/// <summary>
/// modifies a matrix <paramref name="Mtx"/> and a right-hand-side <paramref name="rhs"/>
/// in order to fix the pressure at some reference point
/// </summary>
/// <param name="map">row mapping for <paramref name="Mtx"/> as well as <paramref name="rhs"/></param>
/// <param name="iVar">the index of the pressure variable in the mapping <paramref name="map"/>.</param>
/// <param name="LsTrk"></param>
/// <param name="Mtx"></param>
/// <param name="rhs"></param>
static public void SetPressureReferencePoint <T>(UnsetteledCoordinateMapping map, int iVar, LevelSetTracker LsTrk, BlockMsrMatrix Mtx, T rhs)
where T : IList <double>
{
using (new FuncTrace()) {
var GridDat = map.GridDat;
if (rhs.Count != map.LocalLength)
{
throw new ArgumentException();
}
if (!Mtx.RowPartitioning.EqualsPartition(map) || !Mtx.ColPartition.EqualsPartition(map))
{
throw new ArgumentException();
}
Basis PressureBasis = (Basis)map.BasisS[iVar];
int D = GridDat.SpatialDimension;
long GlobalID, GlobalCellIndex;
bool IsInside, onthisProc;
GridDat.LocatePoint(new double[D], out GlobalID, out GlobalCellIndex, out IsInside, out onthisProc, LsTrk.Regions.GetCutCellSubGrid().VolumeMask.Complement());
int iRowGl = -111;
if (onthisProc)
{
int jCell = (int)GlobalCellIndex - GridDat.CellPartitioning.i0;
NodeSet CenterNode = new NodeSet(GridDat.iGeomCells.GetRefElement(jCell), new double[D]);
MultidimensionalArray LevSetValues = LsTrk.DataHistories[0].Current.GetLevSetValues(CenterNode, jCell, 1);;
MultidimensionalArray CenterNodeGlobal = MultidimensionalArray.Create(1, D);
GridDat.TransformLocal2Global(CenterNode, CenterNodeGlobal, jCell);
//Console.WriteLine("Pressure Ref Point @( {0:0.###E-00} | {1:0.###E-00} )", CenterNodeGlobal[0,0], CenterNodeGlobal[0,1]);
LevelSetSignCode scode = LevelSetSignCode.ComputeLevelSetBytecode(LevSetValues[0, 0]);
ReducedRegionCode rrc;
int No = LsTrk.Regions.GetNoOfSpecies(jCell, out rrc);
int iSpc = LsTrk.GetSpeciesIndex(rrc, scode);
iRowGl = (int)map.GlobalUniqueCoordinateIndex_FromGlobal(iVar, GlobalCellIndex, 0);
}
iRowGl = iRowGl.MPIMax();
// clear row
// ---------
if (onthisProc)
{
// ref. cell is on local MPI process
int jCell = (int)GlobalCellIndex - GridDat.CellPartitioning.i0;
ReducedRegionCode rrc;
int NoOfSpc = LsTrk.Regions.GetNoOfSpecies(jCell, out rrc);
// set matrix row to identity
Mtx.ClearRow(iRowGl);
Mtx.SetDiagonalElement(iRowGl, 1.0);
// clear RHS
int iRow = iRowGl - Mtx.RowPartitioning.i0;
rhs[iRow] = 0;
}
// clear column
// ------------
{
for (int i = Mtx.RowPartitioning.i0; i < Mtx.RowPartitioning.iE; i++)
{
if (i != iRowGl)
{
Mtx[i, iRowGl] = 0;
}
}
}
}
}
public void Solve <P, Q>(P X, Q B)
where P : IList <double>
where Q : IList <double>
{
int n = Mtx.NoOfCols;
double sum = 0;
var tempMtx = Mtx;
// Zeros on diagonal elements because of saddle point structure
for (int bla = 0; bla < n; bla++)
{
if (Mtx.GetDiagonalElement(bla) == 0)
{
throw new Exception("One or more diagonal elements are zero, ILU cannot work");
}
Mtx.SetDiagonalElement(bla, 1);
}
// ILU decomposition of matrix
for (int k = 0; k < n - 1; k++)
{
for (int i = k; i < n; i++)
{
if (tempMtx[i, k] == 0)
{
i = n;
}
else
{
Mtx[i, k] = Mtx[i, k] / Mtx[k, k];
for (int j = k + 1; j < n; j++)
{
if (tempMtx[i, j] == 0)
{
j = n;
}
else
{
Mtx[i, j] = Mtx[i, j] - Mtx[i, k] * Mtx[k, j];
}
}
}
}
}
// LU decomposition of matrix
//for (int i = 0; i < n; i++) {
// for (int j = i; j < n; j++) {
// sum = 0;
// for (int k = 0; k < i; k++)
// sum += Mtx[i, k] * Mtx[k, j];
// Mtx[i, j] = tempMtx[i, j] - sum;
// }
// for (int j = i + 1; j < n; j++) {
// sum = 0;
// for (int k = 0; k < i; k++)
// sum += Mtx[j, k] * Mtx[k, i];
// Mtx[j, i] = (1 / Mtx[i, i]) * (tempMtx[j, i] - sum);
// }
//}
// find solution of Ly = b
double[] y = new double[n];
for (int i = 0; i < n; i++)
{
sum = 0;
for (int k = 0; k < i; k++)
{
sum += Mtx[i, k] * y[k];
}
y[i] = B[i] - sum;
}
// find solution of Ux = y
for (int i = n - 1; i >= 0; i--)
{
sum = 0;
for (int k = i + 1; k < n; k++)
{
sum += Mtx[i, k] * X[k];
}
X[i] = (1 / Mtx[i, i]) * (y[i] - sum);
}
}
