/// <summary>
/// Projects a DG field <paramref name="source"/>, which may be defined on some different mesh,
/// onto the DG field <paramref name="target"/>.
/// </summary>
static public void ProjectFromForeignGrid(this ConventionalDGField target, double alpha, ConventionalDGField source, CellQuadratureScheme scheme = null)
{
using (new FuncTrace()) {
Console.WriteLine(string.Format("Projecting {0} onto {1}... ", source.Identification, target.Identification));
int maxDeg = Math.Max(target.Basis.Degree, source.Basis.Degree);
var CompQuadRule = scheme.SaveCompile(target.GridDat, maxDeg * 3 + 3); // use over-integration
int D = target.GridDat.SpatialDimension;
if (object.ReferenceEquals(source.GridDat, target.GridDat))
{
// +++++++++++++++++
// equal grid branch
// +++++++++++++++++
target.ProjectField(alpha, source.Evaluate, CompQuadRule);
}
else
{
// +++++++++++++++++++++
// different grid branch
// +++++++++++++++++++++
if (source.GridDat.SpatialDimension != D)
{
throw new ArgumentException("Spatial Dimension Mismatch.");
}
var eval = new FieldEvaluation(GridHelper.ExtractGridData(source.GridDat));
//
// Difficulty with MPI parallelism:
// While the different meshes may represent the same geometrical domain,
// their MPI partitioning may be different.
//
// Solution Approach: we circulate unlocated points among all MPI processes.
//
int MPIsize = target.GridDat.MpiSize;
// pass 1: collect all points
// ==========================
MultidimensionalArray allNodes = null;
void CollectPoints(MultidimensionalArray input, MultidimensionalArray output)
{
Debug.Assert(input.Dimension == 2);
Debug.Assert(input.NoOfCols == D);
if (allNodes == null)
{
allNodes = input.CloneAs();
}
else
{
/*
* var newNodes = MultidimensionalArray.Create(allNodes.NoOfRows + input.NoOfRows, D);
* newNodes.ExtractSubArrayShallow(new[] { 0, 0 }, new[] { allNodes.NoOfRows - 1, D - 1 })
* .Acc(1.0, allNodes);
* newNodes.ExtractSubArrayShallow(new[] { allNodes.NoOfRows, 0 }, new[] { newNodes.NoOfRows - 1, D - 1 })
* .Acc(1.0, allNodes);
*/
allNodes = allNodes.CatVert(input);
}
Debug.Assert(allNodes.NoOfCols == D);
}
target.ProjectField(alpha, CollectPoints, CompQuadRule);
int L = allNodes != null?allNodes.GetLength(0) : 0;
// evaluate
// ========
//allNodes = MultidimensionalArray.Create(2, 2);
//allNodes[0, 0] = -1.5;
//allNodes[0, 1] = 2.0;
//allNodes[1, 0] = -0.5;
//allNodes[1, 1] = 2.0;
//L = 2;
var Res = L > 0 ? MultidimensionalArray.Create(L, 1) : default(MultidimensionalArray);
int NoOfUnlocated = eval.EvaluateParallel(1.0, new DGField[] { source }, allNodes, 0.0, Res);
int TotalNumberOfUnlocated = NoOfUnlocated.MPISum();
if (TotalNumberOfUnlocated > 0)
{
Console.Error.WriteLine($"WARNING: {TotalNumberOfUnlocated} unlocalized points in 'ProjectFromForeignGrid(...)'");
}
// perform the real projection
// ===========================
int lc = 0;
void ProjectionIntegrand(MultidimensionalArray input, MultidimensionalArray output)
{
Debug.Assert(input.Dimension == 2);
Debug.Assert(input.NoOfCols == D);
int LL = input.GetLength(0);
output.Set(Res.ExtractSubArrayShallow(new int[] { lc, 0 }, new int[] { lc + LL - 1, -1 }));
lc += LL;
}
target.ProjectField(alpha, ProjectionIntegrand, CompQuadRule);
}
}
}
