private IReadOnlyList <Matrix> EvaluateNaturalGradientsAtGaussPoints(IQuadrature1D quadrature)
{
bool isCached = cachedNaturalGradientsAtGPs.TryGetValue(quadrature,
out IReadOnlyList <Matrix> naturalGradientsAtGPs);
if (isCached)
{
return(naturalGradientsAtGPs);
}
else
{
int numGPs = quadrature.IntegrationPoints.Count;
var naturalGradientsAtGPsArray = new Matrix[numGPs];
for (int gp = 0; gp < numGPs; ++gp)
{
GaussPoint gaussPoint = quadrature.IntegrationPoints[gp];
naturalGradientsAtGPsArray[gp] = EvaluateGradientsAt();
}
cachedNaturalGradientsAtGPs.Add(quadrature, naturalGradientsAtGPsArray);
return(naturalGradientsAtGPsArray);
}
}
public IReadOnlyList <Vector> EvaluateFunctionsAtGaussPoints(IQuadrature1D quadrature)
{
bool isCached = cachedFunctionsAtGPs.TryGetValue(quadrature,
out IReadOnlyList <Vector> shapeFunctionsAtGPs);
if (isCached)
{
return(shapeFunctionsAtGPs);
}
else
{
int numGPs = quadrature.IntegrationPoints.Count;
var shapeFunctionsAtGPsArray = new Vector[numGPs];
for (int gp = 0; gp < numGPs; ++gp)
{
GaussPoint gaussPoint = quadrature.IntegrationPoints[gp];
shapeFunctionsAtGPsArray[gp] = Vector.CreateFromArray(EvaluateAt(gaussPoint.Xi));
}
cachedFunctionsAtGPs.Add(quadrature, shapeFunctionsAtGPsArray);
return(shapeFunctionsAtGPsArray);
}
}
public IReadOnlyList <EvalInterpolation1D> EvaluateAllAtGaussPoints(IReadOnlyList <Node> nodes, IQuadrature1D quadrature)
{
// The shape functions and natural derivatives at each Gauss point are probably cached from previous calls
IReadOnlyList <Vector> shapeFunctionsAtGPs = EvaluateFunctionsAtGaussPoints(quadrature);
IReadOnlyList <Matrix> naturalShapeDerivativesAtGPs = EvaluateNaturalGradientsAtGaussPoints(quadrature);
// Calculate the Jacobians and shape derivatives w.r.t. global cartesian coordinates at each Gauss point
int numGPs = quadrature.IntegrationPoints.Count;
var interpolationsAtGPs = new EvalInterpolation1D[numGPs];
//for (int gp = 0; gp < numGPs; ++gp)
//{
// interpolationsAtGPs[gp] = new EvalInterpolation2D(shapeFunctionsAtGPs[gp],
// naturalShapeDerivativesAtGPs[gp], new IsoparametricJacobian2D(nodes, naturalShapeDerivativesAtGPs[gp]));
//}
return(interpolationsAtGPs);
}
