void TestAgglomeration_Extraploation(MultiphaseCellAgglomerator Agg)
{
_2D SomePolynomial;
if (this.u.Basis.Degree == 0)
{
SomePolynomial = (x, y) => 3.2;
}
else if (this.u.Basis.Degree == 1)
{
SomePolynomial = (x, y) => 3.2 + x - 2.4 * y;
}
else
{
SomePolynomial = (x, y) => x * x + y * y;
}
// ========================================================
// extrapolate polynomial function for species B of a XDG-field
// ========================================================
var Bmask = LsTrk.Regions.GetSpeciesMask("B");
XDGField xt = new XDGField(new XDGBasis(this.LsTrk, this.u.Basis.Degree), "XDG-test");
xt.GetSpeciesShadowField("B").ProjectField(1.0,
SomePolynomial.Vectorize(),
new CellQuadratureScheme(true, Bmask));
double[] bkupVec = xt.CoordinateVector.ToArray();
Agg.ClearAgglomerated(xt.Mapping);
Agg.Extrapolate(xt.Mapping);
double Err = GenericBlas.L2DistPow2(bkupVec, xt.CoordinateVector).MPISum().Sqrt();
Console.WriteLine("Agglom: extrapolation error: " + Err);
Assert.LessOrEqual(Err, 1.0e-10);
// ========================================================
// extrapolate polynomial function for a single-phase-field
// ========================================================
SinglePhaseField xt2 = new SinglePhaseField(this.u.Basis, "DG-test");
xt2.ProjectField(SomePolynomial);
double[] bkupVec2 = xt2.CoordinateVector.ToArray();
Agg.ClearAgglomerated(xt2.Mapping);
Agg.Extrapolate(xt2.Mapping);
double Err2 = GenericBlas.L2DistPow2(bkupVec, xt.CoordinateVector).MPISum().Sqrt();
Console.WriteLine("Agglom: extrapolation error: " + Err2);
Assert.LessOrEqual(Err2, 1.0e-10);
}
void TestAgglomeration_Projection(int quadOrder, MultiphaseCellAgglomerator Agg)
{
var Bmask = LsTrk.Regions.GetSpeciesMask("B");
var BbitMask = Bmask.GetBitMask();
var XDGmetrics = LsTrk.GetXDGSpaceMetrics(new SpeciesId[] { LsTrk.GetSpeciesId("B") }, quadOrder, 1);
int degree = Math.Max(0, this.u.Basis.Degree - 1);
_2D SomePolynomial;
if (degree == 0)
{
SomePolynomial = (x, y) => 3.2;
}
else if (degree == 1)
{
SomePolynomial = (x, y) => 3.2 + x - 2.4 * y;
}
else
{
SomePolynomial = (x, y) => x * x + y * y;
}
// ------------------------------------------------
// project the polynomial onto a single-phase field
// ------------------------------------------------
SinglePhaseField NonAgglom = new SinglePhaseField(new Basis(this.GridData, degree), "NonAgglom");
NonAgglom.ProjectField(1.0,
SomePolynomial.Vectorize(),
new CellQuadratureScheme(true, Bmask));
// ------------------------------------------------
// project the polynomial onto the aggomerated XDG-field
// ------------------------------------------------
var qsh = XDGmetrics.XQuadSchemeHelper;
// Compute the inner product of 'SomePolynomial' with the cut-cell-basis, ...
SinglePhaseField xt = new SinglePhaseField(NonAgglom.Basis, "test");
xt.ProjectField(1.0,
SomePolynomial.Vectorize(),
qsh.GetVolumeQuadScheme(this.LsTrk.GetSpeciesId("B")).Compile(this.GridData, Agg.CutCellQuadratureOrder));
CoordinateMapping map = xt.Mapping;
// ... change to the cut-cell-basis, ...
double[] xVec = xt.CoordinateVector.ToArray();
Agg.ManipulateMatrixAndRHS(default(MsrMatrix), xVec, map, null);
{
double[] xVec2 = xVec.CloneAs();
Agg.ClearAgglomerated(xVec2, map); // clearing should have no effect now.
double Err3 = GenericBlas.L2DistPow2(xVec, xVec2).MPISum().Sqrt();
Assert.LessOrEqual(Err3, 0.0);
}
// ... multiply with the inverse mass-matrix, ...
var Mfact = XDGmetrics.MassMatrixFactory;
BlockMsrMatrix MassMtx = Mfact.GetMassMatrix(map, false);
Agg.ManipulateMatrixAndRHS(MassMtx, default(double[]), map, map);
var InvMassMtx = MassMtx.InvertBlocks(OnlyDiagonal: true, Subblocks: true, ignoreEmptyBlocks: true, SymmetricalInversion: true);
double[] xAggVec = new double[xVec.Length];
InvMassMtx.SpMV(1.0, xVec, 0.0, xAggVec);
// ... and extrapolate.
// Since we projected a polynomial, the projection is exact and after extrapolation, must be equal
// to the polynomial.
xt.CoordinateVector.SetV(xAggVec);
Agg.Extrapolate(xt.Mapping);
// ------------------------------------------------
// check the error
// ------------------------------------------------
//double Err2 = xt.L2Error(SomePolynomial.Vectorize(), new CellQuadratureScheme(domain: Bmask));
double Err2 = NonAgglom.L2Error(xt);
Console.WriteLine("Agglom: projection and extrapolation error: " + Err2);
Assert.LessOrEqual(Err2, 1.0e-10);
}
