/// <summary>
/// Boundary quadrature for the surface elements, i.e. for each cut background-cell \f$ K_j \f$ a quadrature to approximate
/// \f[
/// \int_{\partial K_j \cap \mathfrak{I} } \ldots \mathrm{dS} .
/// \f]
/// </summary>
public EdgeQuadratureScheme GetEdgeQuadScheme(SpeciesId sp, bool UseDefaultFactories = true, EdgeMask IntegrationDomain = null, int?fixedOrder = null)
{
if (!this.SpeciesList.Contains(sp))
{
throw new ArgumentException("Given species (id = " + sp.cntnt + ") is not supported.");
}
// determine domain
// ================
var allRelevantEdges = GetEdgeMask(sp, IntegrationDomain);
// create quadrature scheme
// ========================
{
// default rules for all edges:
EdgeQuadratureScheme edgeQrIns = new EdgeQuadratureScheme(UseDefaultFactories, allRelevantEdges);
// overwrite with cut-cell-rules in cut-cells:
foreach (var Kref in XDGSpaceMetrics.GridDat.Grid.RefElements)
{
for (int iLevSet = 0; iLevSet < XDGSpaceMetrics.NoOfLevelSets; iLevSet++) // loop over level sets...
{
EdgeMask cutEdges = this.GetCutEdges(Kref, iLevSet).Intersect(allRelevantEdges);
#if DEBUG
CellMask difference = cutEdges.GetAdjacentCells(XDGSpaceMetrics.GridDat).Except(XDGSpaceMetrics.LevelSetRegions.GetCutCellMask4LevSet(iLevSet));
if (difference.Count() > 0)
{
throw new ArithmeticException("Edges of the Cells" + difference.GetSummary() + " are detected as cut, but these cells are not contained in the cut Cell-Mask of the Level-Set-Tracker");
}
#endif
var jmp = IdentifyWing(iLevSet, sp);
var factory = this.XDGSpaceMetrics.XQuadFactoryHelper.GetEdgeRuleFactory(iLevSet, jmp, Kref);
edgeQrIns.AddFactoryDomainPair(factory, cutEdges, fixedOrder);
}
}
return(edgeQrIns);
}
}
/// <summary>
/// Constructs the quadrature rules all edges of all cells in
/// <paramref name="mask"/>. For edges that are not intersected by the
/// zero iso-contour, standard Gaussian quadrature rules of
/// sufficiently high order will be used.
/// </summary>
/// <param name="mask">
/// Cells for which quadrature rules shall be created
/// </param>
/// <param name="order">
/// Desired order of the moment-fitting system. Assuming that
/// <see cref="edgeSurfaceRuleFactory"/> integrates the basis
/// polynomials exactly over the zero iso-contour (which it usually
/// doesn't!), the resulting quadrature rules will be exact up to this
/// order.
/// </param>
/// <returns>A set of quadrature rules</returns>
/// <remarks>
/// Since the selected level set is generally discontinuous across cell
/// boundaries, this method does not make use of the fact that
/// neighboring cells share edges. That is, the optimization will be
/// performed twice for each inner edge in <paramref name="mask"/>.
/// </remarks>
public IEnumerable <IChunkRulePair <CellBoundaryQuadRule> > GetQuadRuleSet(ExecutionMask mask, int order)
{
using (var tr = new FuncTrace()) {
if (!(mask is CellMask))
{
throw new ArgumentException("CellMask required", "mask");
}
#if DEBUG
CellMask differingCells = ((CellMask)mask).Except(this.LevelSetData.Region.GetCutCellMask4LevSet(this.levelSetIndex));
if (differingCells.NoOfItemsLocally > 0)
{
throw new ArgumentException("The provided mask has to be a sub-set of the cut cells. Cells " + differingCells.GetSummary() + " are not in the CutCellMaks of this tracker.");
}
#endif
int noOfEdges = LevelSetData.GridDat.Grid.RefElements[0].NoOfFaces;
subGrid = new SubGrid((CellMask)mask);
localCellIndex2SubgridIndex = subGrid.LocalCellIndex2SubgridIndex;
if (order != lastOrder)
{
cache.Clear();
SwitchOrder(order);
}
var result = new List <ChunkRulePair <CellBoundaryQuadRule> >(mask.NoOfItemsLocally);
CellBoundaryQuadRule[] optimizedRules = GetOptimizedRules((CellMask)mask, order);
int n = 0;
foreach (Chunk chunk in mask)
{
foreach (int cell in chunk.Elements)
{
if (cache.ContainsKey(cell))
{
result.Add(new ChunkRulePair <CellBoundaryQuadRule>(
Chunk.GetSingleElementChunk(cell), cache[cell]));
}
else
{
cache.Add(cell, optimizedRules[n]);
result.Add(new ChunkRulePair <CellBoundaryQuadRule>(
Chunk.GetSingleElementChunk(cell), optimizedRules[n]));
}
n++;
}
}
return(result);
}
}