public FiniteElement(FEM3D.Node node0, FEM3D.Node node1, FEM3D.Node node2, FEM3D.Node node3)
{
var feNode0 = new Node(node0.Position, node1.Position, node2.Position, node3.Position, node0.Index, node0.IsInside);
var feNode1 = new Node(node1.Position, node2.Position, node3.Position, node0.Position, node1.Index, node1.IsInside);
var feNode2 = new Node(node2.Position, node3.Position, node0.Position, node1.Position, node2.Index, node2.IsInside);
var feNode3 = new Node(node3.Position, node0.Position, node1.Position, node2.Position, node3.Index, node3.IsInside);
Nodes = new ReadOnlyCollection<Node>(new[] { feNode0, feNode1, feNode2, feNode3 });
}
public static double Integrate(Func<Vector3, double> function, FEM3D.FiniteElement finiteElement)
{
double w0 = -74.0 / 5625,
w1 = 343.0 / 45000,
w2 = 56.0 / 2250;
var weights = new[] { w0, w1, w1, w1, w1, w2, w2, w2, w2, w2, w2 };
double c = 11.0 / 14,
d = 1.0 / 14,
a = 0.3994035761667992,
b = 0.1005964238332008;
var points = new[] { new Vector3(0.25, 0.25, 0.25),
new Vector3(c, d, d),
new Vector3(d, c, d),
new Vector3(d, d, c),
new Vector3(d, d, d),
new Vector3(a, a, b),
new Vector3(a, b, a),
new Vector3(a, b, b),
new Vector3(b, a, a),
new Vector3(b, a, b),
new Vector3(b, b, a) };
double sum = 0;
Vector3 x0 = finiteElement.Nodes[0].Position,
u = finiteElement.Nodes[1].Position - x0,
v = finiteElement.Nodes[2].Position - x0,
w = finiteElement.Nodes[3].Position - x0;
for (int i = 0; i < 11; i++)
{
var baricentricPoint = x0 + points[i].x*u + points[i].y*v + points[i].z*w;
sum += weights[i] * function(baricentricPoint);
}
var volumn = Math.Abs(u.x*v.y*w.z + u.y*v.z*w.z + u.z*v.x*w.y - u.z*v.y*w.x - u.y*v.x*w.z - u.x*v.z*w.y) / 6;
return sum * volumn * 6;
}
