Laplace and Poisson equation solution by RELAX3D

The program RELAX3D is useful for the solution of the three‐dimensional, second‐order, elliptic partial differential equation, ∇2V(x,y,z)=F(x,y,z), which includes Laplace’s equation and Poisson’s equation. It uses the finite‐difference algorithm known as symmetric successive over‐relaxation. After a brief survey of other solution techniques, the program is described in detail and several examples of its actual use are given. The program is interactive and accurately solves for V according to the function F and the arbitrary boundary conditions, both supplied via the user‐encoded subroutine ‘‘BND.’’ The functions V and F are defined on grids of two or three dimensions, in Cartesian, cylindrical, or polar coordinates. To improve the efficiency of the repetitive five‐point or seven‐point relaxation iterations on the grid, conventional fortran array addressing is replaced by a fast hard‐coded addressing method. In the inner loop where the program spends most of its time, references to the V and F arrays are a...