/// <summary>
///
/// </summary>
/// <param name="field"></param>
/// <param name="result"></param>
/// <param name="parallel"></param>
public static void GetLaplacian(this GridField2d <double> field, double[] result, bool parallel = false)
{
if (parallel)
{
Parallel.ForEach(Partitioner.Create(0, field.CountXY), range => Body(range.Item1, range.Item2));
}
else
{
Body(0, field.CountXY);
}
void Body(int from, int to)
{
var vals = field.Values;
(var nx, var ny) = field.Count;
(var dx, var dy) = field.Scale;
dx = 1.0 / (dx * dx);
dy = 1.0 / (dy * dy);
(int di, int dj) = field.GetBoundaryOffsets();
(int i, int j) = field.ToGridSpace(from);
for (int index = from; index < to; index++, i++)
{
if (i == nx)
{
j++; i = 0;
}
double tx0 = (i == 0) ? vals[index + di] : vals[index - 1];
double tx1 = (i == nx - 1) ? vals[index - di] : vals[index + 1];
double ty0 = (j == 0) ? vals[index + dj] : vals[index - nx];
double ty1 = (j == ny - 1) ? vals[index - dj] : vals[index + nx];
double t = vals[index] * 2.0;
result[index] = (tx0 + tx1 - t) * dx + (ty0 + ty1 - t) * dy;
}
}
}
/// <summary>
///
/// </summary>
/// <param name="field"></param>
/// <param name="result"></param>
/// <param name="parallel"></param>
public static void GetCurl(this GridField2d <Vector2d> field, double[] result, bool parallel = false)
{
// implementation reference
// http://www.math.harvard.edu/archive/21a_spring_09/PDF/13-05-curl-and-divergence.pdf
if (parallel)
{
Parallel.ForEach(Partitioner.Create(0, field.CountXY), range => Body(range.Item1, range.Item2));
}
else
{
Body(0, field.CountXY);
}
void Body(int from, int to)
{
var vals = field.Values;
(var nx, var ny) = field.Count;
(var tx, var ty) = (0.5 / field.Scale);
(int di, int dj) = field.GetBoundaryOffsets();
(int i, int j) = field.ToGridSpace(from);
for (int index = from; index < to; index++, i++)
{
if (i == nx)
{
j++; i = 0;
}
Vector2d tx0 = (i == 0) ? vals[index + di] : vals[index - 1];
Vector2d tx1 = (i == nx - 1) ? vals[index - di] : vals[index + 1];
Vector2d ty0 = (j == 0) ? vals[index + dj] : vals[index - nx];
Vector2d ty1 = (j == ny - 1) ? vals[index - dj] : vals[index + nx];
result[index] = (tx1.Y - tx0.Y) * tx - (ty1.X - ty0.X) * ty;
}
}
}
/// <summary>
///
/// </summary>
/// <param name="field"></param>
/// <param name="result"></param>
/// <param name="parallel"></param>
public static void GetDivergence(this GridField2d <Vector2d> field, double[] result, bool parallel = false)
{
if (parallel)
{
Parallel.ForEach(Partitioner.Create(0, field.CountXY), range => Body(range.Item1, range.Item2));
}
else
{
Body(0, field.CountXY);
}
void Body(int from, int to)
{
var vals = field.Values;
(var nx, var ny) = field.Count;
(var dx, var dy) = (0.5 / field.Scale);
(int di, int dj) = field.GetBoundaryOffsets();
(int i, int j) = field.ToGridSpace(from);
for (int index = from; index < to; index++, i++)
{
if (i == nx)
{
j++; i = 0;
}
Vector2d tx0 = (i == 0) ? vals[index + di] : vals[index - 1];
Vector2d tx1 = (i == nx - 1) ? vals[index - di] : vals[index + 1];
Vector2d ty0 = (j == 0) ? vals[index + dj] : vals[index - nx];
Vector2d ty1 = (j == ny - 1) ? vals[index - dj] : vals[index + nx];
result[index] = (tx1.X - tx0.X) * dx + (ty1.Y - ty0.Y) * dy;
}
}
}