public static double SecondDerivative(SinglePhaseField field, int localCellIndex, NodeSet nodeSet)
{
// Evaluate gradient
int length = 1;
int noOfNodes = 1;
int D = 2;
MultidimensionalArray gradient = MultidimensionalArray.Create(length, noOfNodes, D);
field.EvaluateGradient(localCellIndex, 1, nodeSet, gradient, ResultCellindexOffset: 0, ResultPreScale: 1.0);
// Evalaute Hessian matrix
MultidimensionalArray hessian = MultidimensionalArray.Create(length, noOfNodes, D, D);
field.EvaluateHessian(localCellIndex, 1, nodeSet, hessian);
// Compute second derivative along curve
double g_alpha_alpha = 2 * ((hessian[0, 0, 0, 0] * gradient[0, 0, 0]
+ hessian[0, 0, 0, 1] * gradient[0, 0, 1])
* gradient[0, 0, 0]
+ (hessian[0, 0, 1, 0] * gradient[0, 0, 0]
+ hessian[0, 0, 1, 1] * gradient[0, 0, 1])
* gradient[0, 0, 1]);
if (g_alpha_alpha == 0.0 || g_alpha_alpha.IsNaN())
{
throw new NotSupportedException("Second derivative is zero");
}
return(g_alpha_alpha);
}
