/// <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);
}
}
/// <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>
/// 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);
}
/// <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>
/// Auto-tuning
/// </summary>
public void PerformanceVsCachesize()
{
double[] dummy = new double[this.u.CoordinateVector.Count];
SpatialOperator.Evaluator eval = diffOp.GetEvaluatorEx(new DGField[] { this.u }, this.Velocity.ToArray(), this.u.Mapping,
edgeQrCtx: new EdgeQuadratureScheme(false, EdgeMask.GetEmptyMask(this.GridData)),
volQrCtx: new CellQuadratureScheme(true, null));
Stopwatch stw = new Stopwatch();
int NoOfRuns = 10;
Console.WriteLine("BlkSz\tNoChks\tRunTime");
foreach (int bulkSize in new int[] { 1, 2, 4, 8, 16, 32, 64, 256, 512, 1024, 2048, 8192, 16384, 16384 * 2, 16384 * 4 })
{
Quadrature_Bulksize.CHUNK_DATA_LIMIT = bulkSize;
stw.Reset();
stw.Start();
for (int i = 0; i < NoOfRuns; i++)
{
eval.Evaluate(1.0, 0.0, dummy);
}
stw.Stop();
double runTime = stw.Elapsed.TotalSeconds;
Console.WriteLine("{0}\t{2}\t{1}", bulkSize, runTime.ToStringDot("0.####E-00"), this.GridData.Cells.NoOfLocalUpdatedCells / bulkSize);
}
}
/// <summary>
///
/// </summary>
/// <param name="jCell"></param>
/// <param name="AcceptedMask"></param>
/// <param name="Phi"></param>
/// <param name="gradPhi"></param>
/// <param name="__DiffusionCoeff">Output: if artificial diffusion is turned</param>
/// <param name="MaxAllowedPhi">Input: upper threshold for the values of <paramref name="Phi"/> in cell <see cref="jCell"/>.</param>
/// <param name="MinAllowedPhi">Input: lower threshold for the values of <paramref name="Phi"/> in cell <see cref="jCell"/>.</param>
/// <returns></returns>
public bool LocalSolve_Iterative(int jCell, BitArray AcceptedMask, SinglePhaseField Phi, VectorField <SinglePhaseField> gradPhi, SinglePhaseField __DiffusionCoeff, double MaxAllowedPhi, double MinAllowedPhi)
{
//this.LocalSolve_Geometric(jCell, AcceptedMask, Phi, +1, out MinAllowedPhi, out MaxAllowedPhi);) {
int N = this.LevelSetBasis.GetLength(jCell);
int i0G = this.LevelSetMapping.GlobalUniqueCoordinateIndex(0, jCell, 0);
int i0L = this.LevelSetMapping.LocalUniqueCoordinateIndex(0, jCell, 0);
SinglePhaseField __AcceptedMask = new SinglePhaseField(new Basis(this.GridDat, 0), "accepted");
for (int j = 0; j < AcceptedMask.Length; j++)
{
__AcceptedMask.SetMeanValue(j, AcceptedMask[j] ? 1.0 : 0.0);
}
// subgrid on which we are working, consisting only of one cell
SubGrid jCellGrid = new SubGrid(new CellMask(this.GridDat, Chunk.GetSingleElementChunk(jCell)));
// create spatial operator
IEvaluatorNonLin evo;
{
SpatialOperator op = new SpatialOperator(1, 2, 1, QuadOrderFunc.NonLinear(2), "Phi", "dPhi_dx0", "dPhi_dx1", "cod1");
op.EquationComponents["cod1"].Add(new ReinitOperator());
op.EdgeQuadraturSchemeProvider = g => (new EdgeQuadratureScheme(domain: EdgeMask.GetEmptyMask(g)));
op.VolumeQuadraturSchemeProvider = g => (new CellQuadratureScheme(domain: jCellGrid.VolumeMask));
op.Commit();
evo = op.GetEvaluatorEx(Phi.Mapping.Fields, gradPhi.Mapping.Fields, Phi.Mapping);
evo.ActivateSubgridBoundary(jCellGrid.VolumeMask, subGridBoundaryTreatment: SubGridBoundaryModes.InnerEdge);
}
// create artificial diffusion operator
MultidimensionalArray DiffMtx;
double[] DiffRhs;
SpatialOperator dop;
{
double penaltyBase = this.LevelSetBasis.Degree + 2;
penaltyBase = penaltyBase.Pow2();
dop = (new ArtificialViscosity(AcceptedMask, penaltyBase, GridDat.Cells.h_min, jCell, -1.0)).Operator(1);
MsrMatrix _DiffMtx = new MsrMatrix(this.LevelSetMapping, this.LevelSetMapping);
double[] _DiffRhs = new double[this.LevelSetMapping.LocalLength];
dop.ComputeMatrixEx(this.LevelSetMapping, new DGField[] { Phi, null, null }, this.LevelSetMapping,
_DiffMtx, _DiffRhs, OnlyAffine: false,
edgeQuadScheme: (new EdgeQuadratureScheme(domain: jCellGrid.AllEdgesMask)),
volQuadScheme: (new CellQuadratureScheme(domain: jCellGrid.VolumeMask)));
// extract matrix for 'jCell'
DiffMtx = MultidimensionalArray.Create(N, N);
DiffRhs = new double[N];
for (int n = 0; n < N; n++)
{
#if DEBUG
int Lr;
int[] row_cols = null;
double[] row_vals = null;
Lr = _DiffMtx.GetRow(i0G + n, ref row_cols, ref row_vals);
for (int lr = 0; lr < Lr; lr++)
{
int ColIndex = row_cols[lr];
double Value = row_vals[lr];
Debug.Assert((ColIndex >= i0G && ColIndex < i0G + N) || (Value == 0.0), "Matrix is expected to be block-diagonal.");
}
#endif
for (int m = 0; m < N; m++)
{
DiffMtx[n, m] = _DiffMtx[i0G + n, i0G + m];
}
DiffRhs[n] = _DiffRhs[i0L + n];
}
#if DEBUG
var Test = DiffMtx.Transpose();
Test.Acc(-1.0, DiffMtx);
Debug.Assert(Test.InfNorm() <= 1.0e-8);
#endif
}
// find 'good' initial value by geometric solve AND
// thresholds for the maximum an minimal value of Phi
double Range = MaxAllowedPhi - MinAllowedPhi;
MinAllowedPhi -= 0.1 * Range;
MaxAllowedPhi += 0.1 * Range;
// timestep for pseudo-timestepping
double dt = 0.5 * this.GridDat.Cells.h_min[jCell] / (((double)(this.LevelSetBasis.Degree)).Pow2());
DGField[] PlotFields = new DGField[] { Phi, gradPhi[0], gradPhi[1], __DiffusionCoeff, __AcceptedMask };
//Tecplot.Tecplot.PlotFields(Params, "itt_0", "EllipicReinit", 0, 3);
double[] PrevVal = new double[N];
double[] NextVal = new double[N];
Phi.Coordinates.GetRow(jCell, PrevVal);
// pseudo-timestepping
//if(jCell == 80)
// Tecplot.Tecplot.PlotFields(PlotFields, "itt_0", "EllipicReinit", 0, 3);
//Console.Write(" Local solve cell " + jCell + " ... ");
bool converged = false;
double DiffusionCoeff = 0;
int IterGrowCount = 0; // number of iterations in which the residual grew
double LastResi = double.NaN;
for (int iIter = 0; iIter < 1000; iIter++)
{
//Console.Write(" Local solve iteration " + iIter + " ... ");
PerformRKstep(dt, jCell, AcceptedMask, Phi, gradPhi, evo);
__DiffusionCoeff.SetMeanValue(jCell, DiffusionCoeff);
if (jCell == 80)
{
DiffusionCoeff = 0.1;
}
if (DiffusionCoeff > 0)
{
//Console.WriteLine(" Diffusion on.");
double[] _DiffRhs = new double[this.LevelSetMapping.LocalLength];
dop.ComputeMatrixEx(this.LevelSetMapping, new DGField[] { Phi, gradPhi[0], gradPhi[1] }, this.LevelSetMapping,
default(MsrMatrix), _DiffRhs, OnlyAffine: true,
edgeQuadScheme: (new EdgeQuadratureScheme(domain: jCellGrid.AllEdgesMask)),
volQuadScheme: (new CellQuadratureScheme(domain: CellMask.GetEmptyMask(this.GridDat))));
// extract matrix for 'jCell'
for (int n = 0; n < N; n++)
{
DiffRhs[n] = _DiffRhs[i0L + n];
}
PerformArtificialDiffusion(dt * DiffusionCoeff, jCell, Phi, DiffMtx, DiffRhs);
}
Phi.Coordinates.GetRow(jCell, NextVal);
double resi = Math.Sqrt(GenericBlas.L2DistPow2(NextVal, PrevVal) / GenericBlas.L2NormPow2(PrevVal));
double[] A = NextVal;
NextVal = PrevVal;
PrevVal = A;
if (iIter > 0 && resi > LastResi)
{
IterGrowCount++;
}
else
{
IterGrowCount = 0;
}
LastResi = resi;
if (resi < 1.0e-10)
{
converged = true;
break;
}
double maxPhi, minPhi;
Phi.GetExtremalValuesInCell(out minPhi, out maxPhi, jCell);
bool MinAlarm = minPhi < MinAllowedPhi;
bool Maxalarm = maxPhi > MaxAllowedPhi;
bool GrowAlarm = IterGrowCount > 4;
bool IterAlarm = iIter >= 50;
if (MinAlarm || Maxalarm || GrowAlarm)
{
// Diffusion coefficient should be increased
if (DiffusionCoeff == 0)
{
DiffusionCoeff = 1.0e-2;
}
else
{
if (DiffusionCoeff < 1.0e3)
{
DiffusionCoeff *= 2;
}
}
//Console.WriteLine(" increasing Diffusion: {0}, Alarms : {1}{2}{3}{4}", DiffusionCoeff, MinAlarm ? 1 : 0, Maxalarm ? 1 : 0, GrowAlarm ? 1 : 0, IterAlarm ? 1 : 0);
}
//if(jCell == 80 && iIter < 100)
// Tecplot.Tecplot.PlotFields(PlotFields, "itt_" + (iIter + 1), "EllipicReinit", iIter + 1, 3);
}
return(converged);
}
/// <summary>
/// Auto-tuning
/// </summary>
public void PerformanceVsCachesize()
{
double[] dummy = new double[this.u.CoordinateVector.Count];
diffOp.EdgeQuadraturSchemeProvider = g => new EdgeQuadratureScheme(false, EdgeMask.GetEmptyMask(g));
diffOp.VolumeQuadraturSchemeProvider = g => new CellQuadratureScheme(true, null);
var eval = diffOp.GetEvaluatorEx(new DGField[] { this.u }, this.Velocity.ToArray(), this.u.Mapping);
Stopwatch stw = new Stopwatch();
int NoOfRuns = 1;
Console.WriteLine("BlkSz\tNoChks\tRunTime");
//var testsizes = new int[] { 1, 2, 4, 8, 16, 32, 64, 256, 512, 1024, 2048, 8192, 16384, 16384 * 2, 16384 * 4, 100000000 };
var testsizes = new int[] { 1, 2, 4, 1024, 16384 * 2, 16384 * 4, 100000000 };
foreach (int bulkSize in testsizes)
{
Quadrature_Bulksize.CHUNK_DATA_LIMIT = bulkSize;
stw.Reset();
stw.Start();
for (int i = 0; i < NoOfRuns; i++)
{
eval.Evaluate(1.0, 0.0, dummy);
}
stw.Stop();
double runTime = stw.Elapsed.TotalSeconds;
Console.WriteLine("{0}\t{2}\t{1}", bulkSize, runTime.ToStringDot("0.####E-00"), this.GridData.iGeomCells.Count / bulkSize);
}
}