public void AddBoundary(IMatrix A, double[] b, FirstBoundary boundary)
{
Func <double, double>[] basis = new Func <double, double>[4]
{
(double x) => 0.5 * (1 - x) * (3 * (1 - x) - 1) * (3 * (1 - x) - 2),
(double x) => 4.5 * (1 - x) * x * (3 * (1 - x) - 1),
(double x) => 4.5 * (1 - x) * x * (3 * x - 1),
(double x) => 0.5 * x * (3 * x - 1) * (3 * x - 2)
};
foreach (Edge edge in boundary.Edges)
{
double[][] M = new double[4][]
{
new double[4] {
8.0 / 105, 33.0 / 560, -3.0 / 140, 19.0 / 1680
},
new double[4] {
33.0 / 560, 27.0 / 70, -27.0 / 560, -3.0 / 140
},
new double[4] {
-3.0 / 140, -27.0 / 560, 27.0 / 70, 33.0 / 560
},
new double[4] {
19.0 / 1680, -3.0 / 140, 33.0 / 560, 8.0 / 105
}
};
double[] f = new double[4];
double r0 = Info.Points[edge.V1].R;
double r1 = Info.Points[edge.V4].R;
double z0 = Info.Points[edge.V1].Z;
double z1 = Info.Points[edge.V4].Z;
for (int i = 0; i < 4; i++)
{
f[i] = Utilities.NewtonCotes(0.0, 1.0, (double t) => edge.Function(r0 + t * (r1 - r0), z0 + t * (z1 - z0)) * basis[i](t));
}
double[] q = Utilities.Gauss(M, f);
if (!(Math.Abs(r0 - Info.R0) < 1.0e-15 && Math.Abs(z0 - Info.Z0) < 1.0e-15))
{
A.DI[edge.V1] = 1.0E+50;
b[edge.V1] = 1.0E+50 * q[0];
}
A.DI[edge.V2] = 1.0E+50;
b[edge.V2] = 1.0E+50 * q[1];
A.DI[edge.V3] = 1.0E+50;
b[edge.V3] = 1.0E+50 * q[2];
if (!(Math.Abs(r1 - Info.R0) < 1.0e-15 && Math.Abs(z1 - Info.Z0) < 1.0e-15))
{
A.DI[edge.V4] = 1.0E+50;
b[edge.V4] = 1.0E+50 * q[3];
}
}
}
public void BuildBoundary(FirstBoundary boundary)
{
foreach (Edge edge in boundary.Edges)
{
int a = edge.V1;
int b = edge.V4;
bool f = a > b;
if (f)
{
(a, b) = (b, a);
}
edge.V2 = EdgeMatrix[a][b] + (f ? 1 : 0);
edge.V3 = EdgeMatrix[a][b] + (f ? 0 : 1);
}
}