public static double[,] ComputeConvectionMatrix(PolyMatrix N, double u, double v, double w, Point Size)
{
var ConvectionMatrix = N.Transpose() * (u * N.Differentiate(0) + v * N.Differentiate(1) + w * N.Differentiate(2));
var Zero = new Point(); // point that starts at the origin
return(ConvectionMatrix.Integrate(Zero, Size));
}
static private void PrintNaturalCoordinates(PolyMatrix N)
{
for (int iNode = 0; iNode < N.Data.Length; iNode++)
{
var Id = new Index(N.Data [iNode, 0].Order);
string ScreenOutput = "N" + iNode.ToString() + " = ";
for (int jCoeff = 0; jCoeff < N.Data[iNode, 0].Coefficients.Length; jCoeff++)
{
double a = N.Data [iNode, 0].Coefficients [jCoeff];
if (a != 0.0)
{
var Sub = Id.Ind2Sub(jCoeff);
ScreenOutput = ScreenOutput + a.ToString("F2");
for (int iSub = 0; iSub < Sub.Length; iSub++)
{
if (Sub [iSub] > 1)
{
ScreenOutput = ScreenOutput + "L" + iSub.ToString() + "^" + Sub [iSub] + "*";
}
else if (Sub[iSub] == 1)
{
ScreenOutput = ScreenOutput + "L" + iSub.ToString() + "*";
}
}
ScreenOutput = ScreenOutput.Remove(ScreenOutput.Length - 1);
ScreenOutput = ScreenOutput + " + ";
}
}
Console.WriteLine(ScreenOutput.Remove(ScreenOutput.Length - 3));
}
}
public static double[] ComputeHeatGenerationMatrix(double G, PolyMatrix N, Point a, Point b)
{
var P = N.Transpose().Integrate(a, b);
var P1 = new double[P.Length];
for (int i = 0; i < P1.Length; i++)
{
P1 [i] = G * P [i, 0];
}
return(P1);
}
public static double[,] ComputeConductionMatrix(PolyMatrix B, Point a, Point b, double kx, double ky, double kz)
{
double[,] D = new double[3, 3];
D [0, 0] = kx;
D [1, 1] = ky;
D [2, 2] = kz;
var Kn = B.Transpose() * D * B;
var Ke = Kn.Integrate(a, b);
return(Ke);
}
// For Volume Elements
#region Volume Terms
public static double[,] ComputeMassMatrix(PolyMatrix N, Point a, Point b)
{
if (N.Rows > 1)
{
throw new Exception("N must be 1 row x n cols");
}
N = N.Transpose() * N;
var Me = N.Integrate(a, b);
return(Me);
}
public static double[,] ComputeCapacitanceMatrix(PolyMatrix N, Point a, Point b, double rho, double cp)
{
var CapMatrix = ComputeMassMatrix(N, a, b);
var Cp = rho * cp;
for (int i = 0; i < N.Rows; i++)
{
for (int j = 0; j < N.Cols; j++)
{
CapMatrix[i, j] = CapMatrix[i, j] * Cp;
}
}
return(CapMatrix);
}
public static PolyMatrix ComputeGradientMatrix(PolyMatrix N)
{
if (N.Rows > 1)
{
throw new Exception("N must be 1 row x n cols");
}
var Ndx = N.Differentiate(0);
var Ndy = N.Differentiate(1);
var Ndz = N.Differentiate(2);
var B = new PolyMatrix(3, N.Cols);
for (int j = 0; j < N.Cols; j++)
{
B.Data[0, j] = Ndx.Data[0, j];
B.Data[1, j] = Ndy.Data[0, j];
B.Data[2, j] = Ndz.Data[0, j];
}
return(B);
}
public static double[,] ComputeConductionMatrix(PolyMatrix B, Point a, Point b, double k)
{
return(ComputeConductionMatrix(B, a, b, k, k, k));
}
