEdges = this.XDGSpaceMetrics.LevelSetRegions.GetCutCellSubGrid().InnerEdgesMask;
// cut edges sorted according to reference element and level-set
// =============================================================
int NoOfLs = this.XDGSpaceMetrics.NoOfLevelSets;
this.m_CutEdges = new EdgeMask[Krefs.Length, NoOfLs];
this.m_HMFEdgesDomain = new EdgeMask[Krefs.Length, NoOfLs];
for (int iKref = 0; iKref < this.m_CutEdges.GetLength(0); iKref++)
{
for (int iLevSet = 0; iLevSet < this.m_CutEdges.GetLength(1); iLevSet++)
{
EdgeMask cutEdges = this.XDGSpaceMetrics.LevelSetRegions.GetCutCellSubgrid4LevSet(iLevSet).InnerEdgesMask.Union(
this.XDGSpaceMetrics.LevelSetRegions.GetCutCellSubgrid4LevSet(iLevSet).AllEdgesMask.Intersect(this.XDGSpaceMetrics.GridDat.BoundaryEdges));
cutEdges = cutEdges.Intersect(this.XDGSpaceMetrics.GridDat.GetRefElementSubGrid(iKref).AllEdgesMask);
cutEdges = cutEdges.ToGeometicalMask();
Debug.Assert(cutEdges.MaskType == MaskType.Geometrical);
this.m_CutEdges[iKref, iLevSet] = cutEdges;
// (all edges of 'Kref'-elements) \cap (all edges of cells cut by 'iLevSet')
this.m_HMFEdgesDomain[iKref, iLevSet] = this.XDGSpaceMetrics.LevelSetRegions.GetCutCellSubgrid4LevSet(iLevSet).AllEdgesMask.Intersect(this.XDGSpaceMetrics.GridDat.GetRefElementSubGrid(iKref).AllEdgesMask);
}
}
}
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);
}
private MsrMatrix PenaltyMatrix(EdgeMask em, Basis LevSetBasis, Basis JumpBasis)
{
var OpA = new SpatialOperator(1, 0, 1, QuadOrderFunc.Linear(), "Phi", "c1");
OpA.EquationComponents["c1"].Add(new JumpForm());
//OpA.EquationComponents["c1"].Add(new GradientJumpForm() { ATerm = true, BTerm = true });
OpA.EquationComponents["c1"].Add(new GradientJumpForm2());
OpA.Commit();
//var OpB = new SpatialOperator(1, 0, 1, "Phi", "c1");
//Op.EquationComponents["c1"].Add(new JumpForm());
//OpB.EquationComponents["c1"].Add(new GradientJumpForm() { BTerm = true });
//Op.EquationComponents["c1"].Add(new GradientJumpForm2());
//OpB.Commit();
var inp_LevSet_Mapping = new UnsetteledCoordinateMapping(LevSetBasis);
var outp_Result_Mapping = new UnsetteledCoordinateMapping(JumpBasis);
MsrMatrix MatrixA;
MatrixA = new MsrMatrix(outp_Result_Mapping, inp_LevSet_Mapping);
double[] AffineA = new double[inp_LevSet_Mapping.LocalLength];
OpA.ComputeMatrixEx(inp_LevSet_Mapping, null, outp_Result_Mapping,
MatrixA, AffineA, OnlyAffine: false,
edgeQuadScheme: new EdgeQuadratureScheme(true, em),
volQuadScheme: new CellQuadratureScheme(true, CellMask.GetEmptyMask(em.GridData)));
MatrixA.CheckForNanOrInfM();
//MsrMatrix MatrixB;
//MatrixB = new MsrMatrix(outp_Result_Mapping, inp_LevSet_Mapping);
//double[] AffineB = new double[inp_LevSet_Mapping.LocalLength];
//OpB.ComputeMatrixEx(inp_LevSet_Mapping, null, outp_Result_Mapping,
// MatrixB, AffineB, OnlyAffine: false
// );//,
// //edgeQrCtx: new EdgeQuadratureScheme(true, em),
// //volQrCtx: new CellQuadratureScheme(true, CellMask.GetEmptyMask(em.GridData)));
//Debug.Assert(AffineB.L2Norm() == 0);
//var Err = MatrixA.Transpose();
//Err.Acc(-1.0, MatrixB);
//double errnorm = Err.InfNorm();
//Debug.Assert(errnorm < 1.0e-10);
////Console.WriteLine("Errnorm:" + errnorm);
return(MatrixA);
}
internal void BuildEvaluatorsAndMasks()
{
CellMask fluidCells = speciesMap.SubGrid.VolumeMask.Intersect(ABSubGrid.VolumeMask);
cutCells = speciesMap.Tracker.Regions.GetCutCellMask().Intersect(ABSubGrid.VolumeMask);
cutAndTargetCells = cutCells.Union(speciesMap.Agglomerator.AggInfo.TargetCells).Intersect(ABSubGrid.VolumeMask);
IBMControl control = speciesMap.Control;
SpeciesId species = speciesMap.Tracker.GetSpeciesId(control.FluidSpeciesName);
CellQuadratureScheme volumeScheme = speciesMap.QuadSchemeHelper.GetVolumeQuadScheme(
species, true, fluidCells, control.LevelSetQuadratureOrder);
// Does _not_ include agglomerated edges
EdgeMask nonVoidEdges = speciesMap.QuadSchemeHelper.GetEdgeMask(species);
nonVoidEdges = nonVoidEdges.Intersect(ABSubGrid.AllEdgesMask.ToGeometicalMask());
EdgeQuadratureScheme edgeScheme = speciesMap.QuadSchemeHelper.GetEdgeQuadScheme(
species, true, nonVoidEdges, control.LevelSetQuadratureOrder);
this.m_Evaluator = new Lazy <IEvaluatorNonLin>(delegate() {
this.Operator.EdgeQuadraturSchemeProvider = g => edgeScheme;
this.Operator.VolumeQuadraturSchemeProvider = g => volumeScheme;
var opi = this.Operator.GetEvaluatorEx(
Mapping,
boundaryParameterMap,
Mapping);
opi.ActivateSubgridBoundary(ABSubGrid.VolumeMask, subGridBoundaryTreatment: SubGridBoundaryModes.InnerEdgeLTS);
return(opi);
});
// Evaluator for boundary conditions at level set zero contour
CellQuadratureScheme boundaryVolumeScheme = speciesMap.QuadSchemeHelper.GetLevelSetquadScheme(
0, cutCells, control.LevelSetQuadratureOrder);
this.boundaryEvaluator = new Lazy <IEvaluatorNonLin>(delegate() {
boundaryOperator.EdgeQuadraturSchemeProvider = g => null; // Contains no boundary terms --> PROBLEM??????????
boundaryOperator.VolumeQuadraturSchemeProvider = g => boundaryVolumeScheme;
return(boundaryOperator.GetEvaluatorEx(
Mapping,
boundaryParameterMap,
Mapping));
});
}
/// <summary>
/// Calculates the DG-projection (with respect to the DG-basis
/// of this field, <see cref="Basis"/>) of
/// <paramref name="alpha"/>*<paramref name="a"/>/<paramref name="b"/>
/// and, depending on the value of <paramref name="accumulateResult"/>,
/// either adds or assigns it to this field.
/// </summary>
/// <param name="a">1st multiplicand</param>
/// <param name="b">2nd multiplicand</param>
/// <param name="alpha">scaling for <paramref name="a"/>*<paramref name="b"/></param>
/// <param name="accumulateResult">
/// Tells this method whether to accumulate (true) or not (false)
/// </param>
/// <param name="cm">
/// optional restriction to computational domain
/// </param>
virtual public void ProjectQuotient(
double alpha, DGField a, DGField b, CellMask cm, bool accumulateResult)
{
if (!object.ReferenceEquals(a.Basis.GridDat, this.Basis.GridDat))
{
throw new ArgumentException("field is associated to another grid.", "a");
}
if (!object.ReferenceEquals(b.Basis.GridDat, this.Basis.GridDat))
{
throw new ArgumentException("field is associated to another grid.", "b");
}
if (!accumulateResult)
{
if (a == this)
{
a = (DGField)a.Clone();
if (b == this)
{
b = a;
}
}
else if (b == this)
{
b = (DGField)b.Clone();
}
this.Clear();
}
SpatialOperator fracOp = new SpatialOperator(new string[] { "a", "b" },
new string[] { "res" },
QuadOrderFunc.Linear());
fracOp.EquationComponents["res"].Add(new QuotientSource());
fracOp.Commit();
CoordinateVector coDom = this.CoordinateVector;
var ev = fracOp.GetEvaluatorEx(
new CoordinateMapping(a, b), null, coDom.Mapping,
edgeQrCtx: new EdgeQuadratureScheme(true, EdgeMask.GetEmptyMask(this.Basis.GridDat)),
volQrCtx: new CellQuadratureScheme(true, cm));
ev.Evaluate <CoordinateVector>(alpha, 1.0, coDom);
}
private void BuildEvaluatorsAndMasks()
{
CellMask fluidCells = speciesMap.SubGrid.VolumeMask;
cutCells = speciesMap.Tracker.Regions.GetCutCellMask();
cutAndTargetCells = cutCells.Union(speciesMap.Agglomerator.AggInfo.TargetCells);
IBMControl control = speciesMap.Control;
SpeciesId species = speciesMap.Tracker.GetSpeciesId(control.FluidSpeciesName);
CellQuadratureScheme volumeScheme = speciesMap.QuadSchemeHelper.GetVolumeQuadScheme(
species, true, fluidCells, control.LevelSetQuadratureOrder);
// Does _not_ include agglomerated edges
EdgeMask nonVoidEdges = speciesMap.QuadSchemeHelper.GetEdgeMask(species);
EdgeQuadratureScheme edgeScheme = speciesMap.QuadSchemeHelper.GetEdgeQuadScheme(
species, true, nonVoidEdges, control.LevelSetQuadratureOrder);
this.m_Evaluator = new Lazy <IEvaluatorNonLin>(delegate() {
this.Operator.EdgeQuadraturSchemeProvider = g => edgeScheme;
this.Operator.VolumeQuadraturSchemeProvider = g => volumeScheme;
var opi = this.Operator.GetEvaluatorEx(
Mapping,
null, // TO DO: I SIMPLY REMOVE PARAMETERMAP HERE; MAKE THIS MORE PRETTY
//this.boundaryParameterMap, // TO DO: I SIMPLY REMOVE PARAMETERMAP HERE; MAKE THIS MORE PRETTY
Mapping);
opi.ActivateSubgridBoundary(volumeScheme.Domain, subGridBoundaryTreatment: SubGridBoundaryModes.InnerEdgeLTS);
//opi.ActivateSubgridBoundary(fluidCells, subGridBoundaryTreatment: SubGridBoundaryModes.InnerEdgeLTS);
return(opi);
});
// Evaluator for boundary conditions at level set zero contour
CellQuadratureScheme boundaryVolumeScheme = speciesMap.QuadSchemeHelper.GetLevelSetquadScheme(
0, cutCells, control.LevelSetQuadratureOrder);
this.boundaryEvaluator = new Lazy <IEvaluatorNonLin>(delegate() {
boundaryOperator.EdgeQuadraturSchemeProvider = g => null; // Contains no boundary terms
boundaryOperator.VolumeQuadraturSchemeProvider = g => boundaryVolumeScheme;
return(boundaryOperator.GetEvaluatorEx(
Mapping,
boundaryParameterMap,
Mapping));
});
}
internal void BuildEvaluatorsAndMasks()
{
CellMask fluidCells = speciesMap.SubGrid.VolumeMask.Intersect(ABSubGrid.VolumeMask);
cutCells = speciesMap.Tracker.Regions.GetCutCellMask().Intersect(ABSubGrid.VolumeMask);
cutAndTargetCells = cutCells.Union(speciesMap.Agglomerator.AggInfo.TargetCells).Intersect(ABSubGrid.VolumeMask);
IBMControl control = speciesMap.Control;
SpeciesId species = speciesMap.Tracker.GetSpeciesId(control.FluidSpeciesName);
CellQuadratureScheme volumeScheme = speciesMap.QuadSchemeHelper.GetVolumeQuadScheme(
species, true, fluidCells, control.LevelSetQuadratureOrder);
// Does _not_ include agglomerated edges
EdgeMask nonVoidEdges = speciesMap.QuadSchemeHelper.GetEdgeMask(species);
nonVoidEdges = nonVoidEdges.Intersect(ABSubGrid.AllEdgesMask);
EdgeQuadratureScheme edgeScheme = speciesMap.QuadSchemeHelper.GetEdgeQuadScheme(
species, true, nonVoidEdges, control.LevelSetQuadratureOrder);
this.m_Evaluator = new Lazy <SpatialOperator.Evaluator>(() =>
this.Operator.GetEvaluatorEx(
Mapping,
boundaryParameterMap,
Mapping,
edgeScheme,
volumeScheme,
ABSubGrid,
subGridBoundaryTreatment: SpatialOperator.SubGridBoundaryModes.InnerEdgeLTS));
// Evaluator for boundary conditions at level set zero contour
CellQuadratureScheme boundaryVolumeScheme = speciesMap.QuadSchemeHelper.GetLevelSetquadScheme(
0, cutCells, control.LevelSetQuadratureOrder);
this.boundaryEvaluator = new Lazy <SpatialOperator.Evaluator>(() =>
boundaryOperator.GetEvaluatorEx(
Mapping,
boundaryParameterMap,
Mapping,
null, // Contains no boundary terms --> PROBLEM??????????
boundaryVolumeScheme));
}
/// <summary>
/// Saves the sum of weights of each edge rule in the given
/// <paramref name="compositeRule"/> together with the coordinates of
/// the corresponding edge center into a text file.
/// </summary>
public static void SumOfWeightsToTextFileEdge(this ICompositeQuadRule <QuadRule> compositeRule, IGridData g, string filename)
{
int E = g.iLogicalEdges.Count;
var bMask = new System.Collections.BitArray(E);
double[] wSum = new double[E];
foreach (IChunkRulePair <QuadRule> crp in compositeRule)
{
for (int iEdge = crp.Chunk.i0; iEdge < crp.Chunk.JE; iEdge++)
{
bMask[iEdge] = true;
wSum[iEdge] = crp.Rule.Weights.Sum();
}
}
var mask = new EdgeMask(g, bMask);
mask.SaveToTextFile(filename, false, (X, i, ii) => wSum[i]);
}
/// <summary>
/// Boundary quadrature for the surface elements, i.e. for each cut background-cell \f$ K_j \f$ a quadrature to approximate
/// \f[
/// \int_{\partial K_j \cap \mathfrak{I} } \ldots \mathrm{dS} .
/// \f]
/// </summary>
public EdgeQuadratureScheme GetEdgeQuadScheme(SpeciesId sp, bool UseDefaultFactories = true, EdgeMask IntegrationDomain = null, int?fixedOrder = null)
{
if (!this.SpeciesList.Contains(sp))
{
throw new ArgumentException("Given species (id = " + sp.cntnt + ") is not supported.");
}
// determine domain
// ================
var allRelevantEdges = GetEdgeMask(sp, IntegrationDomain);
// create quadrature scheme
// ========================
{
// default rules for all edges:
EdgeQuadratureScheme edgeQrIns = new EdgeQuadratureScheme(UseDefaultFactories, allRelevantEdges);
// overwrite with cut-cell-rules in cut-cells:
foreach (var Kref in XDGSpaceMetrics.GridDat.Grid.RefElements)
{
for (int iLevSet = 0; iLevSet < XDGSpaceMetrics.NoOfLevelSets; iLevSet++) // loop over level sets...
{
EdgeMask cutEdges = this.GetCutEdges(Kref, iLevSet).Intersect(allRelevantEdges);
#if DEBUG
CellMask difference = cutEdges.GetAdjacentCells(XDGSpaceMetrics.GridDat).Except(XDGSpaceMetrics.LevelSetRegions.GetCutCellMask4LevSet(iLevSet));
if (difference.Count() > 0)
{
throw new ArithmeticException("Edges of the Cells" + difference.GetSummary() + " are detected as cut, but these cells are not contained in the cut Cell-Mask of the Level-Set-Tracker");
}
#endif
var jmp = IdentifyWing(iLevSet, sp);
var factory = this.XDGSpaceMetrics.XQuadFactoryHelper.GetEdgeRuleFactory(iLevSet, jmp, Kref);
edgeQrIns.AddFactoryDomainPair(factory, cutEdges, fixedOrder);
}
}
return(edgeQrIns);
}
}
/// <summary>
/// Initializes the integral
/// </summary>
/// <param name="grdDat">Information about the grid</param>
/// <param name="edgeTag">
/// The edge tag of the boundary edges to be considered in the integral
/// </param>
/// <param name="flux">
/// The integrand. To be more specific,
/// <see cref="INonlinearFlux.BorderEdgeFlux"/> will be evaluated on
/// every relevant edge to compute the value of the integrand
/// </param>
/// <param name="mapping">
/// The coordinate mapping that maps field values to the arguments of
/// <paramref name="flux"/> (see
/// <see cref="IEquationComponent.ArgumentOrdering"/>)
/// </param>
/// <param name="integrationOrder">
/// The desired order of the applied quadrature rule
/// </param>
public EdgeIntegral(GridData grdDat, byte edgeTag, INonlinearFlux flux, CoordinateMapping mapping, int integrationOrder)
{
byte[] edgeTags = grdDat.Edges.EdgeTags;
BitArray mask = new BitArray(edgeTags.Length);
int numberOfRelevantEdges = 0;
for (int i = 0; i < edgeTags.Length; i++)
{
if (edgeTag == edgeTags[i])
{
mask[i] = true;
numberOfRelevantEdges++;
}
}
relevantEdgesMask = new EdgeMask(grdDat, mask);
// Just use first ref element for the moment
edgeQuadrature = new MyEdgeQuadrature(grdDat, integrationOrder, flux, mapping, 0, relevantEdgesMask);
}
protected void UpdateEvaluatorsAndMasks()
{
CellMask fluidCells = speciesMap.SubGrid.VolumeMask;
cutCells = speciesMap.Tracker.Regions.GetCutCellMask();
cutAndTargetCells = cutCells.Union(speciesMap.Agglomerator.AggInfo.TargetCells);
IBMControl control = speciesMap.Control;
SpeciesId species = speciesMap.Tracker.GetSpeciesId(control.FluidSpeciesName);
CellQuadratureScheme volumeScheme = speciesMap.QuadSchemeHelper.GetVolumeQuadScheme(
species, true, fluidCells, control.LevelSetQuadratureOrder);
// Does _not_ include agglomerated edges
EdgeMask nonVoidEdges = speciesMap.QuadSchemeHelper.GetEdgeMask(species);
EdgeQuadratureScheme edgeScheme = speciesMap.QuadSchemeHelper.GetEdgeQuadScheme(
species, true, nonVoidEdges, control.LevelSetQuadratureOrder);
this.m_Evaluator = new Lazy <IEvaluatorNonLin>(delegate() {
var opi = this.Operator.GetEvaluatorEx(
Mapping,
boundaryParameterMap,
Mapping,
edgeScheme,
volumeScheme);
opi.ActivateSubgridBoundary(volumeScheme.Domain.ToLogicalMask(), subGridBoundaryTreatment: SpatialOperator.SubGridBoundaryModes.InnerEdgeLTS);
return(opi);
});
// Evaluator for boundary conditions at level set zero contour
CellQuadratureScheme boundaryVolumeScheme = speciesMap.QuadSchemeHelper.GetLevelSetquadScheme(
0, cutCells, control.LevelSetQuadratureOrder);
this.boundaryEvaluator = new Lazy <IEvaluatorNonLin>(() =>
boundaryOperator.GetEvaluatorEx(
Mapping,
boundaryParameterMap,
Mapping,
null, // Contains no boundary terms
boundaryVolumeScheme));
}
/// <summary>
/// accumulates
/// <paramref name="alpha"/>*<paramref name="f"/>(<paramref name="U"/>)
/// to this field;
/// </summary>
/// <param name="alpha">scaling</param>
/// <param name="f">
/// some function
/// - 1st argument: position in physical space
/// - 2nd argument: values of fields in <paramref name="U"/> at respective position
/// - 3rd argument: cell index
/// - return value: value of function that should be projected at the respective position
/// </param>
/// <param name="cqs">
/// cell quadrature scheme: domain and quadrature rule
/// </param>
/// <param name="U">
/// arguments for <paramref name="f"/>
/// </param>
public void ProjectFunction(double alpha, Func <Vector, double[], int, double> f, CellQuadratureScheme cqs, params DGField[] U)
{
string[] Dom = new string[U.Length];
for (int i = 0; i < Dom.Length; i++)
{
Dom[i] = "_" + i;
}
string[] Cod = new string[] { "res" };
SpatialOperator src = new SpatialOperator(Dom, Cod, QuadOrderFunc.NonLinear(3));
src.EquationComponents[Cod[0]].Add(new ProjectFunctionSource(Dom, f));
src.EdgeQuadraturSchemeProvider = g => new EdgeQuadratureScheme(false, EdgeMask.GetEmptyMask(this.Basis.GridDat));
src.VolumeQuadraturSchemeProvider = g => cqs;
src.Commit();
var ev = src.GetEvaluatorEx(
new CoordinateMapping(U), null, this.Mapping);
ev.Evaluate(alpha, 1.0, this.CoordinateVector);
}
/// <summary>
/// Accumulates the DG-projection (with respect to the DG-basis
/// of this field, <see cref="Basis"/>) of
/// <paramref name="alpha"/>*<paramref name="f"/>^<paramref name="pow"/> to this field;
/// </summary>
/// <param name="alpha">scaling for accumulation</param>
/// <param name="f">operand</param>
/// <param name="pow">exponent</param>
/// <param name="em">
/// An optional restriction to the domain in which the projection is
/// computed (it may, e.g. be only required in boundary cells, so a
/// computation over the whole domain would be a waste of computation
/// power. A proper execution mask would be see e.g.
/// <see cref="GridData.BoundaryCells"/>.)
/// if null, the computation is carried out in the whole domain;
/// </param>
virtual public void ProjectPow(double alpha, DGField f, double pow, CellMask em)
{
if (!object.ReferenceEquals(f.Basis.GridDat, this.Basis.GridDat))
{
throw new ArgumentException("field is associated to another context.", "a");
}
SpatialOperator powOp = new SpatialOperator(new string[] { "f" },
new string[] { "res" },
QuadOrderFunc.SumOfMaxDegrees());
powOp.EquationComponents["res"].Add(new PowSource(pow));
powOp.Commit();
CoordinateVector coDom = this.CoordinateVector;
var ev = powOp.GetEvaluatorEx(
new CoordinateMapping(f), null, coDom.Mapping,
edgeQrCtx: new EdgeQuadratureScheme(true, EdgeMask.GetEmptyMask(this.Basis.GridDat)),
volQrCtx: new CellQuadratureScheme(true, em));
ev.Evaluate <CoordinateVector>(alpha, 1.0, coDom); // only sources, no edge integrals required
}
/// <summary>
/// Calculates the DG-projection (with respect to the DG-basis
/// of this field, <see cref="Basis"/>) of
/// <paramref name="alpha"/>*<paramref name="a"/>*<paramref name="b"/>
/// and, depending on the value of <paramref name="accumulateResult"/>,
/// either adds or assigns it to this field.
/// </summary>
/// <param name="a">1st multiplicand</param>
/// <param name="b">2nd multiplicand</param>
/// <param name="alpha">scaling for <paramref name="a"/>*<paramref name="b"/></param>
/// <param name="em">
/// An optional restriction to the domain in which the projection is
/// computed (it may, e.g. be only required in boundary cells, so a
/// computation over the whole domain would be a waste of computational
/// power. A proper execution mask would be see e.g.
/// <see cref="GridData.BoundaryCells"/>.)<br/>
/// if null, the computation is carried out in the whole domain;
/// </param>
/// <param name="accumulateResult">
/// Tells this method whether to accumulate (true) or not (false)
/// </param>
virtual public void ProjectProduct(double alpha, DGField a, DGField b, CellMask em, bool accumulateResult)
{
if (!object.ReferenceEquals(a.Basis.GridDat, this.Basis.GridDat))
{
throw new ArgumentException("field is associated to another grid.", "a");
}
if (!object.ReferenceEquals(b.Basis.GridDat, this.Basis.GridDat))
{
throw new ArgumentException("field is associated to another grid.", "b");
}
if (!accumulateResult)
{
if (a == this)
{
a = (DGField)a.Clone();
if (b == this)
{
b = a;
}
}
else if (b == this)
{
b = (DGField)b.Clone();
}
this.Clear();
}
SpatialOperator multOp = new SpatialOperator(new string[] { "a", "b" },
new string[] { "res" },
QuadOrderFunc.NonLinear(2));
multOp.EdgeQuadraturSchemeProvider = g => new EdgeQuadratureScheme(true, EdgeMask.GetEmptyMask(g));
multOp.VolumeQuadraturSchemeProvider = g => new CellQuadratureScheme(true, em);
multOp.EquationComponents["res"].Add(new MultiplySource());
multOp.Commit();
var ev = multOp.GetEvaluatorEx(
new[] { a, b }, null, this.Mapping);
ev.Evaluate <CoordinateVector>(alpha, 1.0, this.CoordinateVector);
}
/// <summary>
/// Calculates the drag (x-component) and lift (y-component) forces acting on a wall of a boundary fitted grid
/// </summary>
/// <param name="U"></param>
/// <param name="P"></param>
/// <param name="muA"></param>
/// <returns></returns>
static public double[] GetForces_BoundaryFitted(VectorField <SinglePhaseField> GradU, VectorField <SinglePhaseField> GradV, SinglePhaseField StressXX,
SinglePhaseField StressXY, SinglePhaseField StressYY, SinglePhaseField P, LevelSetTracker LsTrk, double muA, double beta)
{
int D = LsTrk.GridDat.SpatialDimension;
if (D > 2)
{
throw new ArgumentException("Method GetForces_BoundaryFitted only implemented for 2D (viscoelastic)!");
}
// var UA = U.Select(u => u.GetSpeciesShadowField("A")).ToArray();
//var UA = U.ToArray();
MultidimensionalArray Grad_U = new MultidimensionalArray(D);
var _GradU = GradU.ToArray();
var _GradV = GradV.ToArray();
int RequiredOrder = _GradU[0].Basis.Degree * 3 + 2;
//int RequiredOrder = U[0].Basis.Degree * 3 + 2;
//int RequiredOrder = LsTrk.GetXQuadFactoryHelper(momentFittingVariant).GetCachedSurfaceOrders(0).Max();
//Console.WriteLine("Order reduction: {0} -> {1}", _RequiredOrder, RequiredOrder);
//if (RequiredOrder > agg.HMForder)
// throw new ArgumentException();
Console.WriteLine("Forces coeff: {0}, order = {1}", LsTrk.CutCellQuadratureType, RequiredOrder);
SinglePhaseField _StressXX = StressXX;
SinglePhaseField _StressXY = StressXY;
SinglePhaseField _StressYY = StressYY;
SinglePhaseField pA = null;
//pA = P.GetSpeciesShadowField("A");
pA = P;
double[] forces = new double[D];
for (int d = 0; d < D; d++)
{
ScalarFunctionEx ErrFunc = delegate(int j0, int Len, NodeSet Ns, MultidimensionalArray result) {
int K = result.GetLength(1); // No nof Nodes
MultidimensionalArray Grad_URes = MultidimensionalArray.Create(Len, K, D);
MultidimensionalArray Grad_VRes = MultidimensionalArray.Create(Len, K, D);
MultidimensionalArray pARes = MultidimensionalArray.Create(Len, K);
MultidimensionalArray StressXXRes = MultidimensionalArray.Create(Len, K);
MultidimensionalArray StressXYRes = MultidimensionalArray.Create(Len, K);
MultidimensionalArray StressYYRes = MultidimensionalArray.Create(Len, K);
var Normals = LsTrk.GridDat.Edges.NormalsCache.GetNormals_Edge(Ns, j0, Len);
//var Normals = MultidimensionalArray.Create(1, Ns.Length, 1);
//var Normals = LsTrk.GridDat.Edges.NormalsForAffine;
for (int i = 0; i < D; i++)
{
_GradU[i].EvaluateEdge(j0, Len, Ns, Grad_URes.ExtractSubArrayShallow(-1, -1, i),
Grad_URes.ExtractSubArrayShallow(-1, -1, i), ResultIndexOffset: 0, ResultPreScale: 1);
_GradV[i].EvaluateEdge(j0, Len, Ns, Grad_VRes.ExtractSubArrayShallow(-1, -1, i),
Grad_VRes.ExtractSubArrayShallow(-1, -1, i), ResultIndexOffset: 0, ResultPreScale: 1);
//UA[i].EvaluateGradient(j0, Len, Ns, Grad_UARes.ExtractSubArrayShallow(-1, -1, i, -1), 0, 1);
}
//pA.Evaluate(j0, Len, Ns, pARes);
pA.EvaluateEdge(j0, Len, Ns, pARes, pARes, ResultIndexOffset: 0, ResultPreScale: 1);
_StressXX.EvaluateEdge(j0, Len, Ns, StressXXRes, StressXXRes, ResultIndexOffset: 0, ResultPreScale: 1);
_StressXY.EvaluateEdge(j0, Len, Ns, StressXYRes, StressXYRes, ResultIndexOffset: 0, ResultPreScale: 1);
_StressYY.EvaluateEdge(j0, Len, Ns, StressYYRes, StressYYRes, ResultIndexOffset: 0, ResultPreScale: 1);
//if (LsTrk.GridDat.SpatialDimension == 2)
//{
for (int j = 0; j < Len; j++)
{
for (int k = 0; k < K; k++)
{
double acc = 0.0;
// pressure
switch (d)
{
case 0:
acc += pARes[j, k] * Normals[j, k, 0];
acc -= (2 * muA * beta) * Grad_URes[j, k, 0] * Normals[j, k, 0];
acc -= (muA * beta) * Grad_URes[j, k, 1] * Normals[j, k, 1];
acc -= (muA * beta) * Grad_VRes[j, k, 0] * Normals[j, k, 1];
acc -= (muA * (1 - beta)) * StressXXRes[j, k] * Normals[j, k, 0];
acc -= (muA * (1 - beta)) * StressXYRes[j, k] * Normals[j, k, 1];
break;
case 1:
acc += pARes[j, k] * Normals[j, k, 1];
acc -= (2 * muA * beta) * Grad_VRes[j, k, 1] * Normals[j, k, 1];
acc -= (muA * beta) * Grad_VRes[j, k, 0] * Normals[j, k, 0];
acc -= (muA * beta) * Grad_URes[j, k, 1] * Normals[j, k, 0];
acc -= (muA * (1 - beta)) * StressXYRes[j, k] * Normals[j, k, 0];
acc -= (muA * (1 - beta)) * StressYYRes[j, k] * Normals[j, k, 1];
break;
default:
throw new NotImplementedException();
}
result[j, k] = acc;
}
}
//}
//else
//{
// for (int j = 0; j < Len; j++)
// {
// for (int k = 0; k < K; k++)
// {
// double acc = 0.0;
// // pressure
// switch (d)
// {
// case 0:
// acc += pARes[j, k] * Normals[j, k, 0];
// acc -= (2 * muA) * Grad_UARes[j, k, 0, 0] * Normals[j, k, 0];
// acc -= (muA) * Grad_UARes[j, k, 0, 2] * Normals[j, k, 2];
// acc -= (muA) * Grad_UARes[j, k, 0, 1] * Normals[j, k, 1];
// acc -= (muA) * Grad_UARes[j, k, 1, 0] * Normals[j, k, 1];
// acc -= (muA) * Grad_UARes[j, k, 2, 0] * Normals[j, k, 2];
// break;
// case 1:
// acc += pARes[j, k] * Normals[j, k, 1];
// acc -= (2 * muA) * Grad_UARes[j, k, 1, 1] * Normals[j, k, 1];
// acc -= (muA) * Grad_UARes[j, k, 1, 2] * Normals[j, k, 2];
// acc -= (muA) * Grad_UARes[j, k, 1, 0] * Normals[j, k, 0];
// acc -= (muA) * Grad_UARes[j, k, 0, 1] * Normals[j, k, 0];
// acc -= (muA) * Grad_UARes[j, k, 2, 1] * Normals[j, k, 2];
// break;
// case 2:
// acc += pARes[j, k] * Normals[j, k, 2];
// acc -= (2 * muA) * Grad_UARes[j, k, 2, 2] * Normals[j, k, 2];
// acc -= (muA) * Grad_UARes[j, k, 2, 0] * Normals[j, k, 0];
// acc -= (muA) * Grad_UARes[j, k, 2, 1] * Normals[j, k, 1];
// acc -= (muA) * Grad_UARes[j, k, 0, 2] * Normals[j, k, 0];
// acc -= (muA) * Grad_UARes[j, k, 1, 2] * Normals[j, k, 1];
// break;
// default:
// throw new NotImplementedException();
// }
// result[j, k] = acc;
//}
//}
//}
};
var SchemeHelper = LsTrk.GetXDGSpaceMetrics(new[] { LsTrk.GetSpeciesId("A") }, RequiredOrder, 1).XQuadSchemeHelper;
EdgeMask Mask = new EdgeMask(LsTrk.GridDat, "Wall_cylinder");
EdgeQuadratureScheme eqs = SchemeHelper.GetEdgeQuadScheme(LsTrk.GetSpeciesId("A"), IntegrationDomain: Mask);
EdgeQuadrature.GetQuadrature(new int[] { 1 }, LsTrk.GridDat,
eqs.Compile(LsTrk.GridDat, RequiredOrder), // agg.HMForder),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
ErrFunc(i0, Length, QR.Nodes, EvalResult.ExtractSubArrayShallow(-1, -1, 0));
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
for (int i = 0; i < Length; i++)
{
forces[d] += ResultsOfIntegration[i, 0];
}
}
).Execute();
}
//for (int i = 0; i < D; i++)
// forces[i] = MPI.Wrappers.MPIExtensions.MPISum(forces[i]);
return(forces);
}
/// <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>
/// Legacy interface, preserved as static function.
/// </summary>
static public void ComputeMatrixEx <M, V>(
this XSpatialOperator xOp,
LevelSetTracker lsTrk,
UnsetteledCoordinateMapping DomainMap, IList <DGField> Parameters, UnsetteledCoordinateMapping CodomainMap,
M Matrix, V AffineOffset, bool OnlyAffine, double time, bool MPIParameterExchange,
IDictionary <SpeciesId, XSpatialOperator.QrSchemPair> SpeciesSchemes,
IDictionary <SpeciesId, MultidimensionalArray> CellLengthScales,
IDictionary <SpeciesId, MultidimensionalArray> InterfaceLengthScales,
MultidimensionalArray SlipLengths = null,
SubGrid SubGrid = null)
where M : IMutableMatrixEx
where V : IList <double> //
{
CellMask SubGridCellMask = null;
EdgeMask SubGridEdgeMask = null;
if (SubGrid != null)
{
SubGridCellMask = SubGrid.VolumeMask;
/// I don't know why, but this seems to work:
SubGridEdgeMask = SubGrid.AllEdgesMask;
/// And this does not:
//SubGridEdgeMask = SubGrid.InnerEdgesMask;
}
SpeciesId[] ReqSpecies = SpeciesSchemes.Keys.ToArray();
//int order = xOp.GetOrderFromQuadOrderFunction(DomainMap, Parameters, CodomainMap);
//var SchemeHelper = lsTrk.GetXDGSpaceMetrics(ReqSpecies, order, 1).XQuadSchemeHelper;
//var SpeciesSchemes_out = new Dictionary<SpeciesId, XSpatialOperator.QrSchemPair>();
//foreach(var SpeciesId in SpeciesSchemes.Keys) {
// EdgeQuadratureScheme edgeScheme;
// CellQuadratureScheme cellScheme;
// var qrSchemes = SpeciesSchemes[SpeciesId];
// bool AssembleOnFullGrid = (SubGrid == null);
// if(qrSchemes.EdgeScheme == null) {
// edgeScheme = SchemeHelper.GetEdgeQuadScheme(SpeciesId, AssembleOnFullGrid, SubGridEdgeMask);
// } else {
// //edgeScheme = qrSchemes.EdgeScheme;
// //throw new ArgumentException();
// }
// if(qrSchemes.CellScheme == null) {
// cellScheme = SchemeHelper.GetVolumeQuadScheme(SpeciesId, AssembleOnFullGrid, SubGridCellMask);
// } else {
// //cellScheme = qrSchemes.CellScheme;
// throw new ArgumentException();
// }
// SpeciesSchemes_out.Add(SpeciesId,
// new XSpatialOperator.QrSchemPair() {
// CellScheme = cellScheme,
// EdgeScheme = edgeScheme
// });
//}
var ev = xOp.GetMatrixBuilder(lsTrk, DomainMap, Parameters, CodomainMap, SpeciesSchemes);
ev.time = time;
ev.MPITtransceive = MPIParameterExchange;
foreach (var s in CellLengthScales.Keys)
{
if (ev.SpeciesOperatorCoefficients.ContainsKey(s))
{
ev.SpeciesOperatorCoefficients[s].CellLengthScales = CellLengthScales[s];
}
else
{
ev.SpeciesOperatorCoefficients.Add(s,
new CoefficientSet()
{
CellLengthScales = CellLengthScales[s],
GrdDat = lsTrk.GridDat
});
}
if (InterfaceLengthScales != null)
{
ev.SpeciesOperatorCoefficients[s].UserDefinedValues["InterfaceLengths"] = InterfaceLengthScales[s];
}
if (SlipLengths != null)
{
ev.SpeciesOperatorCoefficients[s].UserDefinedValues["SlipLengths"] = SlipLengths;
}
}
if (OnlyAffine)
{
ev.ComputeAffine(AffineOffset);
}
else
{
ev.ComputeMatrix(Matrix, AffineOffset);
}
}
