protected override void BuildLocalMatrix(FiniteElement e)
{
Point a = points[e[0]];
Point b = points[e[1]];
Point c = points[e[2]];
Point center = (a + b + c) / 3;
double D = Math.Abs(Utilities.Det(a, b, c));
double[] alpha = Alpha(a, b, c);
(double a1, double a2)[] grads = new (double, double)[3]
private void AddLocalToGlobal(IMatrix A, double[] b, FiniteElement e)
{
for (int i = 0; i < info.Basis.Size; i++)
{
for (int j = 0; j < info.Basis.Size; j++)
{
A.Add(e[i], e[j], local[i, j]);
}
}
for (int i = 0; i < info.Basis.Size; i++)
{
b[e[i]] += localb[i];
}
}
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 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;
}
}
static Mesh LoadMesh(
string pointsFile,
string elementsFile,
string firstBoundaryFile,
string secondBoundaryFile,
string thirdBoundaryFile,
ProblemInfo info,
IMeshBuilder builder)
{
// Points Parsing --------------------------------------------------------
string[] lines = File.ReadAllLines(pointsFile);
int pointCount = int.Parse(lines[0]);
Point[] points = new Point[pointCount];
for (int i = 0; i < pointCount; i++)
{
points[i] = Point.Parse(lines[i + 1]);
}
// -----------------------------------------------------------------------
// Elements Parsing ------------------------------------------------------
lines = File.ReadAllLines(elementsFile);
int elementsCount = int.Parse(lines[0]);
List <FiniteElement> elements = new List <FiniteElement>();
for (int i = 0; i < elementsCount; i++)
{
FiniteElement e = new FiniteElement(info.Basis.Size);
string[] tokens = lines[i + 1].Split(' ');
e.Vertices[0] = int.Parse(tokens[0]) - 1;
e.Vertices[1] = int.Parse(tokens[1]) - 1;
e.Vertices[2] = int.Parse(tokens[2]) - 1;
e.Material = info.MaterialDictionary[int.Parse(tokens[3])];
elements.Add(e);
}
// -----------------------------------------------------------------------
// First Boundary Parsing ------------------------------------------------
lines = File.ReadAllLines(firstBoundaryFile);
int firstBoundaryCount = int.Parse(lines[0]);
List <FirstBoundaryEdge> firstBondary = new List <FirstBoundaryEdge>();
for (int i = 0; i < firstBoundaryCount; i++)
{
FirstBoundaryEdge e = new FirstBoundaryEdge(info.BoundaryBasis.Size);
string[] tokens = lines[i + 1].Split(' ');
e.Vertices[0] = int.Parse(tokens[0]) - 1;
e.Vertices[info.BoundaryBasis.Size - 1] = int.Parse(tokens[1]) - 1;
e.F = info.FirstBoundaryDictionary[int.Parse(tokens[2])];
firstBondary.Add(e);
}
// -----------------------------------------------------------------------
// Second Boundary Parsing -----------------------------------------------
lines = File.ReadAllLines(secondBoundaryFile);
int secondBoundaryCount = int.Parse(lines[0]);
List <SecondBoundaryEdge> secondBondary = new List <SecondBoundaryEdge>();
for (int i = 0; i < secondBoundaryCount; i++)
{
SecondBoundaryEdge e = new SecondBoundaryEdge(info.BoundaryBasis.Size);
string[] tokens = lines[i + 1].Split(' ');
e.Vertices[0] = int.Parse(tokens[0]) - 1;
e.Vertices[info.BoundaryBasis.Size - 1] = int.Parse(tokens[1]) - 1;
e.Theta = info.SecondBoundaryDictionary[int.Parse(tokens[2])];
secondBondary.Add(e);
}
// -----------------------------------------------------------------------
// Third Boundary Parsing ------------------------------------------------
lines = File.ReadAllLines(thirdBoundaryFile);
int thirdBoundaryCount = int.Parse(lines[0]);
List <ThirdBoundaryEdge> thirdBondary = new List <ThirdBoundaryEdge>();
for (int i = 0; i < thirdBoundaryCount; i++)
{
ThirdBoundaryEdge e = new ThirdBoundaryEdge(info.BoundaryBasis.Size);
string[] tokens = lines[i + 1].Split(' ');
e.Vertices[0] = int.Parse(tokens[0]) - 1;
e.Vertices[info.BoundaryBasis.Size - 1] = int.Parse(tokens[1]) - 1;
int boundaryNo = int.Parse(tokens[2]);
e.UBeta = info.ThirdBoundaryDictionary[boundaryNo].ubeta;
e.Beta = info.ThirdBoundaryDictionary[boundaryNo].beta;
thirdBondary.Add(e);
}
// -----------------------------------------------------------------------
builder.AddPoints(points);
builder.AddElements(elements);
builder.AddFirstBoundary(firstBondary);
builder.AddSecondBoundary(secondBondary);
builder.AddThirdBoundary(thirdBondary);
return(builder.Build());
}