protected virtual void AddThirdBoundary(IMatrix A, double[] b, ThirdBoundaryEdge edge)
{
double[,] M = info.BoundaryBasis.MassMatrix;
Func <double, double, double, double> ubetatime = edge.UBeta;
Func <double, double, double> ubeta = (double x, double y) => ubetatime(x, y, 0);
double beta = edge.Beta;
Point p1 = info.Mesh.Points[edge[0]];
Point p2 = info.Mesh.Points[edge[edge.NodeCount - 1]];
double x0 = p1.X;
double y0 = p1.Y;
double x1 = p2.X;
double y1 = p2.Y;
double h = Point.Distance(p1, p2);
for (int i = 0; i < info.BoundaryBasis.Size; i++)
{
b[edge[i]] += beta * h * Quadratures.NewtonCotes(0.0, 1.0, (double ksi) => ubeta(x0 + ksi * (x1 - x0), y0 + ksi * (y1 - y0)) * boundaryPsi[i](ksi));
}
for (int i = 0; i < info.BoundaryBasis.Size; i++)
{
for (int j = 0; j < info.BoundaryBasis.Size; j++)
{
A.Add(edge[i], edge[j], beta * h * M[i, j]);
}
}
}
protected virtual void BuildLocalMatrix(FiniteElement e)
{
Point a = points[e[0]];
Point b = points[e[1]];
Point c = points[e[2]];
double D = Math.Abs(Utilities.Det(a, b, c));
for (int i = 0; i < info.Basis.Size; i++)
{
for (int j = 0; j < info.Basis.Size; j++)
{
double G = Quadratures.TriangleGauss18(GetGrad(i, j, a, b, c));
double M = Quadratures.TriangleGauss18((double ksi, double etta) => psi[i](ksi, etta) * psi[j](ksi, etta));
local[i, j] = (e.Material.Lambda * G + e.Material.RoCp * M) * D;
}
}
}
protected virtual void AddSecondBoundary(IMatrix A, double[] b, SecondBoundaryEdge edge)
{
Func <double, double, double, double> thetatime = edge.Theta;
Func <double, double, double> theta = (double x, double y) => thetatime(x, y, 0);
Point p1 = info.Mesh.Points[edge[0]];
Point p2 = info.Mesh.Points[edge[edge.NodeCount - 1]];
double x0 = p1.X;
double y0 = p1.Y;
double x1 = p2.X;
double y1 = p2.Y;
double h = Point.Distance(p1, p2);
for (int i = 0; i < info.BoundaryBasis.Size; i++)
{
b[edge[i]] += h * Quadratures.NewtonCotes(0.0, 1.0, (double ksi) => theta(x0 + ksi * (x1 - x0), y0 + ksi * (y1 - y0)) * boundaryPsi[i](ksi));
}
}
protected virtual void BuildLocalB(FiniteElement e)
{
// TODO: implement this method
Point a = points[e[0]];
Point b = points[e[1]];
Point c = points[e[2]];
double D = Math.Abs(Utilities.Det(a, b, c));
for (int i = 0; i < info.Basis.Size; i++)
{
localb[i] = Quadratures.TriangleGauss18((double ksi, double etta) =>
{
double x = a.X * ksi + b.X * etta + c.X * (1 - ksi - etta);
double y = a.Y * ksi + b.Y * etta + c.Y * (1 - ksi - etta);
return(e.Material.F(x, y, 0) * psi[i](ksi, etta));
});
localb[i] *= D;
}
}