/// <summary>
///
/// </summary>
/// <param name="field"></param>
/// <param name="result"></param>
/// <param name="parallel"></param>
public static void GetCurl(this GridField3d <Vector3d> field, Vector3d[] 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.CountXYZ), range => Body(range.Item1, range.Item2));
}
else
{
Body(0, field.CountXYZ);
}
void Body(int from, int to)
{
var vals = field.Values;
(var nx, var ny, var nz) = field.Count;
int nxy = field.CountXY;
(var dx, var dy, var dz) = (0.5 / field.Scale);
(int di, int dj, int dk) = field.GetBoundaryOffsets();
(int i, int j, int k) = field.ToGridSpace(from);
for (int index = from; index < to; index++, i++)
{
if (i == nx)
{
j++; i = 0;
}
if (j == ny)
{
k++; j = 0;
}
Vector3d tx0 = (i == 0) ? vals[index + di] : vals[index - 1];
Vector3d tx1 = (i == nx - 1) ? vals[index - di] : vals[index + 1];
Vector3d ty0 = (j == 0) ? vals[index + dj] : vals[index - nx];
Vector3d ty1 = (j == ny - 1) ? vals[index - dj] : vals[index + nx];
Vector3d tz0 = (k == 0) ? vals[index + dk] : vals[index - nxy];
Vector3d tz1 = (k == nz - 1) ? vals[index - dk] : vals[index + nxy];
result[index] = new Vector3d(
(ty1.Z - ty0.Z) * dy - (tz1.Y - tz0.Y) * dz,
(tz1.X - tz0.X) * dz - (tx1.Z - tx0.Z) * dx,
(tx1.Y - tx0.Y) * dx - (ty1.X - ty0.X) * dy);
}
}
}
/// <summary>
///
/// </summary>
/// <param name="field"></param>
/// <param name="result"></param>
/// <param name="parallel"></param>
public static void GetLaplacian(this GridField3d <double> field, double[] result, bool parallel = false)
{
if (parallel)
{
Parallel.ForEach(Partitioner.Create(0, field.CountXYZ), range => Body(range.Item1, range.Item2));
}
else
{
Body(0, field.CountXYZ);
}
void Body(int from, int to)
{
var vals = field.Values;
(var nx, var ny, var nz) = field.Count;
int nxy = field.CountXY;
(var dx, var dy, var dz) = field.Scale;
dx = 1.0 / (dx * dx);
dy = 1.0 / (dy * dy);
dz = 1.0 / (dz * dz);
(int di, int dj, int dk) = field.GetBoundaryOffsets();
(int i, int j, int k) = field.ToGridSpace(from);
for (int index = from; index < to; index++, i++)
{
if (i == nx)
{
j++; i = 0;
}
if (j == ny)
{
k++; j = 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 tz0 = (k == 0) ? vals[index + dk] : vals[index - nxy];
double tz1 = (k == nz - 1) ? vals[index - dk] : vals[index + nxy];
double t = vals[index] * 2.0;
result[index] = (tx0 + tx1 - t) * dx + (ty0 + ty1 - t) * dy + (tz0 + tz1 - t) * dz;
}
}
}
/// <summary>
///
/// </summary>
/// <param name="field"></param>
/// <param name="result"></param>
/// <param name="parallel"></param>
public static void GetGradient(this GridField3d <double> field, Vector3d[] result, bool parallel = false)
{
if (parallel)
{
Parallel.ForEach(Partitioner.Create(0, field.CountXYZ), range => Body(range.Item1, range.Item2));
}
else
{
Body(0, field.CountXYZ);
}
void Body(int from, int to)
{
var vals = field.Values;
(var nx, var ny, var nz) = field.Count;
int nxy = field.CountXY;
(var dx, var dy, var dz) = (0.5 / field.Scale);
(int di, int dj, int dk) = field.GetBoundaryOffsets();
(int i, int j, int k) = field.ToGridSpace(from);
for (int index = from; index < to; index++, i++)
{
if (i == nx)
{
j++; i = 0;
}
if (j == ny)
{
k++; j = 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 tz0 = (k == 0) ? vals[index + dk] : vals[index - nxy];
double tz1 = (k == nz - 1) ? vals[index - dk] : vals[index + nxy];
result[index] = new Vector3d((tx1 - tx0) * dx, (ty1 - ty0) * dy, (tz1 - tz0) * dz);
}
}
}