protected override SayeQuadRule SetGaussQuadratureNodes(SayeSquare arg)
{
//Aquire needed data
//------------------------------------------------------------------------------------------------------------
QuadRule gaussRule_2D = Square.Instance.GetQuadratureRule(order);
MultidimensionalArray nodes_GaussRule_2D = ((MultidimensionalArray)gaussRule_2D.Nodes).CloneAs();
MultidimensionalArray weights_GaussRule_2D = gaussRule_2D.Weights.CloneAs();
double[] diameters = arg.Diameters;
MultidimensionalArray centerArr = arg.GetCellCenter().ExtractSubArrayShallow(new int[] { 0, -1 });
double jacobian = diameters[0] * diameters[1];
//AffineTransformation of nodes, scale weights
//------------------------------------------------------------------------------------------------------------
//Scale Nodes
for (int i = 0; i < 2; ++i)
{
nodes_GaussRule_2D.ColScale(i, diameters[i]);
}
//Scale Weights
weights_GaussRule_2D.Scale(jacobian);
//Move Nodes
int[] index = new int[] { 0, -1 };
for (int i = 0; i < gaussRule_2D.NoOfNodes; ++i)
{
index[0] = i;
nodes_GaussRule_2D.AccSubArray(1, centerArr, index);
}
//Set return data
//------------------------------------------------------------------------------------------------------------
SayeQuadRule transformed_GaussRule_2D = new SayeQuadRule(nodes_GaussRule_2D, weights_GaussRule_2D);
return(transformed_GaussRule_2D);
}
private QuadRule CombineQr(QuadRule qrEdge, CellBoundaryQuadRule givenRule, int iFace)
{
int D = grd.SpatialDimension;
var volSplx = m_cellBndQF.RefElement;
int coD = D - 1;
Debug.Assert(this.RefElement.SpatialDimension == coD);
// extract edge rule
// -----------------
int i0 = 0, iE = 0;
for (int i = 0; i < iFace; i++)
{
i0 += givenRule.NumbersOfNodesPerFace[i];
}
iE = i0 + givenRule.NumbersOfNodesPerFace[iFace] - 1;
if (iE < i0)
{
// rule is empty (measure is zero).
if (qrEdge == null)
{
QuadRule ret = new QuadRule();
ret.OrderOfPrecision = int.MaxValue - 1;
ret.Nodes = new NodeSet(this.RefElement, 1, Math.Max(1, D - 1));
ret.Weights = MultidimensionalArray.Create(1); // this is an empty rule, since the weight is zero!
// (rules with zero nodes may cause problems at various places.)
return(ret);
}
else
{
qrEdge.Nodes.Scale(0.5);
qrEdge.Weights.Scale(0.5);
return(qrEdge);
}
}
MultidimensionalArray NodesVol = givenRule.Nodes.ExtractSubArrayShallow(new int[] { i0, 0 }, new int[] { iE, D - 1 });
MultidimensionalArray Weigts = givenRule.Weights.ExtractSubArrayShallow(new int[] { i0 }, new int[] { iE }).CloneAs();
NodeSet Nodes = new NodeSet(this.RefElement, iE - i0 + 1, coD);
volSplx.GetInverseFaceTrafo(iFace).Transform(NodesVol, Nodes);
Nodes.LockForever();
//Debug.Assert((Weigts.Sum() - grd.Grid.GridSimplex.EdgeSimplex.Volume).Abs() < 1.0e-6, "i've forgotten the gramian");
// combine
// -------
if (qrEdge == null)
{
// no rule defined yet - just set the one we have got
// ++++++++++++++++++++++++++++++++++++++++++++++++++
qrEdge = new QuadRule();
qrEdge.Weights = Weigts;
qrEdge.Nodes = Nodes;
qrEdge.OrderOfPrecision = givenRule.OrderOfPrecision;
}
else
{
// take the mean of already defined and new rule
// +++++++++++++++++++++++++++++++++++++++++++++
int L1 = qrEdge.Nodes.GetLength(0);
int L2 = Nodes.GetLength(0);
Debug.Assert(coD == qrEdge.Nodes.GetLength(1));
NodeSet newNodes = new NodeSet(this.RefElement, L1 + L2, coD);
newNodes.SetSubArray(qrEdge.Nodes, new int[] { 0, 0 }, new int[] { L1 - 1, coD - 1 });
newNodes.SetSubArray(Nodes, new int[] { L1, 0 }, new int[] { L1 + L2 - 1, coD - 1 });
newNodes.LockForever();
MultidimensionalArray newWeights = MultidimensionalArray.Create(L1 + L2);
newWeights.AccSubArray(0.5, qrEdge.Weights, new int[] { 0 }, new int[] { L1 - 1 });
newWeights.AccSubArray(0.5, Weigts, new int[] { L1 }, new int[] { L1 + L2 - 1 });
double oldSum = qrEdge.Weights.Sum();
double newSum = Weigts.Sum();
WeightInbalance += Math.Abs(oldSum - newSum);
qrEdge.Nodes = newNodes;
qrEdge.Weights = newWeights;
qrEdge.OrderOfPrecision = Math.Min(qrEdge.OrderOfPrecision, givenRule.OrderOfPrecision);
}
// return
// ------
return(qrEdge);
}