/// <summary>
/// Returns all cells with the respective artificial viscosity value
/// if the value is larger than zero
/// </summary>
/// <param name="gridData">The needed <see cref="GridData"/></param>
/// <param name="avField">The artificial visocsity <see cref="SinglePhaseField"/></param>
/// <returns> <see cref="MultidimensionalArray"/>
/// Lenghts --> [0]: number of points (AV > 0), [1]: 2
/// [1] --> [0]: cellIndex, [2:] AV value
/// </returns>
public static MultidimensionalArray GetAVMeanValues(GridData gridData, SinglePhaseField avField)
{
CellMask allCells = CellMask.GetFullMask(gridData);
double[] cellIndices = new double[allCells.NoOfItemsLocally];
double[] avValues = new double[allCells.NoOfItemsLocally];
int count = 0;
foreach (int cell in allCells.ItemEnum)
{
double avValue = avField.GetMeanValue(cell);
if (avValue > 0.0)
{
cellIndices[count] = cell;
avValues[count] = avValue;
count++;
}
}
Array.Resize(ref cellIndices, count);
Array.Resize(ref avValues, count);
MultidimensionalArray result = MultidimensionalArray.Create(count, 2);
result.SetSubVector(cellIndices, new int[] { -1, 0 });
result.SetSubVector(avValues, new int[] { -1, 1 });
return(result);
}
/// <summary>
/// Determines the admissible step-size within
/// <paramref name="subGrid"/> by calling
/// <see cref="GetLocalStepSize"/> for all contiguous chunks of cells.
/// </summary>
/// <param name="subGrid">
/// The sub-grid for which the step size shall be determined. If null
/// is given, the full domain will be considered.
/// </param>
/// <returns>
/// The maximum step size dictated by the CFL restriction in the given
/// <paramref name="subGrid"/>.
/// </returns>
/// <remarks>
/// This is a collective call which requires all processes to
/// synchronize.
/// </remarks>
public double GetGloballyAdmissibleStepSize(SubGrid subGrid = null)
{
MPICollectiveWatchDog.Watch();
subGrid = subGrid ?? new SubGrid(CellMask.GetFullMask(gridData));
double maxTimeStep = double.MaxValue;
double globalMaxTimeStep;
System.Exception e = null;
try {
foreach (Chunk chunk in subGrid.VolumeMask)
{
maxTimeStep = Math.Min(
maxTimeStep,
GetLocalStepSize(chunk.i0, chunk.Len));
}
} catch (System.Exception ee) {
e = ee;
}
e.ExceptionBcast();
unsafe
{
csMPI.Raw.Allreduce(
(IntPtr)(&maxTimeStep),
(IntPtr)(&globalMaxTimeStep),
1,
csMPI.Raw._DATATYPE.DOUBLE,
csMPI.Raw._OP.MIN,
csMPI.Raw._COMM.WORLD);
}
return(dtFraction * globalMaxTimeStep);
}
/// <summary>
/// Utility function to evaluate DG fields together with global nodes.
/// </summary>
/// <param name="f">DG field to evaluate.</param>
/// <param name="NS">node set.</param>
/// <param name="cm">optional cell mask.</param>
/// <returns>
/// Global nodes and function values at these nodes;
/// 1st index: cell index;
/// 2nd index: node index;
/// 3rd index: spatial direction
/// </returns>
public static MultidimensionalArray Evaluate(this DGField f, NodeSet NS, CellMask cm = null)
{
IGridData g = f.GridDat;
if (cm == null)
{
cm = CellMask.GetFullMask(g);
}
int D = g.SpatialDimension;
MultidimensionalArray ret = MultidimensionalArray.Create(new int[] { cm.NoOfItemsLocally, NS.NoOfNodes, D + 1 });
int jsub = 0;
foreach (Chunk ck in cm)
{
var globNodes = ret.ExtractSubArrayShallow(new int[] { jsub, 0, 0 }, new int[] { jsub + ck.Len - 1, NS.NoOfNodes - 1, D - 1 });
var fldValues = ret.ExtractSubArrayShallow(new int[] { jsub, 0, D }, new int[] { jsub + ck.Len - 1, NS.NoOfNodes - 1, D - 1 });
g.TransformLocal2Global(NS, ck.i0, ck.Len, globNodes);
f.Evaluate(ck.i0, ck.Len, NS, fldValues);
}
return(ret);
}
/// <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>
/// Calculate A Level-Set field from the Explicit description
/// </summary>
/// <param name="LevelSet">Target Field</param>
/// <param name="LsTrk"></param>
public void ProjectToDGLevelSet(SinglePhaseField LevelSet, LevelSetTracker LsTrk = null)
{
CellMask VolMask;
if (LsTrk == null)
{
VolMask = CellMask.GetFullMask(LevelSet.Basis.GridDat);
}
else
{
// set values in positive and negative FAR region to +1 and -1
CellMask Near = LsTrk.Regions.GetNearMask4LevSet(0, 1);
CellMask PosFar = LsTrk.Regions.GetLevelSetWing(0, +1).VolumeMask.Except(Near);
CellMask NegFar = LsTrk.Regions.GetLevelSetWing(0, -1).VolumeMask.Except(Near);
LevelSet.Clear(PosFar);
LevelSet.AccConstant(1, PosFar);
LevelSet.Clear(NegFar);
LevelSet.AccConstant(-1, NegFar);
// project Fourier levelSet to DGfield on near field
VolMask = Near;
}
LevelSet.Clear(VolMask);
// scalar function is already vectorized for parallel execution
// nodes in global coordinates
LevelSet.ProjectField(1.0,
PhiEvaluation(mode),
new Foundation.Quadrature.CellQuadratureScheme(true, VolMask));
// check the projection error
projErr_phiDG = LevelSet.L2Error(
PhiEvaluation(mode),
new Foundation.Quadrature.CellQuadratureScheme(true, VolMask));
//if (projErr_phiDG >= 1e-5)
// Console.WriteLine("WARNING: LevelSet projection error onto PhiDG = {0}", projErr_phiDG);
// project on higher degree field and take the difference
//SinglePhaseField higherLevSet = new SinglePhaseField(new Basis(LevelSet.GridDat, LevelSet.Basis.Degree * 2), "higherLevSet");
//higherLevSet.ProjectField(1.0, PhiEvaluator(), new Foundation.Quadrature.CellQuadratureScheme(true, VolMask));
//double higherProjErr = higherLevSet.L2Error(
// PhiEvaluator(),
// new Foundation.Quadrature.CellQuadratureScheme(true, VolMask));
//Console.WriteLine("LevelSet projection error onto higherPhiDG = {0}", higherProjErr.ToString());
// check the projection from current sample points on the DGfield
//MultidimensionalArray interP = MultidimensionalArray.Create(current_interfaceP.Lengths);
//if (this is PolarFourierLevSet) {
// interP = ((PolarFourierLevSet)this).interfaceP_cartesian;
//} else {
// interP = current_interfaceP;
//}
//projErr_interface = InterfaceProjectionError(LevelSet, current_interfaceP);
//if (projErr_interface >= 1e-3)
// Console.WriteLine("WARNING: Interface projection Error onto PhiDG = {0}", projErr_interface);
}
/// <summary>
/// Reinitializes <paramref name="Phi"/> on <paramref name="reinitField"/> using the <paramref name="Accepted"/> cells as start value.
/// </summary>
/// <param name="Phi">Level Set</param>
/// <param name="Accepted">Given Field</param>
/// <param name="NegativeField">Field, on which the level set function is negative</param>
/// <param name="reinitField">Field , on which the level set function should be initialized</param>
public void FirstOrderReinit(SinglePhaseField Phi, CellMask Accepted, CellMask NegativeField, CellMask reinitField)
{
//Idea: Add options : FirstOrder, Elliptic, Geometric, Iterative. That is, include the existing Local Solvers.
CellMask ReinitField;
if (reinitField == null)
{
ReinitField = CellMask.GetFullMask(Phi.GridDat);
}
else
{
ReinitField = reinitField;
}
//Build Local Solver that solves the Eikonal in each cell.
FastMarching.ILocalSolver localSolver = new FastMarching.LocalMarcher.LocalMarcher_2DStructured(Phi.Basis);
//Build Global Solver that marches through all cells
FastMarching.GlobalMarcher.CellMarcher fastMarcher = new FastMarching.GlobalMarcher.CellMarcher(Phi.Basis, localSolver);
//Solve
fastMarcher.Reinit(Phi, Accepted, ReinitField);
//Invert Negative Domain that is part of ReinitField
Phi.Scale(-1, NegativeField.Intersect(ReinitField).Except(Accepted));
}
/// <summary>
/// integrates this field over the domain specified in <paramref name="volumemask"/>
/// </summary>
/// <param name="volumemask">
/// an optional volume mask; if null, the whole grid is taken;
/// </param>
public double IntegralOver(CellMask volumemask)
{
using (new FuncTrace()) {
MPICollectiveWatchDog.Watch(csMPI.Raw._COMM.WORLD);
if (volumemask == null)
{
volumemask = CellMask.GetFullMask(Basis.GridDat);
}
double acc = 0;
foreach (var chunk in volumemask)
{
int iE = chunk.i0 + chunk.Len;
for (int j = chunk.i0; j < iE; j++)
{
double mv = GetMeanValue(j);
double vol = Basis.GridDat.iLogicalCells.GetCellVolume(j);
acc += mv * vol;
}
}
double accglob = double.NaN;
unsafe {
csMPI.Raw.Allreduce((IntPtr)(&acc), (IntPtr)(&accglob), 1, csMPI.Raw._DATATYPE.DOUBLE, csMPI.Raw._OP.SUM, csMPI.Raw._COMM.WORLD);
}
return(accglob);
}
}
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>
///
/// </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));
}
}
/// <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>
/// Reinitializes levelset in <paramref name="LevelSetTracker"/> on all cells except the cut cells
/// </summary>
/// <param name="LevelSetTracker"></param>
/// <param name="NameNegativeSpecies">Name of the negative species of Levelset</param>
public void FirstOrderReinit(LevelSetTracker LevelSetTracker, string NameNegativeSpecies)
{
//Extract Data from LevelSetTracker
CellMask accepted = LevelSetTracker.Regions.GetCutCellMask();
CellMask negativeDomain = LevelSetTracker.Regions.GetSpeciesMask(NameNegativeSpecies);
CellMask ReInitField = CellMask.GetFullMask(LevelSetTracker.GridDat).Except(accepted);
//Solve
FirstOrderReinit((SinglePhaseField)LevelSetTracker.LevelSets[0], accepted, negativeDomain, ReInitField);
}
//public static MultidimensionalArray SortPoints(GridData gridData, SinglePhaseField field, MultidimensionalArray points, bool byFlux = false) {
// double[] sortedXCoords = new double[points.Lengths[0]];
// double[] sortedYCoords = new double[points.Lengths[0]];
// int keptEntries = 0;
// for (int i = 0; i < points.Lengths[0]; i++) {
// // Compute global cell index of the point
// double[] currentPoint = points.ExtractSubArrayShallow(i, 0, -1).To1DArray();
// gridData.LocatePoint(currentPoint, out long GlobalId, out long GlobalIndex, out bool IsInside, out bool OnThisProcess);
// // Compute local node set
// NodeSet nodeSet = GetLocalNodeSet(gridData, currentPoint, (int)GlobalIndex);
// // Get local cell index of current point
// int j0Grd = gridData.CellPartitioning.i0;
// int jLocal = (int)(GlobalIndex - j0Grd);
// // Calculate secondDerivative
// double secondDerivative;
// if (byFlux) {
// secondDerivative = SecondDerivativeByFlux(field, jLocal, nodeSet,);
// } else {
// secondDerivative = SecondDerivative(field, jLocal, nodeSet);
// }
// // Select points where second derivative is larger than zero
// if (secondDerivative > 0.0) {
// sortedXCoords[keptEntries] = currentPoint[0];
// sortedYCoords[keptEntries] = currentPoint[1];
// keptEntries++;
// }
// }
// // Resize final array
// MultidimensionalArray result = MultidimensionalArray.Create(keptEntries, points.Lengths[1], points.Lengths[2]);
// for (int i = 0; i < keptEntries; i++) {
// result[i, 0, 0] = sortedXCoords[i];
// result[i, 0, 1] = sortedYCoords[i];
// }
// return result;
//}
/// <summary>
/// Performs the patch recovery on a given DG field
/// </summary>
/// <param name="input">A <see cref="SinglePhaseField"/></param>
/// <returns>A patch recovered <see cref="SinglePhaseField"/> with a degree of inputDegreee + 2</returns>
public static SinglePhaseField PatchRecovery(SinglePhaseField input)
{
Console.WriteLine(String.Format("Patch recovery of field {0} started...", input.Identification));
Basis prcBasis = new Basis(input.GridDat, input.Basis.Degree + 2);
L2PatchRecovery prc = new L2PatchRecovery(input.Basis, prcBasis, CellMask.GetFullMask(input.GridDat), RestrictToCellMask: true);
SinglePhaseField prcField = new SinglePhaseField(prcBasis, input.Identification + "_prc");
prc.Perform(prcField, input);
Console.WriteLine(String.Format("finished", input.Identification));
return(prcField);
}
/// <summary>
/// accumulate this field to a DG field
/// </summary>
/// <param name="alpha"></param>
/// <param name="DGField"></param>
/// <param name="mask">optional cell mask</param>
public void AccToDGField(double alpha, ConventionalDGField DGField, CellMask mask = null)
{
if (!DGField.Basis.Equals(this.m_Basis.ContainingDGBasis))
{
throw new ArgumentException("Basis does not match.");
}
var Trafo = m_Basis.GridDat.ChefBasis.Scaling;
var C2N = m_Basis.CellNode_To_Node;
var MtxM2N = m_Basis.m_Modal2Nodal;
var CellData = this.Basis.GridDat.Cells;
int[] _K = m_Basis.NodesPerCell;
int L = m_Basis.ContainingDGBasis.Length;
double[][] _NodalCoordinates = _K.Select(K => new double[K]).ToArray();
double[] ModalCoordinates = new double[L];
if (mask == null)
{
mask = CellMask.GetFullMask(this.Basis.GridDat);
}
foreach (var chunk in mask)
{
int j0 = chunk.i0;
int JE = chunk.JE;
for (int j = j0; j < JE; j++) // loop over cells...
{
int iKref = CellData.GetRefElementIndex(j);
double[] NodalCoordinates = _NodalCoordinates[iKref];
int K = _K[iKref];
// collect coordinates for cell 'j':
for (int k = 0; k < K; k++)
{
int _c2n = C2N[j, k];
NodalCoordinates[k] = m_Coordinates[_c2n];
}
// transform
DGField.Coordinates.GetRow(j, ModalCoordinates);
MtxM2N[iKref].gemv(alpha / Trafo[j], NodalCoordinates, 1.0, ModalCoordinates);
// save
DGField.Coordinates.SetRow(j, ModalCoordinates);
}
}
}
public static void ProjectArtificalViscosityToDGField(SinglePhaseField avField, PerssonSensor sensor, double sensorLimit, double maxViscosity, CellMask cellMask = null)
{
MultidimensionalArray h_min = avField.GridDat.iGeomCells.h_min;
int p = sensor.fieldToTestRestricted.Basis.Degree + 1;
if (cellMask == null)
{
cellMask = CellMask.GetFullMask(avField.GridDat);
}
avField.Clear();
foreach (int cell in cellMask.ItemEnum)
{
double localViscosity = GetViscosity(cell, h_min[cell], p, sensor.GetValue(cell), sensorLimit, maxViscosity);
avField.SetMeanValue(cell, localViscosity);
}
}
public void UpdateSensorValues(DGField fieldToTest)
{
int degree = fieldToTest.Basis.Degree;
int noOfCells = fieldToTest.GridDat.iLogicalCells.NoOfLocalUpdatedCells;
if (sensorValues == null || sensorValues.Length != noOfCells)
{
sensorValues = new double[noOfCells];
}
CellMask cellMask = CellMask.GetFullMask(fieldToTest.GridDat);
foreach (int cell in cellMask.ItemEnum)
{
double numerator = 0.0;
foreach (int coordinate in fieldToTest.Basis.GetPolynomialIndicesForDegree(cell, degree))
{
numerator += fieldToTest.Coordinates[cell, coordinate] * fieldToTest.Coordinates[cell, coordinate];
}
double denominator = 0.0;
for (int coordinate = 0; coordinate < fieldToTest.Basis.Length; coordinate++)
{
denominator += fieldToTest.Coordinates[cell, coordinate] * fieldToTest.Coordinates[cell, coordinate];
}
double result;
if (denominator == 0.0) //say what?!
{
result = 0.0;
}
else
{
result = numerator / denominator;
}
//Debug.Assert(denominator != 0, "Persson sensor: Denominator is zero!");
//Debug.Assert(!(numerator / denominator).IsNaN(), "Persson sensor: Sensor value is NaN!");
//Debug.Assert(numerator / denominator >= 0, "Persson sensor: Sensor value is negative!");
sensorValues[cell] = result;
}
}
/// <summary>
/// calculate the curvature corresponding to the Level-Set
/// </summary>
/// <param name="Curvature"></param>
/// <param name="LevSetGradient"></param>
/// <param name="VolMask"></param>
public void ProjectToDGCurvature(SinglePhaseField Curvature, out VectorField <SinglePhaseField> LevSetGradient, CellMask VolMask = null)
{
if (VolMask == null)
{
VolMask = CellMask.GetFullMask(Curvature.Basis.GridDat);
}
Curvature.Clear();
Curvature.ProjectField(1.0,
CurvEvaluation(mode),
new Foundation.Quadrature.CellQuadratureScheme(true, VolMask));
// check the projection error
projErr_curv = Curvature.L2Error(
CurvEvaluation(mode),
new Foundation.Quadrature.CellQuadratureScheme(true, VolMask));
//if (projErr_curv >= 1e-5)
// Console.WriteLine("WARNING: Curvature projection error onto PhiDG = {0}", projErr_curv);
LevSetGradient = null;
}
/// <summary>
/// Update the actual sensor field
/// </summary>
public void Update(DGField fieldToTest)
{
sensorField.Clear();
fieldToTestRestricted.Clear();
fieldToTestRestricted.AccLaidBack(1.0, fieldToTest);
DGField difference = fieldToTestRestricted - fieldToTest;
foreach (Chunk chunk in CellMask.GetFullMask(fieldToTest.GridDat))
{
for (int i = 0; i < chunk.Len; i++)
{
int cell = i + chunk.i0;
CellMask singleCellMask = new CellMask(fieldToTest.GridDat, Chunk.GetSingleElementChunk(cell));
CellQuadratureScheme scheme = new CellQuadratureScheme(domain: singleCellMask);
var rule = scheme.SaveCompile(fieldToTest.GridDat, 2 * fieldToTest.Basis.Degree);
double[] a = difference.LocalLxError((ScalarFunction)null, null, rule);
double[] b = fieldToTest.LocalLxError((ScalarFunction)null, null, rule);
double mySensorValue = a[0] / b[0];
// not using L2-norm, but rather only the scalar product
mySensorValue = mySensorValue * mySensorValue;
if (double.IsNaN(mySensorValue))
{
mySensorValue = 0.0;
}
sensorField.SetMeanValue(cell, mySensorValue);
}
}
}
/// <summary>
/// computes derivatives in various ways and compares them against known values.
/// </summary>
protected override double RunSolverOneStep(int TimestepNo, double phystime, double dt)
{
base.EndTime = 0.0;
base.NoOfTimesteps = 0;
int D = this.GridData.SpatialDimension;
int J = this.GridData.iLogicalCells.NoOfLocalUpdatedCells;
Console.WriteLine("DerivativeTest.exe, test case #" + GRID_CASE + " ******************************");
//var Fix = this.GridData.iGeomEdges.FaceIndices;
//for(int iEdge = 0; iEdge < Fix.GetLength(0); iEdge++) {
// Debug.Assert(Fix[iEdge, 0] >= 0);
// Debug.Assert(Fix[iEdge, 1] >= 0);
//}
// sealing test
// =================
if (this.GridData is Foundation.Grid.Classic.GridData)
{
TestSealing(this.GridData);
}
// cell volume and edge area check, if possible
// ===============================================
if (this.CellVolume > 0)
{
double err = 0;
double Treshold = 1.0e-10;
for (int j = 0; j < J; j++)
{
err += Math.Abs(this.GridData.iLogicalCells.GetCellVolume(j) - this.CellVolume);
}
bool passed = (err < Treshold);
m_passed = m_passed && passed;
Console.WriteLine("Cell volume error: " + err + " passed? " + passed);
Console.WriteLine("--------------------------------------------");
}
if (this.EdgeArea > 0)
{
double err = 0;
double Treshold = 1.0e-10;
int E = this.GridData.iLogicalEdges.Count;
for (int e = 0; e < E; e++)
{
err += Math.Abs(this.GridData.iLogicalEdges.GetEdgeArea(e) - this.EdgeArea);
}
bool passed = (err < Treshold);
m_passed = m_passed && passed;
Console.WriteLine("Edge area error: " + err + " passed? " + passed);
Console.WriteLine("--------------------------------------------");
}
// Orthonormality of basis in physical coords
// ==========================================
{
Basis Bs = this.f1.Basis;
int N = Bs.Length;
int degQuad = this.GridData.iLogicalCells.GetInterpolationDegree(0) * D + Bs.Degree + 3;
int[] jG2jL = this.GridData.iGeomCells.GeomCell2LogicalCell;
// mass matrix: should be identity!
MultidimensionalArray MassMatrix = MultidimensionalArray.Create(J, N, N);
// compute mass matrix by quadrature.
var quad = CellQuadrature.GetQuadrature(new int[] { N, N }, base.GridData,
(new CellQuadratureScheme()).Compile(base.GridData, degQuad),
delegate(int i0, int Length, QuadRule QR, MultidimensionalArray EvalResult) {
NodeSet QuadNodes = QR.Nodes;
MultidimensionalArray BasisVals = Bs.CellEval(QuadNodes, i0, Length);
EvalResult.Multiply(1.0, BasisVals, BasisVals, 0.0, "jknm", "jkn", "jkm");
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) {
if (jG2jL != null)
{
for (int i = 0; i < Length; i++)
{
int jG = i + i0;
MassMatrix.ExtractSubArrayShallow(jG2jL[jG], -1, -1)
.Acc(1.0, ResultsOfIntegration.ExtractSubArrayShallow(i, -1, -1));
}
}
else
{
MassMatrix.SetSubArray(ResultsOfIntegration, new int[] { i0, 0, 0 }, new int[] { i0 + Length - 1, N - 1, N - 1 });
}
},
cs: CoordinateSystem.Physical);
quad.Execute();
// check that mass matrix is Id.
int MaxErrorCell = -1;
double MaxError = -1;
for (int j = 0; j < J; j++)
{
MultidimensionalArray MassMatrix_j = MassMatrix.ExtractSubArrayShallow(j, -1, -1);
MassMatrix_j.AccEye(-1.0);
double Norm_j = MassMatrix_j.InfNorm();
if (Norm_j > MaxError)
{
MaxError = Norm_j;
MaxErrorCell = j;
}
}
bool passed = (MaxError < 1.0e-8);
m_passed = m_passed && passed;
Console.WriteLine("Mass Matrix, maximum error in Cell #" + MaxErrorCell + ", mass matrix error norm: " + MaxError + " passed? " + passed);
}
// Broken Derivatives
// =================
double totalVolume = (new SubGrid(CellMask.GetFullMask(this.GridData))).Volume;
for (int d = 0; d < D; d++)
{
// compute
f1Gradient_Numerical[d].Clear();
f1Gradient_Numerical[d].Derivative(1.0, f1, d);
f2Gradient_Numerical[d].Clear();
f2Gradient_Numerical[d].Derivative(1.0, f2, d);
// subtract analytical
var Errfield1 = f1Gradient_Numerical[d].CloneAs();
Errfield1.Acc(-1, f1Gradient_Analytical[d]);
var Errfield2 = f2Gradient_Numerical[d].CloneAs();
Errfield2.Acc(-1, f2Gradient_Analytical[d]);
Console.WriteLine("Broken Derivatives: ");
double Treshold = 1.0e-10;
if (AltRefSol)
{
Treshold = 1.0e-4; // not exactly polynomial, therefore a higher threshold
}
double err1_dx = Errfield1.L2Norm() / totalVolume;
bool passed = (err1_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df1/dx{0}_Numerical - df1/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err1_dx, passed));
double err2_dx = Errfield2.L2Norm() / totalVolume;
passed = (err2_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df2/dx{0}_Numerical - df2/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err2_dx, passed));
Console.WriteLine("--------------------------------------------");
}
// Flux Derivatives
// =================
for (int d = 0; d < D; d++)
{
// compute
f1Gradient_Numerical[d].Clear();
f1Gradient_Numerical[d].DerivativeByFlux(1.0, f1, d);
f2Gradient_Numerical[d].Clear();
f2Gradient_Numerical[d].DerivativeByFlux(1.0, f2, d);
f1Gradient_Numerical[d].CheckForNanOrInf(true, true, true);
f2Gradient_Numerical[d].CheckForNanOrInf(true, true, true);
// subtract analytical
var Errfield1 = f1Gradient_Numerical[d].CloneAs();
Errfield1.Acc(-1, f1Gradient_Analytical[d]);
var Errfield2 = f2Gradient_Numerical[d].CloneAs();
Errfield2.Acc(-1, f2Gradient_Analytical[d]);
Console.WriteLine("Flux Derivatives: ");
double Treshold = 1.0e-10;
if (AltRefSol)
{
Treshold = 1.0e-4; // not exactly polynomial, therefore a higher threshold
}
double err1_dx = Errfield1.L2Norm() / totalVolume;
bool passed = (err1_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df1/dx{0}_Numerical - df1/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err1_dx, passed));
double err2_dx = Errfield2.L2Norm() / totalVolume;
passed = (err2_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df2/dx{0}_Numerical - df2/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err2_dx, passed));
Console.WriteLine("--------------------------------------------");
}
// Linear flux Derivatives
// =======================
for (int d = 0; d < D; d++)
{
double[] korrekto = f1Gradient_Numerical[d].CoordinateVector.ToArray();
// compute
DerivativeByFluxLinear(f1, f1Gradient_Numerical[d], d, f1);
DerivativeByFluxLinear(f2, f2Gradient_Numerical[d], d, f2);
// subtract analytical
var Errfield1 = f1Gradient_Numerical[d].CloneAs();
Errfield1.Acc(-1, f1Gradient_Analytical[d]);
var Errfield2 = f2Gradient_Numerical[d].CloneAs();
Errfield2.Acc(-1, f2Gradient_Analytical[d]);
Console.WriteLine("Linear Flux Derivatives: ");
double Treshold = 1.0e-10;
if (AltRefSol)
{
Treshold = 1.0e-4; // not exactly polynomial, therefore a higher threshold
}
double err1_dx = Errfield1.L2Norm() / totalVolume;
bool passed = (err1_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df1/dx{0}_Numerical - df1/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err1_dx, passed));
double err2_dx = Errfield2.L2Norm() / totalVolume;
passed = (err2_dx < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| df2/dx{0}_Numerical - df2/dx{0}_Analytical ||_2 = {1}, passed? {2}", d, err2_dx, passed));
Console.WriteLine("--------------------------------------------");
}
// Laplacian, nonlinear
// ====================
if (!AltRefSol)
{
var Laplace = (new ipLaplace()).Operator(1);
Laplace.Evaluate(new DGField[] { this.f1 }, new DGField[] { this.Laplace_f1_Numerical });
Laplace.Evaluate(new DGField[] { this.f2 }, new DGField[] { this.Laplace_f2_Numerical });
double Treshold = 1.0e-8;
// subtract analytical
var Errfield1 = Laplace_f1_Numerical.CloneAs();
Errfield1.Acc(-1, Laplace_f1_Analytical);
var Errfield2 = Laplace_f2_Numerical.CloneAs();
Errfield2.Acc(-1, Laplace_f2_Analytical);
double err_Lf1 = Errfield1.L2Norm() / totalVolume;
bool passed = (err_Lf1 < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| /\\f1 Numerical - /\\f1 Analytical ||_2 = {0} (nonlinear evaluation), passed? {1}", err_Lf1, passed));
double err_Lf2 = Errfield2.L2Norm() / totalVolume;
passed = (err_Lf2 < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| /\\f2 Numerical - /\\f2 Analytical ||_2 = {0} (nonlinear evaluation), passed? {1}", err_Lf2, passed));
Console.WriteLine("--------------------------------------------");
}
// Laplacian, linear
// ====================
if (!AltRefSol)
{
var Laplace = (new ipLaplace()).Operator(1);
var LaplaceMtx = new BlockMsrMatrix(this.f1.Mapping, this.Laplace_f1_Numerical.Mapping);
var LaplaceAffine = new double[LaplaceMtx.RowPartitioning.LocalLength];
Laplace.ComputeMatrix(this.f1.Mapping, null, this.Laplace_f1_Numerical.Mapping,
LaplaceMtx, LaplaceAffine, false);
this.Laplace_f1_Numerical.CoordinateVector.SetV(LaplaceAffine);
LaplaceMtx.SpMV(1.0, this.f1.CoordinateVector, 1.0, this.Laplace_f1_Numerical.CoordinateVector);
this.Laplace_f2_Numerical.CoordinateVector.SetV(LaplaceAffine);
LaplaceMtx.SpMV(1.0, this.f2.CoordinateVector, 1.0, this.Laplace_f2_Numerical.CoordinateVector);
// subtract analytical
var Errfield1 = Laplace_f1_Numerical.CloneAs();
Errfield1.Acc(-1, Laplace_f1_Analytical);
var Errfield2 = Laplace_f2_Numerical.CloneAs();
Errfield2.Acc(-1, Laplace_f2_Analytical);
double Treshold = 1.0e-8;
double err_Lf1 = Errfield1.L2Norm() / totalVolume;
bool passed = (err_Lf1 < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| /\\f1 Numerical - /\\f1 Analytical ||_2 = {0} (linear evaluation), passed? {1}", err_Lf1, passed));
double err_Lf2 = Errfield2.L2Norm() / totalVolume;
passed = (err_Lf2 < Treshold);
m_passed = m_passed && passed;
Console.WriteLine(string.Format("|| /\\f2 Numerical - /\\f2 Analytical ||_2 = {0} (linear evaluation), passed? {1}", err_Lf2, passed));
// comparison of finite difference Jacobian and Operator matrix
if (TestFDJacobian)
{
this.f1.Clear();
var FDJbuilder = Laplace.GetFDJacobianBuilder(this.f1.Mapping.Fields, null, this.f1.Mapping,
delegate(IEnumerable <DGField> U0, IEnumerable <DGField> Params) {
return;
});
var CheckMatrix = new BlockMsrMatrix(FDJbuilder.CodomainMapping, FDJbuilder.DomainMapping);
var CheckAffine = new double[FDJbuilder.CodomainMapping.LocalLength];
FDJbuilder.ComputeMatrix(CheckMatrix, CheckAffine);
var ErrMatrix = LaplaceMtx.CloneAs();
var ErrAffine = LaplaceAffine.CloneAs();
ErrMatrix.Acc(-1.0, CheckMatrix);
ErrAffine.AccV(-1.0, CheckAffine);
double LinfMtx = ErrMatrix.InfNorm();
double L2Aff = ErrAffine.L2NormPow2().MPISum().Sqrt();
bool passed1 = (LinfMtx < 1.0e-3);
bool passed2 = (L2Aff < Treshold);
Console.WriteLine("Finite Difference Jacobian: Matrix/Affine delta norm {0} {1}, passed? {2} {3}", LinfMtx, L2Aff, passed1, passed2);
m_passed = m_passed && passed1;
m_passed = m_passed && passed2;
}
Console.WriteLine("--------------------------------------------");
}
// finally...
// =================
if (m_passed)
{
Console.WriteLine("All tests passed. *****************************");
}
else
{
Console.WriteLine("Some error above threshold. *******************");
}
return(0.0); // return some artificial timestep
}
/// <summary>
/// Injects a DG field from a coarser grid to a fine grid.
/// </summary>
public static void InjectDGField(int[] CellIdxFine2Coarse, ConventionalDGField onFineGrid, ConventionalDGField onCoarseGrid, CellMask subGrd = null)
{
if (subGrd == null)
{
subGrd = CellMask.GetFullMask(onFineGrid.GridDat);
}
if (onFineGrid.Basis.GridDat.iGeomCells.RefElements.Length != 1)
{
throw new NotImplementedException("todo");
}
var QR = onFineGrid.Basis.GridDat.iGeomCells.RefElements[0].GetQuadratureRule(onFineGrid.Basis.Degree * 2);
if (!object.ReferenceEquals(subGrd.GridData, onFineGrid.GridDat))
{
throw new ArgumentException();
}
int N = onFineGrid.Basis.Length;
int K = QR.NoOfNodes;
int D = onFineGrid.Basis.GridDat.SpatialDimension;
NodeSet xi = QR.Nodes; // quadrature nodes in local coordsys. of cell to extrapolate TO
//MultidimensionalArray eta = MultidimensionalArray.Create(K, D); // quadrature nodes in local coordsys. of cell to extrapolate FROM
MultidimensionalArray tmp = MultidimensionalArray.Create(K, D); // quadrature nodes in global coordinates
MultidimensionalArray a = MultidimensionalArray.Create(K, N);
for (int n = 0; n < N; n++)
{
onFineGrid.Basis.Polynomials[0][n].Evaluate(a.ExtractSubArrayShallow(-1, n), xi);
for (int k = 0; k < K; k++)
{
a[k, n] *= QR.Weights[k];
}
}
MultidimensionalArray v = MultidimensionalArray.Create(K, N);
MultidimensionalArray[] v_ = new MultidimensionalArray[N];
for (int n = 0; n < N; n++)
{
v_[n] = v.ExtractSubArrayShallow(-1, n);
}
double[,] eps = new double[N, N];
double[] u2 = new double[N];
double[] u1 = new double[N];
//double[] ooScales = m_context.GridDat.OneOverSqrt_AbsDetTransformation;
IGridData ctxFine = onFineGrid.Basis.GridDat;
IGridData ctxCors = onCoarseGrid.Basis.GridDat;
var ooScalesFine = ctxFine.ChefBasis.Scaling;
var ooScalesCors = ctxCors.ChefBasis.Scaling;
foreach (var chunk in subGrd)
{
for (int j = chunk.i0; j < chunk.JE; j++)
{
int _1 = CellIdxFine2Coarse[j]; // cell to extrapolate FROM (on coarse grid)
int _2 = j; // cell to extrapolate TO (on fine grid)
int iKref_1 = ctxCors.iGeomCells.GetRefElementIndex(_1);
int iKref_2 = ctxFine.iGeomCells.GetRefElementIndex(_2);
if (!ctxCors.iGeomCells.IsCellAffineLinear(_1))
{
throw new NotImplementedException("todo");
}
if (!ctxFine.iGeomCells.IsCellAffineLinear(_2))
{
throw new NotImplementedException("todo");
}
// get DG coordinates
onCoarseGrid.Coordinates.GetRow(_1, u1);
// transform quad. nodes from cell 2 (extrapolate to) to cell 1 (extrapolate FROM)
ctxFine.TransformLocal2Global(xi, tmp, _2);
NodeSet eta = new NodeSet(ctxFine.iGeomCells.GetRefElement(_2), K, D);
ctxCors.TransformGlobal2Local(tmp, eta, _1, null);
eta.LockForever();
// evaluate Polynomials of cell 1 (fine)
v.Clear();
for (int n = 0; n < N; n++)
{
if (n < onCoarseGrid.Basis.Length)
{
onCoarseGrid.Basis.Polynomials[iKref_1][n].Evaluate(v_[n], eta);
}
else
{
v_[n].Clear();
}
}
// perform quadrature
double scale = ooScalesCors[_1] / ooScalesFine[_2];
for (int m = 0; m < N; m++)
{
for (int n = 0; n < N; n++)
{
double eps_m_n = 0;
for (int k = 0; k < K; k++)
{
eps_m_n += a[k, m] * v[k, n];
}
eps[m, n] = eps_m_n * scale;
}
}
// new DG coordinates
for (int m = 0; m < N; m++)
{
double u2_m = 0;
for (int n = 0; n < N; n++)
{
u2_m += eps[m, n] * u1[n];
}
u2[m] = u2_m;
}
// set DG coordinates
onFineGrid.Coordinates.SetRow(_2, u2);
}
}
}
/// <summary>
/// Creates the sub-grids of the clustering
/// </summary>
/// <param name="numOfClusters">Number of clusters</param>
/// <returns>A list of sub-grids</returns>
public Clustering CreateClustering(int numOfClusters, SubGrid subGrid = null)
{
if (subGrid == null)
{
subGrid = new SubGrid(CellMask.GetFullMask(gridData));
}
// Attention: numOfCells can equal all local cells or only the local cells of a subgrid,
// e.g., the fluid cells in an IBM simulation
int numOfCells = subGrid.LocalNoOfCells;
MultidimensionalArray cellMetric = GetStableTimestepSize(subGrid);
MultidimensionalArray means = CreateInitialMeans(cellMetric, numOfClusters);
Kmeans Kmean = new Kmeans(cellMetric.To1DArray(), numOfClusters, means.To1DArray());
// The corresponding sub-grid IDs
int[] subGridCellToClusterMap = Kmean.Cluster();
int[] noOfCellsPerCluster = Kmean.ClusterCount;
unsafe {
int[] globalCC = new int[numOfClusters];
// send = means[]
// receive = globalMeans[]
fixed(int *pSend = &noOfCellsPerCluster[0], pRcv = &globalCC[0])
{
csMPI.Raw.Allreduce((IntPtr)(pSend), (IntPtr)(pRcv), numOfClusters, csMPI.Raw._DATATYPE.INT, csMPI.Raw._OP.SUM, csMPI.Raw._COMM.WORLD);
}
noOfCellsPerCluster = globalCC;
}
int counter = numOfClusters;
for (int i = 0; i < numOfClusters; i++)
{
if (noOfCellsPerCluster[i] == 0)
{
System.Console.WriteLine("Sub-grid/Cluster " + (i + 1) + ", with mean value " + Kmean.Means[i] + ", is empty and not used anymore!");
counter--;
}
}
// Generating BitArray for all Subgrids, even for those which are empty, i.e ClusterCount == 0
BitArray[] baMatrix = new BitArray[numOfClusters];
for (int i = 0; i < numOfClusters; i++)
{
//baMatrix[i] = new BitArray(gridData.iLogicalCells.NoOfCells);
baMatrix[i] = new BitArray(gridData.iLogicalCells.NoOfLocalUpdatedCells);
}
// Filling the BitArrays
for (int i = 0; i < numOfCells; i++)
{
baMatrix[subGridCellToClusterMap[i]][subGrid.SubgridIndex2LocalCellIndex[i]] = true;
}
// Generating the sub-grids
List <SubGrid> clusters = new List <SubGrid>(counter);
for (int i = 0; i < numOfClusters; i++)
{
// Generating only the sub-grids which are not empty
if (noOfCellsPerCluster[i] != 0)
{
BitArray ba = baMatrix[i];
clusters.Add(new SubGrid(new CellMask(gridData, ba)));
}
}
return(new Clustering(clusters, subGrid));
}
/// <summary>
/// Returns a <see cref="CellBoundaryQuadRule"/> for each cell in the
/// given <paramref name="mask"/>. This rule consists of Gaussian
/// quadrature rules on each continuous line segment on the edges of a
/// given cell (where continuous means 'not intersected by the zero
/// level set'
/// </summary>
/// <param name="mask"></param>
/// <param name="order"></param>
/// <returns></returns>
public IEnumerable <IChunkRulePair <CellBoundaryQuadRule> > GetQuadRuleSet(ExecutionMask mask, int order)
{
if (!(mask is CellMask))
{
throw new ArgumentException("This works on cell basis, so a volume mask is required.");
}
//Console.WriteLine("boundary order: " + order);
if (mask == null)
{
mask = CellMask.GetFullMask(levelSetData.GridDat);
}
if (order != lastOrder)
{
cache.Clear();
}
double[] EdgeToVolumeTransformationDeterminants = this.RefElement.FaceTrafoGramianSqrt;
QuadRule baseRule = lineSimplex.GetQuadratureRule(order);
int D = levelSetData.GridDat.SpatialDimension;
var _Cells = levelSetData.GridDat.Cells;
var result = new List <ChunkRulePair <CellBoundaryQuadRule> >(mask.NoOfItemsLocally);
foreach (Chunk chunk in mask)
{
for (int i = 0; i < chunk.Len; i++)
{
int cell = i + chunk.i0;
if (cache.ContainsKey(cell))
{
Debug.Assert(cache[cell].Nodes.IsLocked, "Quadrule with non-locked nodes in cache.");
result.Add(new ChunkRulePair <CellBoundaryQuadRule>(
Chunk.GetSingleElementChunk(cell), cache[cell]));
continue;
}
List <double[]> nodes = new List <double[]>();
List <double> weights = new List <double>();
int[] noOfNodesPerEdge = new int[referenceLineSegments.Length];
for (int e = 0; e < referenceLineSegments.Length; e++)
{
LineSegment referenceSegment = referenceLineSegments[e];
int iKref = _Cells.GetRefElementIndex(cell);
double[] roots = referenceSegment.GetRoots(levelSetData.LevelSet, cell, iKref);
double edgeDet = EdgeToVolumeTransformationDeterminants[e];
LineSegment[] subSegments = referenceSegment.Split(roots);
for (int k = 0; k < subSegments.Length; k++)
{
// Evaluate sub segment at center to determine sign
NodeSet _point = new NodeSet(this.RefElement, subSegments[k].GetPointOnSegment(0.0));
double weightFactor = subSegments[k].Length / referenceSegment.Length;
if (weightFactor < 1.0e-14)
{
// segment has a length of approximately 0.0 => no need to care about it.
continue;
}
weightFactor *= edgeDet;
if (jumpType != JumpTypes.Implicit)
{
//using (tracker.GridDat.NSC.CreateLock(MultidimensionalArray.CreateWrapper(point, 1, D), this.iKref, -1.0)) {
MultidimensionalArray levelSetValue = this.levelSetData.GetLevSetValues(_point, cell, 1);
switch (jumpType)
{
case JumpTypes.Heaviside:
if (levelSetValue[0, 0] <= -Tolerance)
{
continue;
}
break;
case JumpTypes.OneMinusHeaviside:
if (levelSetValue[0, 0] >= Tolerance)
{
continue;
}
break;
case JumpTypes.Sign:
weightFactor *= levelSetValue[0, 0].Sign();
break;
default:
throw new NotImplementedException();
}
//}
}
for (int m = 0; m < baseRule.NoOfNodes; m++)
{
// Base rule _always_ is a line rule, thus Nodes[*, _0_]
double[] point = subSegments[k].GetPointOnSegment(baseRule.Nodes[m, 0]);
weights.Add(weightFactor * baseRule.Weights[m]);
nodes.Add(point);
noOfNodesPerEdge[e]++;
}
}
}
if (weights.Count == 0)
{
result.Add(new ChunkRulePair <CellBoundaryQuadRule>(Chunk.GetSingleElementChunk(cell), emptyrule));
continue;
}
NodeSet localNodes = new NodeSet(this.RefElement, nodes.Count, D);
for (int j = 0; j < nodes.Count; j++)
{
for (int d = 0; d < D; d++)
{
localNodes[j, d] = nodes[j][d];
}
}
localNodes.LockForever();
CellBoundaryQuadRule subdividedRule = new CellBoundaryQuadRule()
{
OrderOfPrecision = order,
Weights = MultidimensionalArray.Create(weights.Count),
Nodes = localNodes,
NumbersOfNodesPerFace = noOfNodesPerEdge
};
subdividedRule.Weights.SetSubVector(weights, -1);
cache.Add(cell, subdividedRule);
result.Add(new ChunkRulePair <CellBoundaryQuadRule>(
Chunk.GetSingleElementChunk(cell), subdividedRule));
}
}
return(result);
}
protected override double RunSolverOneStep(int TimestepNo, double phystime, double dt)
{
Stopwatch globalWatch = new Stopwatch();
globalWatch.Start();
/*
* Configuration options
*/
// Only applies to subdivision-based quadrature (brute force and adaptive)
int[] divisions = new int[] { (int)testCase.GridSize };
// Only applies to adaptive quadrature
int leafDivisions = -1;
// Only applies to regularized quadrature
double[] widths = new double[] { double.NaN };
int[] vanishingMonents = new int[] { int.MinValue };
int[] continuousDerivatives = new int[] { int.MinValue };
// Only applies to HMF quadrature
LineSegment.IRootFindingAlgorithm rootFindingAlgorithm;
/*
* ENTER CONFIGURATION HERE
*/
// Export options
int plotSuperSampling = 3;
bool logVolumeNodes = true;
int logVolumeNodes_selectedCell = -1;
bool logSurfaceNodes = false;
bool logConsole = true;
int selectedShift = -1;
// Quadrature variant
Modes mode = Modes.SayeGaussRules;
int[] orders = new int[] { 3 };
//Modes mode = Modes.HMFClassic;
//int[] orders = new int[] { 3, 4, 5, 6, 7, 8 };
//LevelSetSurfaceQuadRuleFactory.RestrictNodes = false;
//LevelSetSurfaceQuadRuleFactory.UseGaussNodes = true;
//LevelSetVolumeQuadRuleFactory.RestrictNodes = false;
//LevelSetVolumeQuadRuleFactory.UseGaussNodes = true;
//LevelSetVolumeQuadRuleFactory.NodeCountSafetyFactor = 1.0;
//Modes mode = Modes.HMFClassic;
//int[] orders = new int[] { 1 };
//LevelSetSurfaceQuadRuleFactory.RestrictNodes = false;
//LevelSetSurfaceQuadRuleFactory.UseGaussNodes = true;
//LevelSetVolumeQuadRuleFactory.RestrictNodes = false;
//LevelSetVolumeQuadRuleFactory.UseGaussNodes = true;
//LevelSetVolumeQuadRuleFactory.NodeCountSafetyFactor = 1.0;
//Modes mode = Modes.HMFOneStepGaussAndStokes;
//int[] orders = new int[] { 2, 4, 6, 8, 10 };
//Modes mode = Modes.Adaptive;
//int[] orders = new int[] { 1 };
//int[] divisions = new int[] { 0, 1, 2, 3, 4, 5, 6, 7, 8 };
//int leafDivisions = 1;
//Modes mode = Modes.Regularized;
//int[] orders = Enumerable.Range(1, 20).Select(k => 2 * k - 1).ToArray();
//widths = new double[] { 0.1, 0.2 };
//vanishingMonents = new int[] { 0, 2, 4, 6 };
//continuousDerivatives = new int[] { 1, 3, 5 };
//Modes mode = Modes.BruteForce;
//int[] orders = new int[] { 1 };
//divisions = new int[] { 0, 1, 2, 3, 4 };
//Modes mode = Modes.Standard;
//int[] orders = Enumerable.Range(1, 20).Select(k => 2 * k - 1).ToArray();
if (levelSet is IAnalyticLevelSet)
{
rootFindingAlgorithm = new AnalyticLevelSetRootFindingAlgorithm();
}
else
{
rootFindingAlgorithm = new LineSegment.SafeGuardedNewtonMethod(1e-14);
//rootFindingAlgorithm = new LineSegment.GSLRootFindingAlgorithm(1e-14);
}
/*
* END OF CONFIGURATION
*/
SubGrid cutCellGrid = levelSetTracker.Regions.GetCutCellSubGrid();
CellMask cellMask = CellMask.GetFullMask(GridData);
SubGrid selectedSubGrid = new SubGrid(cellMask);
testCase.ScaleShifts(0.5 * testCase.GridSpacing);
double hBase = ((BoSSS.Foundation.Grid.Classic.GridData)GridData).Cells.h_maxGlobal;
string logName = ""
+ testCase.GetType().Name
+ "_" + Grid.RefElements[0].GetType().Name
+ "_" + testCase.GridSize
+ "_" + mode.ToString();
if (logConsole)
{
string filename = logName + "_stdout.txt";
ilPSP.Environment.StdOut.WriterS.Add(new StreamWriter(filename));
}
Console.WriteLine("Test case: " + testCase.GetType().Name);
var errorMap = new Dictionary <Tuple <int, int, double, int, int>, List <Tuple <double, double, int> > >();
foreach (int division in divisions)
{
foreach (int order in orders)
{
foreach (double width in widths)
{
foreach (int vanishingMoment in vanishingMonents)
{
foreach (int continuousDerivative in continuousDerivatives)
{
errorMap[Tuple.Create(division, order, width, vanishingMoment, continuousDerivative)] =
new List <Tuple <double, double, int> >();
}
}
}
}
}
int i = 1;
while (testCase.ProceedToNextShift())
{
Console.WriteLine("Processing shift " + i + " of " + testCase.NumberOfShifts);
if (selectedShift > 0 && i != selectedShift)
{
i++;
continue;
}
cutCellGrid = new SubGrid(
levelSetTracker.Regions.GetCutCellSubGrid().VolumeMask.Intersect(
selectedSubGrid.VolumeMask));
double referenceValue = SetUpConfiguration();
StreamWriter volumeNodesLog = null;
StreamWriter surfaceNodesLog = null;
if (plotSuperSampling >= 0 && i == 1)
{
PlotCurrentState(0.0, 0, plotSuperSampling, cutCellGrid);
}
Console.WriteLine();
foreach (int division in divisions)
{
Console.WriteLine("Number of divisions: " + division);
if (logVolumeNodes)
{
string filename = Path.Combine(
Path.GetFullPath("."),
"volumeNodes_" + testCase.GetType().Name + "_" + i + "_" + division);
volumeNodesLog = new StreamWriter(filename + ".txt");
if (GridData.SpatialDimension == 2)
{
volumeNodesLog.WriteLine("Cell\tNode\tx\ty\tweight");
}
else
{
volumeNodesLog.WriteLine("Cell\tNode\tx\ty\tz\tweight");
}
}
if (logSurfaceNodes)
{
string filename = Path.Combine(
Path.GetFullPath("."),
"surfaceNodes_" + testCase.GetType().Name + "_" + i + "_" + division);
surfaceNodesLog = new StreamWriter(filename + ".txt");
if (Grid.SpatialDimension == 2)
{
surfaceNodesLog.WriteLine("Cell\tNode\tx\ty\tweight");
}
else
{
surfaceNodesLog.WriteLine("Cell\tNode\tx\ty\tz\tweight");
}
}
foreach (int order in orders)
{
Console.WriteLine("Order: " + order);
foreach (double width in widths)
{
foreach (int vanishingMoment in vanishingMonents)
{
foreach (int continuousDerivative in continuousDerivatives)
{
var result = PerformConfiguration(
mode,
order,
division,
volumeNodesLog,
surfaceNodesLog,
leafDivisions,
vanishingMoment,
continuousDerivative,
width,
hBase,
rootFindingAlgorithm,
logVolumeNodes_selectedCell);
double error = Math.Abs(result.Item1 - referenceValue);
var key = Tuple.Create(
division, order, width, vanishingMoment, continuousDerivative);
errorMap[key].Add(Tuple.Create(
result.Item1 + testCase.Solution - referenceValue,
error,
result.Item2));
}
}
}
}
if (volumeNodesLog != null)
{
volumeNodesLog.Close();
}
if (surfaceNodesLog != null)
{
surfaceNodesLog.Close();
}
}
Console.WriteLine();
i++;
}
testCase.ResetShifts();
using (StreamWriter log = new StreamWriter(logName + ".txt")) {
log.WriteLine("Divisions\tOrder\tWidth\tMoments\tDerivatives\tResult\tMeanError\tMeanRelError\tStdDev\tMinError\tMaxError\tMaxErrorCase\tTime");
foreach (var entry in errorMap)
{
if (entry.Value.Count == 0)
{
continue;
}
IEnumerable <double> errors = entry.Value.Select((tuple) => tuple.Item2);
double meanResult = entry.Value.Select(tuple => tuple.Item1).Average();
double meanError = errors.Average();
double stdDev = Math.Sqrt(errors.Select((error) => error * error).Average() - meanError * meanError);
double time = entry.Value.Select((tuple) => tuple.Item3).Average();
string line = string.Format("{0}\t{1}\t{2}\t{3}\t{4}\t{5}\t{6}\t{7}\t{8}\t{9}\t{10}\t{11}\t{12}",
entry.Key.Item1, // division
entry.Key.Item2, // order
entry.Key.Item3, // width
entry.Key.Item4, // vanishing moments
entry.Key.Item5, // continuous derivative
meanResult.ToString(formatInfo),
meanError.ToString(formatInfo),
(meanError / testCase.Solution).ToString(formatInfo),
stdDev.ToString(formatInfo),
errors.Min().ToString(formatInfo),
errors.Max().ToString(formatInfo),
errors.IndexOfMax((d) => d) + 1,
time.ToString(formatInfo));
log.WriteLine(line);
}
}
globalWatch.Stop();
Console.WriteLine("Finished case " + testCase.GetType().Name + " after " + globalWatch.ElapsedMilliseconds + "ms");
return(dt);
}
/// <summary>
/// Returns a set of <see cref="CellEdgeBoundaryQuadRule"/>s that
/// enables the integration over sub-segments of the edges of the edges
/// of a (three-dimensional) domain. This is obviously only useful if
/// the integrand has a discontinuity that is aligned with the zero
/// iso-contour of the level set function.
/// </summary>
/// <param name="mask"></param>
/// <param name="order"></param>
/// <returns></returns>
public IEnumerable <IChunkRulePair <CellEdgeBoundaryQuadRule> > GetQuadRuleSet(ExecutionMask mask, int order)
{
if (mask == null)
{
mask = CellMask.GetFullMask(this.lsData.GridDat, MaskType.Geometrical);
}
if (mask is CellMask == false)
{
throw new ArgumentException("Edge mask required", "mask");
}
if (mask.MaskType != MaskType.Geometrical)
{
throw new ArgumentException("Expecting a geometrical mask.");
}
if (lastOrder != order)
{
cache.Clear();
}
QuadRule baseRule = lineSimplex.GetQuadratureRule(order);
int D = lsData.GridDat.SpatialDimension;
int noOfEdges = lsData.GridDat.Grid.RefElements[0].NoOfFaces;
int noOfEdgesOfEdge = RefElement.FaceRefElement.NoOfFaces;
var result = new List <ChunkRulePair <CellEdgeBoundaryQuadRule> >(mask.NoOfItemsLocally);
foreach (Chunk chunk in mask)
{
for (int i = 0; i < chunk.Len; i++)
{
int cell = i + chunk.i0;
if (cache.ContainsKey(cell))
{
result.Add(new ChunkRulePair <CellEdgeBoundaryQuadRule>(
Chunk.GetSingleElementChunk(cell),
cache[cell]));
continue;
}
List <double[]> nodes = new List <double[]>();
List <double> weights = new List <double>();
if (lsData.GridDat.Cells.Cells2Edges[cell].Length != noOfEdges)
{
throw new NotImplementedException("Not implemented for hanging nodes");
}
int[] noOfNodesPerEdge = new int[noOfEdges];
int[,] noOfNodesPerEdgeOfEdge = new int[noOfEdges, noOfEdgesOfEdge];
for (int e = 0; e < noOfEdges; e++)
{
int edge = Math.Abs(lsData.GridDat.Cells.Cells2Edges[cell][e]) - 1;
double edgeDet = lsData.GridDat.Edges.SqrtGramian[edge];
for (int ee = 0; ee < noOfEdgesOfEdge; ee++)
{
LineSegment refSegment = referenceLineSegments[e, ee];
double edgeOfEdgeDet = RefElement.FaceRefElement.FaceTrafoGramianSqrt[ee];
double[] roots = refSegment.GetRoots(lsData.LevelSet, cell, 0);
LineSegment[] subSegments = refSegment.Split(roots);
for (int k = 0; k < subSegments.Length; k++)
{
// Evaluate sub segment at center to determine sign
NodeSet _point = new NodeSet(this.RefElement, subSegments[k].GetPointOnSegment(0.0));
double scaling = edgeOfEdgeDet * subSegments[k].Length / refSegment.Length;
if (jumpType != JumpTypes.Implicit)
{
//using (tracker.GridDat.NSC.CreateLock(
// MultidimensionalArray.CreateWrapper(point, 1, D), 0, -1.0)) {
MultidimensionalArray levelSetValue = lsData.GetLevSetValues(_point, cell, 1);
switch (jumpType)
{
case JumpTypes.Heaviside:
if (levelSetValue[0, 0] <= 0.0)
{
continue;
}
break;
case JumpTypes.OneMinusHeaviside:
if (levelSetValue[0, 0] > 0.0)
{
continue;
}
break;
case JumpTypes.Sign:
scaling *= levelSetValue[0, 0].Sign();
break;
default:
throw new NotImplementedException();
}
}
for (int m = 0; m < baseRule.NoOfNodes; m++)
{
// Base rule _always_ is a line rule, thus Nodes[*, _0_]
double[] point = subSegments[k].GetPointOnSegment(baseRule.Nodes[m, 0]);
weights.Add(baseRule.Weights[m] * scaling);
nodes.Add(point);
noOfNodesPerEdge[e]++;
noOfNodesPerEdgeOfEdge[e, ee]++;
}
}
}
}
if (weights.Count == 0)
{
CellEdgeBoundaryQuadRule emptyRule =
CellEdgeBoundaryQuadRule.CreateEmpty(1, RefElement);
emptyRule.Nodes.LockForever();
cache.Add(cell, emptyRule);
result.Add(new ChunkRulePair <CellEdgeBoundaryQuadRule>(
Chunk.GetSingleElementChunk(cell), emptyRule));
continue;
}
NodeSet localNodes = new NodeSet(this.RefElement, nodes.Count, D);
for (int j = 0; j < nodes.Count; j++)
{
for (int d = 0; d < D; d++)
{
localNodes[j, d] = nodes[j][d];
}
}
localNodes.LockForever();
CellEdgeBoundaryQuadRule subdividedRule = new CellEdgeBoundaryQuadRule()
{
OrderOfPrecision = order,
Weights = MultidimensionalArray.Create(weights.Count),
Nodes = localNodes,
NumbersOfNodesPerFace = noOfNodesPerEdge,
NumbersOfNodesPerFaceOfFace = noOfNodesPerEdgeOfEdge
};
subdividedRule.Weights.SetSubVector(weights, -1);
cache.Add(cell, subdividedRule);
result.Add(new ChunkRulePair <CellEdgeBoundaryQuadRule>(
Chunk.GetSingleElementChunk(cell), subdividedRule));
}
}
return(result);
}
/// <summary>
/// accumulate this field to a DG field
/// </summary>
/// <param name="alpha"></param>
/// <param name="DGField"></param>
/// <param name="mask">optional cell mask</param>
public void AccToDGField(double alpha, ConventionalDGField DGField, CellMask mask = null)
{
if (!DGField.Basis.Equals(this.m_Basis.ContainingDGBasis))
{
throw new ArgumentException("Basis does not match.");
}
var gdat = m_Basis.GridDat;
var Trafo = gdat.ChefBasis.Scaling;
var C2N = m_Basis.CellNode_To_Node;
var MtxM2N = m_Basis.m_Modal2Nodal;
var CellData = this.Basis.GridDat.Cells;
int[] _K = m_Basis.NodesPerCell;
int L = m_Basis.ContainingDGBasis.Length;
int pDeg = m_Basis.ContainingDGBasis.Degree;
double[][] _NodalCoordinates = _K.Select(K => new double[K]).ToArray();
double[] ModalCoordinates = new double[L];
double[] InterCoordinates = new double[L]; // only used for curved cells
if (mask == null)
{
mask = CellMask.GetFullMask(this.Basis.GridDat);
}
foreach (var chunk in mask)
{
int j0 = chunk.i0;
int JE = chunk.JE;
for (int j = j0; j < JE; j++) // loop over cells...
{
int iKref = CellData.GetRefElementIndex(j);
double[] NodalCoordinates = _NodalCoordinates[iKref];
int K = _K[iKref];
// collect coordinates for cell 'j':
for (int k = 0; k < K; k++)
{
int _c2n = C2N[j, k];
NodalCoordinates[k] = m_Coordinates[_c2n];
}
// transform
DGField.Coordinates.GetRow(j, ModalCoordinates);
if (CellData.IsCellAffineLinear(j))
{
MtxM2N[iKref].GEMV(alpha / Trafo[j], NodalCoordinates, 1.0, ModalCoordinates);
}
else
{
MtxM2N[iKref].GEMV(alpha, NodalCoordinates, 0.0, InterCoordinates);
var OnbTrafo = gdat.ChefBasis.OrthonormalizationTrafo.GetValue_Cell(j, 1, pDeg).ExtractSubArrayShallow(0, -1, -1);
//OnbTrafo.GetInverse().gemv(1.0, InterCoordinates, 0.0, ModalCoordinates);
OnbTrafo.Solve(ModalCoordinates, InterCoordinates);
}
// save
DGField.Coordinates.SetRow(j, ModalCoordinates);
}
}
}
/// <summary>
/// returns global unique indices which correlate to a certain sub-set of ...
/// <list type="bullet">
/// <item>the mappings's basis (<paramref name="mapping"/>, <see cref="UnsetteledCoordinateMapping.BasisS"/>).</item>
/// <item>species (<paramref name="_SpcIds"/>).</item>
/// <item>cells (<paramref name="cm"/>).</item>
/// </list>
/// </summary>
/// <param name="mapping">
/// the mapping
/// </param>
/// <param name="Fields">
/// determines which fields should be in the sub-vector-indices-list
/// </param>
/// <param name="_SpcIds">
/// determines which species should be in the sub-vector-indices-list; null indicates all species.
/// </param>
/// <param name="cm">
/// determines which cells should be in the sub-vector-indices-list; null indicates all cells.
/// </param>
/// <param name="regions">
/// Determines which XDG-coordinate belongs to which species.
/// </param>
/// <param name="presenceTest">
/// if true, cells where some species has zero measure are excluded from the sub-vector-indices-list.
/// </param>
/// <param name="drk">
/// a cell-agglomeration object: if null, ignored; if provided,
/// cells which are eliminated by the agglomeration are excluded from the sub-vector-indices-list
/// </param>
/// <returns>a list of global (over all MPI processes) unique indices.</returns>
static public int[] GetSubvectorIndices(this UnsetteledCoordinateMapping mapping, LevelSetTracker.LevelSetRegions regions, int[] Fields,
ICollection <SpeciesId> _SpcIds = null, CellMask cm = null, bool presenceTest = true, MultiphaseCellAgglomerator drk = null)
{
#region Check Arguments
// =========
SpeciesId[] SpcIds = null;
if (_SpcIds == null)
{
// take all species, if arg is null
SpcIds = regions.SpeciesIdS.ToArray();
}
else
{
SpcIds = _SpcIds.ToArray();
}
if (SpcIds.Length <= 0)
{
// return will be empty for no species
return(new int[0]);
}
#endregion
#region collect cells which are excluded by agglomeration
// =================================================
int[][] ExcludeLists;
if (drk != null)
{
ExcludeLists = new int[regions.SpeciesIdS.Count][]; // new Dictionary<SpeciesId, int[]>();
foreach (var id in SpcIds)
{
int[] ExcludeList = drk.GetAgglomerator(id).AggInfo.AgglomerationPairs.Select(pair => pair.jCellSource).ToArray();
Array.Sort(ExcludeList);
ExcludeLists[id.cntnt - LevelSetTracker.___SpeciesIDOffest] = ExcludeList;
}
}
else
{
ExcludeLists = null;
}
#endregion
#region determine over which cells we want to loop
// ==========================================
CellMask loopCells;
if ((new HashSet <SpeciesId>(regions.SpeciesIdS)).SetEquals(new HashSet <SpeciesId>(SpcIds)))
{
if (cm == null)
{
loopCells = CellMask.GetFullMask(regions.GridDat);
}
else
{
loopCells = cm;
}
}
else
{
loopCells = regions.GetSpeciesMask(SpcIds[0]);
for (int i = 1; i < SpcIds.Length; i++)
{
loopCells = loopCells.Intersect(regions.GetSpeciesMask(SpcIds[i]));
}
if (cm != null)
{
loopCells = loopCells.Intersect(cm);
}
}
#endregion
#region build list
// ==========
var R = new List <int>();
// which basis is XDG?
var _BasisS = mapping.BasisS.ToArray();
XDGBasis[] _XBasisS = new XDGBasis[_BasisS.Length];
for (int i = 0; i < _BasisS.Length; i++)
{
_XBasisS[i] = _BasisS[i] as XDGBasis;
}
Tuple <int, SpeciesId>[] iSpcS = new Tuple <int, SpeciesId> [SpcIds.Length];
int KK;
int Len_iSpcS = iSpcS.Length;
int[] ExcludeListsPointer = new int[regions.SpeciesIdS.Count];
// loop over cells?
foreach (int jCell in loopCells.ItemEnum)
{
int NoOfSpc = regions.GetNoOfSpecies(jCell);
#region
//
// in cell 'jCell', for each species in 'SpcIds' ...
// * is the species present in 'jCell'?
// * what is the species index in 'jCell'?
// * we also have to consider that due to agglomeration, the respective cut-cell for the species might have been agglomerated.
// so we determine
// * 'KK' is the number of species (from 'SpcIds') which is actually present and not agglomerated in 'jCell'
// * for i in (0 ... KK-1), iSpcS[i] is a tuple of (Species-index-in-cell, SpeciesID)
//
// yes, the following code sucks:
KK = 0;
for (int k = 0; k < Len_iSpcS; k++) // loop over all species (provided as argument)...
{
SpeciesId id = SpcIds[k];
int __iSpcS = regions.GetSpeciesIndex(id, jCell);
if (__iSpcS >= 0)
{
// species index is non-negative, so indices for the species are allocated ...
if (!presenceTest || regions.IsSpeciesPresentInCell(id, jCell))
{
// species is also present (i.e. has a greater-than-zero measure ...
if (drk == null)
{
// no agglomeration exclution
iSpcS[KK] = new Tuple <int, SpeciesId>(__iSpcS, id);
KK++;
}
else
{
int q = id.cntnt - LevelSetTracker.___SpeciesIDOffest;
var el = ExcludeLists[q];
while (ExcludeListsPointer[q] < el.Length &&
el[ExcludeListsPointer[q]] < jCell)
{
ExcludeListsPointer[q]++;
}
Debug.Assert(ExcludeListsPointer[q] >= el.Length || el[ExcludeListsPointer[q]] >= jCell);
if (ExcludeListsPointer[q] >= el.Length || el[ExcludeListsPointer[q]] != jCell)
{
// cell is also not agglomerated ...
iSpcS[KK] = new Tuple <int, SpeciesId>(__iSpcS, id);
KK++;
}
}
}
}
}
if (KK > 1)
{
Array.Sort <Tuple <int, SpeciesId> >(iSpcS, 0, KK, new ilPSP.FuncComparer <Tuple <int, SpeciesId> >((a, b) => a.Item1 - b.Item1));
}
// --------- esc (end of sucking code)
#endregion
for (int k = 0; k < KK; k++) // loop over species in cell
{
int iSpc = iSpcS[k].Item1;
for (int i = 0; i < Fields.Length; i++)
{
int iField = Fields[i];
if (_XBasisS[iField] == null)
{
int N = _BasisS[iField].GetLength(jCell);
int i0 = mapping.LocalUniqueCoordinateIndex(iField, jCell, 0);
for (int n = 0; n < N; n++)
{
R.Add(i0 + n);
}
}
else
{
int N = _XBasisS[iField].DOFperSpeciesPerCell;
int i0 = mapping.LocalUniqueCoordinateIndex(iField, jCell, 0) + iSpc * N;
for (int n = 0; n < N; n++)
{
R.Add(i0 + n);
}
}
}
}
}
#endregion
return(R.ToArray());
}
/// <summary>
///
/// </summary>
/// <param name="output">output</param>
/// <param name="cm">mask on which the filtering should be performed</param>
/// <param name="input">input</param>
/// <param name="mode"></param>
public static void FilterStencilProjection(SinglePhaseField output, CellMask cm, SinglePhaseField input, PatchRecoveryMode mode)
{
var GridDat = input.GridDat;
if (!object.ReferenceEquals(output.GridDat, GridDat))
{
throw new ArgumentException();
}
if (!object.ReferenceEquals(input.GridDat, GridDat))
{
throw new ArgumentException();
}
if (cm == null)
{
cm = CellMask.GetFullMask(GridDat);
}
switch (mode)
{
case PatchRecoveryMode.L2_unrestrictedDom:
case PatchRecoveryMode.L2_restrictedDom: {
var Mask = cm.GetBitMaskWithExternal();
bool RestrictToCellMask = mode == PatchRecoveryMode.L2_restrictedDom;
foreach (int jCell in cm.ItemEnum)
{
int[] NeighCells, dummy;
GridDat.GetCellNeighbours(jCell, GetCellNeighbours_Mode.ViaVertices, out NeighCells, out dummy);
if (RestrictToCellMask == true)
{
NeighCells = NeighCells.Where(j => Mask[j]).ToArray();
}
FilterStencilProjection(output, jCell, NeighCells, input);
}
return;
}
case PatchRecoveryMode.ChebychevInteroplation: {
int P = input.Basis.Degree * 3;
double[] ChebyNodes = ChebyshevNodes(P);
NodeSet Nds = new NodeSet(GridDat.iGeomCells.RefElements[0], P, 1);
Nds.SetColumn(0, ChebyNodes);
Nds.LockForever();
Polynomial[] Polynomials = GetNodalPolynomials(ChebyNodes);
MultidimensionalArray PolyVals = MultidimensionalArray.Create(P, P);
for (int p = 0; p < P; p++)
{
Polynomials[p].Evaluate(PolyVals.ExtractSubArrayShallow(p, -1), Nds);
for (int i = 0; i < P; i++)
{
Debug.Assert(Math.Abs(((i == p) ? 1.0 : 0.0) - PolyVals[p, i]) <= 1.0e-8);
}
}
foreach (int jCell in cm.ItemEnum)
{
AffineTrafo T;
var NodalValues = NodalPatchRecovery(jCell, ChebyNodes, input, out T);
/*
* MultidimensionalArray Nodes2D = MultidimensionalArray.Create(P, P, 2);
* for (int i = 0; i < P; i++) {
* for (int j = 0; j < P; j++) {
* Nodes2D[i, j, 0] = ChebyNodes[i];
* Nodes2D[i, j, 1] = ChebyNodes[j];
* }
* }
* var _Nodes2D = Nodes2D.ResizeShallow(P*P, 2);
* var xNodes = _Nodes2D.ExtractSubArrayShallow(new int[] { 0, 0 }, new int[] { P*P - 1, 0 });
* var yNodes = _Nodes2D.ExtractSubArrayShallow(new int[] { 0, 1 }, new int[] { P*P - 1, 1 });
* int K = P*P;
*
* MultidimensionalArray xPolyVals = MultidimensionalArray.Create(P, K);
* MultidimensionalArray yPolyVals = MultidimensionalArray.Create(P, K);
*
* for (int p = 0; p < P; p++) {
* Polynomials[p].Evaluate(yPolyVals.ExtractSubArrayShallow(p, -1), yNodes);
* Polynomials[p].Evaluate(xPolyVals.ExtractSubArrayShallow(p, -1), xNodes);
*
* }
*
*
* double ERR = 0;
* for (int k = 0; k < K; k++) {
*
* double x = xNodes[k, 0];
* double y = yNodes[k, 0];
*
* double acc = 0;
* double BasisHits = 0.0;
* for (int i = 0; i < P; i++) {
* for (int j = 0; j < P; j++) {
*
* bool isNode = (Math.Abs(x - ChebyNodes[i]) < 1.0e-8) && (Math.Abs(y - ChebyNodes[j]) < 1.0e-8);
* double BasisSoll = isNode ? 1.0 : 0.0;
* if (isNode)
* Console.WriteLine();
*
* double Basis_ij = xPolyVals[i, k]*yPolyVals[j, k];
*
* Debug.Assert((Basis_ij - BasisSoll).Abs() < 1.0e-8);
*
* BasisHits += Math.Abs(Basis_ij);
*
* acc += Basis_ij*NodalValues[i, j];
* }
* }
* Debug.Assert(Math.Abs(BasisHits - 1.0) < 1.0e-8);
*
*
*
*
* double soll = yNodes[k,0];
* Debug.Assert((soll - acc).Pow2() < 1.0e-7);
* ERR = (soll - acc).Pow2();
* }
* Console.WriteLine(ERR);
*/
output.ProjectField(1.0,
delegate(int j0, int Len, NodeSet Nodes, MultidimensionalArray result) {
var K = Nodes.NoOfNodes;
MultidimensionalArray NT = T.Transform(Nodes);
var xNodes = new NodeSet(null, NT.ExtractSubArrayShallow(new int[] { 0, 0 }, new int[] { K - 1, 0 }));
var yNodes = new NodeSet(null, NT.ExtractSubArrayShallow(new int[] { 0, 1 }, new int[] { K - 1, 1 }));
MultidimensionalArray xPolyVals = MultidimensionalArray.Create(P, K);
MultidimensionalArray yPolyVals = MultidimensionalArray.Create(P, K);
for (int p = 0; p < P; p++)
{
Polynomials[p].Evaluate(yPolyVals.ExtractSubArrayShallow(p, -1), yNodes);
Polynomials[p].Evaluate(xPolyVals.ExtractSubArrayShallow(p, -1), xNodes);
}
for (int k = 0; k < K; k++)
{
double acc = 0;
for (int i = 0; i < P; i++)
{
for (int j = 0; j < P; j++)
{
acc += xPolyVals[i, k] * yPolyVals[j, k] * NodalValues[i, j];
}
}
result[0, k] = acc;
}
},
new CellQuadratureScheme(true, new CellMask(input.GridDat, Chunk.GetSingleElementChunk(jCell))));
}
return;
}
}
}
/// <summary>
/// projects some DG field onto this
/// </summary>
/// <param name="alpha"></param>
/// <param name="DGField"></param>
/// <param name="_cm">optional restriction to computational domain</param>
/// <remarks>
/// This method computes an exact
/// L2-projection of the DG-field onto the SpecFEM-space, so a global linear system, which contains all
/// DOF's, has to be solved.
/// In contrast, <see cref="ProjectDGFieldCheaply"/> performs an approximate projection which only involves
/// local operations for each cell.
/// </remarks>
public void ProjectDGField(double alpha, ConventionalDGField DGField, CellMask _cm = null)
{
using (var trx = new Transceiver(this.Basis)) {
CellMask cm = _cm;
if (cm == null)
{
cm = CellMask.GetFullMask(this.Basis.GridDat);
}
int J = m_Basis.GridDat.Cells.NoOfLocalUpdatedCells;
var Trafo = m_Basis.GridDat.ChefBasis.Scaling;
var C2N = m_Basis.CellNode_To_Node;
var MtxM2N = m_Basis.m_Modal2Nodal;
var CellData = this.Basis.GridDat.Cells;
// compute RHS
// ===========
var b = MultidimensionalArray.Create(this.m_Basis.NoOfLocalNodes);
{
int[] _K = m_Basis.NodesPerCell;
int L = m_Basis.ContainingDGBasis.Length;
double[][] _NodalCoordinates = _K.Select(K => new double[K]).ToArray(); // temporary storage for nodal coordinates per cell
// 1st idx: ref. elm., 2nd idx: node index
double[] ModalCoordinates = new double[L];
foreach (Chunk cnk in cm)
{
int j0 = cnk.i0;
int jE = cnk.JE;
for (int j = j0; j < jE; j++) // loop over cells...
{
int iKref = CellData.GetRefElementIndex(j);
double[] NodalCoordinates = _NodalCoordinates[iKref];
int K = _K[iKref];
if (!CellData.IsCellAffineLinear(j))
{
throw new NotSupportedException();
}
// Get DG coordinates
Array.Clear(ModalCoordinates, 0, L);
int Lmin = Math.Min(L, DGField.Basis.GetLength(j));
for (int l = 0; l < Lmin; l++)
{
ModalCoordinates[l] = DGField.Coordinates[j, l];
}
var tr = 1.0 / Trafo[j];
// transform
//DGField.Coordinates.GetRow(j, ModalCoordinates);
ModalCoordinates.ClearEntries();
for (int l = 0; l < Lmin; l++)
{
ModalCoordinates[l] = DGField.Coordinates[j, l];
}
MtxM2N[iKref].GEMV(tr, ModalCoordinates, 0.0, NodalCoordinates, transpose: true);
// collect coordinates for cell 'j':
for (int k = 0; k < K; k++)
{
int _c2n = C2N[j, k];
b[_c2n] += NodalCoordinates[k];
}
}
}
}
trx.AccumulateGather(b);
/*
*
* var bcheck = new double[b.Length];
* {
* var polys = this.Basis.NodalBasis;
*
*
* CellQuadrature.GetQuadrature(new int[] { K },
* this.Basis.GridDat.Context,
* (new CellQuadratureScheme()).Compile(this.Basis.GridDat, this.Basis.ContainingDGBasis.Degree*2),
* delegate(MultidimensionalArray NodesUntransformed) { // Del_CreateNodeSetFamily
* var NSC = this.Basis.GridDat.Context.NSC;
* return new NodeSetController.NodeSetContainer[] { NSC.CreateContainer(NodesUntransformed) };
* },
* delegate(int i0, int Length, int _NoOfNodes, MultidimensionalArray EvalResult) {
* var PolyAtNode = MultidimensionalArray.Create(K, _NoOfNodes);
* for (int k = 0; k < K; k++) {
* polys[k].Evaluate(PolyAtNode.ExtractSubArrayShallow(k, -1), this.Basis.GridDat.Context.NSC.Current_NodeSetFamily[0].NodeSet);
* }
*
* var DGFatNodes = MultidimensionalArray.Create(Length, _NoOfNodes);
* DGField.Evaluate(i0, Length, 0, DGFatNodes);
*
* //for(int i = 0; i < Length; i++) {
* // for (int n = 0; n < _NoOfNodes; n++) {
* // for (int k = 0; k < K; k++) {
* // for (int l = 0; l < K; l++) {
* // EvalResult[i, n, k, l] = PolyAtNode[k, n]*PolyAtNode[l, n];
* // }
* // }
* // }
* //}
*
* EvalResult.Multiply(1.0, PolyAtNode, DGFatNodes, 0.0, "jnk", "kn", "jn");
*
* //double errSum = 0;
* //for (int i = 0; i < Length; i++) {
* // for (int n = 0; n < _NoOfNodes; n++) {
* // for (int k = 0; k < K; k++) {
* // for (int l = 0; l < K; l++) {
* // double soll = PolyAtNode[k, n]*PolyAtNode[l, n];
* // errSum += Math.Abs(soll - EvalResult[i, n, k, l]);
* // }
* // }
* // }
* //}
* //Console.WriteLine("errsum = " + errSum);
* },
* delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) { // SaveIntegrationResults
* for (int i = 0; i < Length; i++) {
* int jCell = i + i0;
*
* for (int k = 0; k < K; k++) {
* bcheck[C2N[jCell, k]] += ResultsOfIntegration[i, k];
* }
*
* //CellMass[jCell] = new FullMatrix(K, K);
* //CellMass[jCell].Initialize(ResultsOfIntegration.ExtractSubArrayShallow(i, -1, -1));
* }
* }).Execute();
*
*
* double f**k = GenericBlas.L2Dist(b, bcheck);
* Console.WriteLine("Distance error = " + f**k);
*
* }
*
*
*/
if (_cm == null)
{
// full domain projection branch
// +++++++++++++++++++++++++++++
var x = new double[this.Basis.NoOfLocalOwnedNodes];
var solStat = m_Basis.MassSolver.Solve(x, b.ExtractSubArrayShallow(new int[] { 0 }, new int[] { this.Basis.NoOfLocalOwnedNodes - 1 }).To1DArray());
{
if (solStat.Converged == false)
{
throw new ArithmeticException("DG -> SpecFEM Projection failed because the Mass matrix solver did not converge.");
}
double[] chk = b.ExtractSubArrayShallow(new int[] { 0 }, new int[] { this.Basis.NoOfLocalOwnedNodes - 1 }).To1DArray();
this.Basis.MassMatrix.SpMVpara(-1.0, x, 1.0, chk);
double chk_nomr = chk.L2Norm();
if (chk_nomr >= 1.0e-8)
{
throw new ArithmeticException(string.Format("DG -> SpecFEM Projection failed: solver converged, but with high residual {0}.", chk_nomr.ToStringDot()));
}
}
//m_Basis.MassMatrix.SpMV(1.0, b, 0.0, x);
m_Coordinates.ExtractSubArrayShallow(new int[] { 0 }, new int[] { this.Basis.NoOfLocalOwnedNodes - 1 }).AccVector(alpha, x);
//m_Coordinates.AccV(alpha, b);
}
else
{
// restricted domain projection branch
// +++++++++++++++++++++++++++++++++++
List <int> OccupiedRows_Global = new List <int>();
//List<int> OccupiedRows_Local = new List<int>();
var MM = Basis.ComputeMassMatrix(cm);
int i0 = MM.RowPartitioning.i0, iE = MM.RowPartitioning.iE;
for (int i = i0; i < iE; i++)
{
if (MM.GetNoOfNonZerosPerRow(i) > 0)
{
OccupiedRows_Global.Add(i);
//OccupiedRows_Local.Add(i - i0);
}
}
var CompressedPart = new Partitioning(OccupiedRows_Global.Count);
var CompressedMM = new MsrMatrix(CompressedPart);
MM.WriteSubMatrixTo(CompressedMM, OccupiedRows_Global, default(int[]), OccupiedRows_Global, default(int[]));
var b_sub = new double[OccupiedRows_Global.Count];
//try {
b_sub.AccV(1.0, b.To1DArray(), default(int[]), OccupiedRows_Global, b_index_shift: -i0);
//} catch(Exception e) {
// Debugger.Launch();
//}
//csMPI.Raw.Barrier(csMPI.Raw._COMM.WORLD);
var x_sub = new double[b_sub.Length];
var solver = new ilPSP.LinSolvers.monkey.CG();
solver.MatrixType = ilPSP.LinSolvers.monkey.MatrixType.CCBCSR;
solver.DevType = ilPSP.LinSolvers.monkey.DeviceType.CPU;
solver.ConvergenceType = ConvergenceTypes.Absolute;
solver.Tolerance = 1.0e-12;
solver.DefineMatrix(CompressedMM);
var solStat = solver.Solve(x_sub, b_sub.CloneAs());
{
if (solStat.Converged == false)
{
throw new ArithmeticException("DG -> SpecFEM Projection failed because the Mass matrix solver did not converge.");
}
var chk = b_sub;
CompressedMM.SpMVpara(-1.0, x_sub, 1.0, chk);
double chk_nomr = chk.L2Norm();
if (chk_nomr >= 1.0e-8)
{
throw new ArithmeticException(string.Format("DG -> SpecFEM Projection failed: solver converged, but with high residual {0}.", chk_nomr.ToStringDot()));
}
}
double[] x = new double[this.Basis.NoOfLocalOwnedNodes];
x.AccV(1.0, x_sub, OccupiedRows_Global, default(int[]), acc_index_shift: -i0);
m_Coordinates.ExtractSubArrayShallow(new int[] { 0 }, new int[] { this.Basis.NoOfLocalOwnedNodes - 1 }).AccVector(alpha, x);
}
trx.Scatter(this.m_Coordinates);
}
}
/// <summary>
/// computes <see cref="LaplaceMtx"/> and <see cref="LaplaceAffine"/>
/// </summary>
private void UpdateMatrices()
{
using (var tr = new FuncTrace()) {
// time measurement for matrix assembly
Stopwatch stw = new Stopwatch();
stw.Start();
// Stats:
{
int BlkSize = T.Mapping.MaxTotalNoOfCoordinatesPerCell;
int NoOfMtxBlocks = 0;
foreach (int[] Neigs in this.GridData.iLogicalCells.CellNeighbours)
{
NoOfMtxBlocks++; // diagonal block
NoOfMtxBlocks += Neigs.Length; // off-diagonal block
}
NoOfMtxBlocks = NoOfMtxBlocks.MPISum();
int MtxBlockSize = BlkSize * BlkSize;
int MtxSize = MtxBlockSize * NoOfMtxBlocks;
double MtxStorage = MtxSize * (8.0 + 4.0) / (1024 * 1024); // 12 bytes (double+int) per entry
Console.WriteLine(" System size: {0}", T.Mapping.TotalLength);
Console.WriteLine(" No of blocks: {0}", T.Mapping.TotalNoOfBlocks);
Console.WriteLine(" No of blocks in matrix: {0}", NoOfMtxBlocks);
Console.WriteLine(" DG coordinates per cell: {0}", BlkSize);
Console.WriteLine(" Non-zeros per matrix block: {0}", MtxBlockSize);
Console.WriteLine(" Total non-zeros in matrix: {0}", MtxSize);
Console.WriteLine(" Approx. matrix storage (MB): {0}", MtxStorage);
base.QueryHandler.ValueQuery("MtxBlkSz", MtxBlockSize, true);
base.QueryHandler.ValueQuery("NNZMtx", MtxSize, true);
base.QueryHandler.ValueQuery("NNZblk", NoOfMtxBlocks, true);
base.QueryHandler.ValueQuery("MtxMB", MtxStorage, true);
}
Console.WriteLine("creating sparse system for {0} DOF's ...", T.Mapping.Ntotal);
// quadrature domain
var volQrSch = new CellQuadratureScheme(true, CellMask.GetFullMask(this.GridData, MaskType.Geometrical));
var edgQrSch = new EdgeQuadratureScheme(true, EdgeMask.GetFullMask(this.GridData, MaskType.Geometrical));
using (new BlockTrace("SipMatrixAssembly", tr)) {
LaplaceMtx = new BlockMsrMatrix(T.Mapping);
LaplaceAffine = new double[T.Mapping.LocalLength];
LapaceIp.ComputeMatrixEx(T.Mapping, null, T.Mapping,
LaplaceMtx, LaplaceAffine,
volQuadScheme: volQrSch, edgeQuadScheme: edgQrSch);
}
stw.Stop();
//Print process information
Console.WriteLine("done {0} sec.", stw.Elapsed.TotalSeconds);
LaplaceMtx.GetMemoryInfo(out long AllocatedMem, out long UsedMem);
Console.WriteLine(" Used matrix storage (MB): {0}", UsedMem / (1024.0 * 1024));
Console.WriteLine(" Alloc. matrix storage (MB): {0}", AllocatedMem / (1024.0 * 1024));
}
}
/// <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>
/// Creates the sub-grids of the clustering
/// </summary>
/// <param name="numOfClusters">Number of clusters</param>
/// <returns>A list of sub-grids</returns>
public Clustering CreateClustering(int numOfClusters, IList <TimeStepConstraint> timeStepConstraints, SubGrid subGrid = null)
{
//using (var tr = new ilPSP.Tracing.FuncTrace()) {
if (subGrid == null)
{
subGrid = new SubGrid(CellMask.GetFullMask(gridData));
}
// Attention: numOfCells can equal all local cells or only the local cells of a subgrid,
// e.g., the fluid cells in an IBM simulation
int numOfCells = subGrid.LocalNoOfCells;
MultidimensionalArray cellMetric = GetStableTimestepSize(subGrid, timeStepConstraints);
MultidimensionalArray means = CreateInitialMeans(cellMetric, numOfClusters);
Kmeans Kmean = new Kmeans(cellMetric.To1DArray(), numOfClusters, means.To1DArray());
// The corresponding sub-grid IDs
int[] subGridCellToClusterMap = Kmean.Cluster();
int[] noOfCellsPerCluster = Kmean.ClusterCount;
unsafe {
int[] globalCC = new int[numOfClusters];
// send = means[]
// receive = globalMeans[]
fixed(int *pSend = &noOfCellsPerCluster[0], pRcv = &globalCC[0])
{
csMPI.Raw.Allreduce((IntPtr)(pSend), (IntPtr)(pRcv), numOfClusters, csMPI.Raw._DATATYPE.INT, csMPI.Raw._OP.SUM, csMPI.Raw._COMM.WORLD);
}
noOfCellsPerCluster = globalCC;
}
int counter = numOfClusters;
for (int i = 0; i < numOfClusters; i++)
{
if (noOfCellsPerCluster[i] == 0)
{
if (consoleOutput)
{
Console.WriteLine("Sub-grid/Cluster " + (i + 1) + ", with mean value " + Kmean.Means[i] + ", is empty and not used anymore!");
}
counter--;
}
}
// Generating BitArray for all Subgrids, even for those which are empty, i.e ClusterCount == 0
BitArray[] baMatrix = new BitArray[numOfClusters];
for (int i = 0; i < numOfClusters; i++)
{
//baMatrix[i] = new BitArray(gridData.iLogicalCells.NoOfCells);
baMatrix[i] = new BitArray(gridData.iLogicalCells.NoOfLocalUpdatedCells);
}
// Filling the BitArrays
for (int i = 0; i < numOfCells; i++)
{
baMatrix[subGridCellToClusterMap[i]][subGrid.SubgridIndex2LocalCellIndex[i]] = true;
}
// IBM source cells are assigned to the cluster of the corresponding target cells
// This code is only excuted in IBM simulation runs
if (this.cellAgglomerator != null)
{
// MPI exchange in order to get cellToClusterMap (local + external cells)
int JE = gridData.iLogicalCells.Count;
int J = gridData.iLogicalCells.NoOfLocalUpdatedCells;
int[] cellToClusterMap = new int[JE];
int JSub = subGrid.LocalNoOfCells;
int[] jSub2j = subGrid.SubgridIndex2LocalCellIndex;
for (int jsub = 0; jsub < JSub; jsub++)
{
cellToClusterMap[jSub2j[jsub]] = subGridCellToClusterMap[jsub];
}
cellToClusterMap.MPIExchange(gridData);
foreach (AgglomerationPair aggPair in this.cellAgglomerator.AggInfo.AgglomerationPairs)
{
// AgglomerationPairs can contain combinations where jCellSource is on one MPI rank
// and the corresponding target cell is on another MPI rank. These duplications have to be eleminated.
if (aggPair.jCellSource < J)
{
// Assign source cell to the cluster of the corresponding target cell
int clusterOfTargetCell = cellToClusterMap[aggPair.jCellTarget];
baMatrix[clusterOfTargetCell][aggPair.jCellSource] = true;
// Delete source cell from other clusters
for (int j = 0; j < numOfClusters; j++)
{
if (clusterOfTargetCell != j)
{
baMatrix[j][aggPair.jCellSource] = false;
}
}
}
}
}
// Generating the sub-grids
List <SubGrid> clusters = new List <SubGrid>(counter);
for (int i = 0; i < numOfClusters; i++)
{
// Generating only the sub-grids which are not empty
if (noOfCellsPerCluster[i] != 0)
{
BitArray ba = baMatrix[i];
clusters.Add(new SubGrid(new CellMask(gridData, ba)));
}
}
if (consoleOutput)
{
for (int i = 0; i < clusters.Count; i++)
{
Console.WriteLine("CreateClustering:\t id=" + i + " ->\t\telements=" + clusters[i].GlobalNoOfCells);
}
}
return(new Clustering(clusters, subGrid));
}