/// <summary>
///
/// </summary>
/// <param name="jCell">
/// Local index of cell which should be recalculated.
/// </param>
/// <param name="AcceptedMask">
/// Bitmask which marks accepted cells - if any neighbor of
/// <paramref name="jCell"/> is _accepted_, this defines a Dirichlet
/// boundary; otherwise, the respective cell face is a free boundary.
/// </param>
/// <param name="Phi">
/// Input and output:
/// - input for _accepted_ cells, i.e. Dirichlet boundary values
/// - input and output for <paramref name="jCell"/>: an initial value for the iterative procedure, resp. on exit the result of the iteration.
/// </param>
/// <param name="gradPhi">
/// Auxillary variable to store the gradient of the level-set-field.
/// </param>
/// <returns></returns>
public bool LocalSolve(int jCell, BitArray AcceptedMask, SinglePhaseField Phi, VectorField <SinglePhaseField> gradPhi)
{
Stpw_tot.Start();
int N = this.LevelSetBasis.GetLength(jCell);
int i0G = this.LevelSetMapping.GlobalUniqueCoordinateIndex(0, jCell, 0);
int i0L = this.LevelSetMapping.LocalUniqueCoordinateIndex(0, jCell, 0);
double penaltyBase = ((double)(this.LevelSetBasis.Degree + 2)).Pow2();
double CellVolume = this.GridDat.Cells.GetCellVolume(jCell);
int p = Phi.Basis.Degree;
// subgrid on which we are working, consisting only of one cell
SubGrid jCellGrid = new SubGrid(new CellMask(this.GridDat, Chunk.GetSingleElementChunk(jCell)));
var VolScheme = new CellQuadratureScheme(domain: jCellGrid.VolumeMask);
var EdgScheme = new EdgeQuadratureScheme(domain: jCellGrid.AllEdgesMask);
//var VolRule = VolScheme.SaveCompile(GridDat, 3 * p);
//var EdgRule = EdgScheme.SaveCompile(GridDat, 3 * p);
// parameter list for operator
DGField[] Params = new DGField[] { Phi };
gradPhi.ForEach(f => f.AddToArray(ref Params));
// build operator
var comp = new EllipticReinitForm(AcceptedMask, jCell, penaltyBase, this.GridDat.Cells.cj);
comp.LhsSwitch = 1.0; // matrix is constant -- Lhs Matrix only needs to be computed once
comp.RhsSwitch = -1.0; // Rhs must be updated in every iteration
var op = comp.Operator((DomDeg, ParamDeg, CodDeg) => 3 * p);
// iteration loop:
MultidimensionalArray Mtx = MultidimensionalArray.Create(N, N);
double[] Rhs = new double[N];
double ChangeNorm = 0;
int iIter;
for (iIter = 0; iIter < 100; iIter++)
{
// update gradient
gradPhi.Clear(jCellGrid.VolumeMask);
gradPhi.Gradient(1.0, Phi, jCellGrid.VolumeMask);
// assemble matrix and rhs
{
// clear
for (int n = 0; n < N; n++)
{
if (iIter == 0)
{
m_LaplaceMatrix.ClearRow(i0G + n);
}
this.m_LaplaceAffine[i0L + n] = 0;
}
// compute matrix (only in iteration 0) and rhs
if (iIter == 0)
{
Stpw_Mtx.Start();
}
Stpw_Rhs.Start();
op.ComputeMatrixEx(this.LevelSetMapping, Params, this.LevelSetMapping,
iIter == 0 ? this.m_LaplaceMatrix : null, this.m_LaplaceAffine,
OnlyAffine: iIter > 0,
volQuadScheme: VolScheme, edgeQuadScheme: EdgScheme,
//volRule: VolRule, edgeRule: EdgRule,
ParameterMPIExchange: false);
//op.Internal_ComputeMatrixEx(this.GridDat,
// this.LevelSetMapping, Params, this.LevelSetMapping,
// iIter == 0 ? this.m_LaplaceMatrix : default(MsrMatrix), this.m_LaplaceAffine, iIter > 0,
// 0.0,
// EdgRule, VolRule,
// null, false);
if (iIter == 0)
{
Stpw_Mtx.Stop();
}
Stpw_Rhs.Stop();
// extract matrix for 'jCell'
for (int n = 0; n < N; n++)
{
#if DEBUG
int Lr;
int[] row_cols = null;
double[] row_vals = null;
Lr = this.m_LaplaceMatrix.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
if (iIter == 0)
{
for (int m = 0; m < N; m++)
{
Mtx[n, m] = this.m_LaplaceMatrix[i0G + n, i0G + m];
}
}
else
{
#if DEBUG
for (int m = 0; m < N; m++)
{
Debug.Assert(Mtx[n, m] == this.m_LaplaceMatrix[i0G + n, i0G + m]);
}
#endif
}
Rhs[n] = -this.m_LaplaceAffine[i0L + n];
}
}
// solve
double[] sol = new double[N];
Mtx.Solve(sol, Rhs);
ChangeNorm = GenericBlas.L2Dist(sol, Phi.Coordinates.GetRow(jCell));
Phi.Coordinates.SetRow(jCell, sol);
if (ChangeNorm / CellVolume < 1.0e-10)
{
break;
}
}
//Console.WriteLine("Final change norm: {0}, \t iter: {1}", ChangeNorm, iIter );
if (ChangeNorm > 1.0e-6)
{
Console.WriteLine(" local solver funky in cell: " + jCell + ", last iteration change norm = " + ChangeNorm);
}
Stpw_tot.Stop();
return(true);
}