public double NormaErrorW2(Function u, Function du, FEMContext FEMContext)
{
double norma = 0;
for (int e = 0; e < FEMContext.Data.NT.GetLength(0); e++)
{
Point i = FEMContext.Data.CT[FEMContext.Data.NT[e].GetVertexID(0)];
Point j = FEMContext.Data.CT[FEMContext.Data.NT[e].GetVertexID(1)];
Point m = FEMContext.Data.CT[FEMContext.Data.NT[e].GetVertexID(2)];
Point point = new Point((i.X + j.X + m.X) / 3, (i.Y + j.Y + m.Y) / 3);
if (TriangleOnPoint(point, i, j, m))
{
double fi = CalculateArea(point, j, m) * FEMContext.X[FEMContext.Data.NT[e].GetVertexID(0)];
double fj = CalculateArea(i, point, m) * FEMContext.X[FEMContext.Data.NT[e].GetVertexID(1)];
double fm = CalculateArea(i, j, point) * FEMContext.X[FEMContext.Data.NT[e].GetVertexID(2)];
double Uh = (fi + fj + fm) / AreaTriangles[e];
double dUh = UhDerivative(e, FEMContext);
norma += (Math.Abs(Math.Pow(Uh - u(point.X), 2)) + Math.Abs(Math.Pow(dUh - du(point.X), 2))) * AreaTriangles[e];
}
else
{
MessageBox.Show("Exception - (NormaErrorW2)");
}
}
return(norma);
}
public ErrorSolver(FEMContext fEMContext, TriangleNetHandler triangleNetHandler, List <CustomPoint> points, Equation equation)
{
Points = points;
Equation = equation;
TriangleNetHandler = triangleNetHandler;
CurrentFEMContext = fEMContext;
CalculateAreas(CurrentFEMContext);
CalculateLength(CurrentFEMContext);
}
private void CalculateAreas(FEMContext FEMContext)
{
this.AreaTriangles = new double[FEMContext.Data.NT.GetLength(0)];
for (int k = 0; k < FEMContext.Data.NT.GetLength(0); k++)
{
Point i = FEMContext.Data.CT[FEMContext.Data.NT[k].GetVertexID(0)];
Point j = FEMContext.Data.CT[FEMContext.Data.NT[k].GetVertexID(1)];
Point m = FEMContext.Data.CT[FEMContext.Data.NT[k].GetVertexID(2)];
AreaTriangles[k] = CalculateArea(i, j, m);
}
}
private void CalculateLength(FEMContext FEMContext)
{
this.LengthSegments = new double[FEMContext.Data.GT.Length][];
for (int border = 0; border < FEMContext.Data.GT.Length; border++)
{
LengthSegments[border] = new double[FEMContext.Data.GT[border].GetLength(0)];
for (int k = 0; k < FEMContext.Data.GT[border].GetLength(0); k++)
{
Point p1 = FEMContext.Data.CT[FEMContext.Data.GT[border][k, 0]];
Point p2 = FEMContext.Data.CT[FEMContext.Data.GT[border][k, 1]];
LengthSegments[border][k] = Length(p1, p2);
}
}
}
private double UhDerivative(int numberTriangle, FEMContext FEMContext)
{
double UhDer;
Point i = FEMContext.Data.CT[FEMContext.Data.NT[numberTriangle].GetVertexID(0)];
Point j = FEMContext.Data.CT[FEMContext.Data.NT[numberTriangle].GetVertexID(1)];
Point m = FEMContext.Data.CT[FEMContext.Data.NT[numberTriangle].GetVertexID(2)];
double bI = j.Y - m.Y;
double bJ = m.Y - i.Y;
double bM = i.Y - j.Y;
double Ui = FEMContext.X[FEMContext.Data.NT[numberTriangle].GetVertexID(0)];
double Uj = FEMContext.X[FEMContext.Data.NT[numberTriangle].GetVertexID(1)];
double Um = FEMContext.X[FEMContext.Data.NT[numberTriangle].GetVertexID(2)];
double sigma = 2 * AreaTriangles[numberTriangle];
UhDer = (Ui * bI + Uj * bJ + Um * bM) / sigma;
return(UhDer);
}
public double NormaW2Exact(Function u, Function du, FEMContext FEMContext)
{
double norma = 0;
for (int e = 0; e < FEMContext.Data.NT.GetLength(0); e++)
{
Point i = FEMContext.Data.CT[FEMContext.Data.NT[e].GetVertexID(0)];
Point j = FEMContext.Data.CT[FEMContext.Data.NT[e].GetVertexID(1)];
Point m = FEMContext.Data.CT[FEMContext.Data.NT[e].GetVertexID(2)];
Point point = new Point((i.X + j.X + m.X) / 3, (i.Y + j.Y + m.Y) / 3);
if (TriangleOnPoint(point, i, j, m))
{
norma += (Math.Pow(u(point.X), 2) + Math.Pow(du(point.X), 2)) * AreaTriangles[e];
}
else
{
MessageBox.Show("Exception - (NormaW2_Exact)");
}
}
return(Math.Sqrt(norma));
}
public double NormaL2(FEMContext FEMContext)
{
double norma = 0;
for (int e = 0; e < FEMContext.Data.NT.GetLength(0); e++)
{
Point i = FEMContext.Data.CT[FEMContext.Data.NT[e].GetVertexID(0)];
Point j = FEMContext.Data.CT[FEMContext.Data.NT[e].GetVertexID(1)];
Point m = FEMContext.Data.CT[FEMContext.Data.NT[e].GetVertexID(2)];
Point point = new Point((i.X + j.X + m.X) / 3, (i.Y + j.Y + m.Y) / 3);
if (TriangleOnPoint(point, i, j, m))
{
double fi = CalculateArea(point, j, m) * FEMContext.X[FEMContext.Data.NT[e].GetVertexID(0)];
double fj = CalculateArea(point, m, i) * FEMContext.X[FEMContext.Data.NT[e].GetVertexID(1)];
double fm = CalculateArea(point, i, j) * FEMContext.X[FEMContext.Data.NT[e].GetVertexID(2)];
norma += Math.Pow((fi + fj + fm) / AreaTriangles[e], 2) * AreaTriangles[e];
}
else
{
MessageBox.Show("Exception - (NormaL2)");
}
}
return(Math.Sqrt(norma));
}
