🚀 go-pugleaf

Hi, I've been working on a problem that involves diffusion in a potential
V(x,y,z) that has the symmetry of a diamond lattice.  My probability 
P(x,y,z,t) is given by

  __2
K \/ P - V P = dP/dt

which I would like to solve numerically for some smooth V with its values 
known only on some grid.

This problem easily reduces to a one-dimensional problem in cylindrical or
spherical symmetries, but I've been having some difficulty in the discrete
symmetry of the diamond lattice.  A general 3-D solution with appropriate
boundary conditions would work, but a 100 interval 1-D numerical solution in
the cylindrical or spherical case becomes a 100x100x100 3-D solution in the
diamond symmetry requiring much too much computation time.  There are also 
some problems with stability (not of the PDE solution, but of the 
self-consistent field that it is a part of).

Does anyone know of any references that might provide clue for simplification?
I would expect that there's probably some work out there where Schroedinger's
equation was solved in this symmetry which have an adoptable method, but I
haven't been successful in finding one.  (Perhaps a Hartree-Fock treatment of
the electron distribution in a diamond lattice?)

Please e-mail me.  Any help would be appreciated.

- Jeff