public Matrix GetTaylorSystemCoeffs(int i, int j, int surplus_i, int surplus_j)
{
NCAMRNode[] stencil =
{
nodes[i, j],
nodes[i + 1, j],
nodes[i, j + 1],
nodes[i - 1, j],
nodes[i, j - 1],
nodes[i + surplus_i, j + surplus_j]
};
TaylorSystem t_system = new TaylorSystem(stencil);
Matrix Astar = t_system.TaylorCoefficients;
double k = 20;
double[] kstuff = { k, k, k *k, k *k, k *k };
for (int c = 0; c < 5; c++)
{
for (int d = 0; d < 5; d++)
{
Astar[d, c] = Astar[d, c] * kstuff[c];
}
}
Matrix K = new Matrix(5);
K[0, 0] = k;
K[1, 1] = k;
K[2, 2] = k * k;
K[3, 3] = k * k;
K[4, 4] = k * k;
return(K * Astar.Inverse);
}
public void ApplyMeshMorphGA(double size)
{
int surplus_i = 1;
int surplus_j = 1;
for (int i = 1; i < x_node_count - 1; i++)
{
for (int j = 1; j < y_node_count - 1; j++)
{
NCAMRNode[] stencil =
{
nodes[i, j],
nodes[i + 1, j],
nodes[i, j + 1],
nodes[i - 1, j],
nodes[i, j - 1],
nodes[i + surplus_i, j + surplus_j]
};
TaylorSystem t_system = new TaylorSystem(stencil);
Matrix Astar = t_system.TaylorCoefficients;
double k = 200;
double[] kstuff = { k, k, k *k, k *k, k *k };
for (int c = 0; c < 5; c++)
{
for (int d = 0; d < 5; d++)
{
Astar[d, c] = Astar[d, c] * kstuff[c];
}
}
Matrix K = new Matrix(5);
K[0, 0] = k;
K[1, 1] = k;
K[2, 2] = k * k;
K[3, 3] = k * k;
K[4, 4] = k * k;
Matrix b = K * Astar.Inverse;
Matrix xi = b * t_system.RHS;
double ux = xi[0];
double uxx = xi[2];
double uy = xi[1];
double uyy = xi[3];
double uxy = xi[4];
double _dx = ((uxx * ux) + (uxy * uy));
double _dy = ((uyy * uy) + (ux * uxy));
//normalize to max of gradient?
double step_size = size;
Vector3 move = new Vector3(step_size * _dx, step_size * _dy, 0);
double xnew = (this[i, j] + move).X;
double ynew = (this[i, j] + move).Y;
while (xnew < bounds.Xmin || xnew > bounds.Xmax || ynew > bounds.Ymax || ynew < bounds.Ymin || move.Norm > 0.2 * (dx + dy))
{
move = 0.5 * move;
xnew = (this[i, j] + move).X;
ynew = (this[i, j] + move).Y;
}
this[i, j] = this[i, j] + move;
}
}
}
public Matrix EstimateSecondDerivs(int i, int j, SurplusNodeAccessingMode mode)
{
int surplus_i = 1;
int surplus_j = 1;
switch (mode)
{
case SurplusNodeAccessingMode.RANDOM:
{
surplus_i = 1 - 2 * R.Next(0, 1);
surplus_j = 1 - 2 * R.Next(0, 1);
break;
}
}
NCAMRNode[] stencil =
{
nodes[i, j],
nodes[i + 1, j],
nodes[i, j + 1],
nodes[i - 1, j],
nodes[i, j - 1],
nodes[i + surplus_i, j + surplus_j]
};
TaylorSystem t_system = new TaylorSystem(stencil);
Matrix Astar = t_system.TaylorCoefficients;
double k = 9999;
double[] kstuff = { k, k, k *k, k *k, k *k };
for (int c = 0; c < 5; c++)
{
for (int d = 0; d < 5; d++)
{
Astar[d, c] = Astar[d, c] * kstuff[c];
}
}
Matrix K = new Matrix(5);
K[0, 0] = k;
K[1, 1] = k;
K[2, 2] = k * k;
K[3, 3] = k * k;
K[4, 4] = k * k;
return(K * Astar.Inverse * t_system.RHS);
}