Developments in RELAX3D, a 2D/3D Laplace and Poisson equation solver

The widely used program RELAX3D, in continual development at TRIUMF since its inception in 1973, employs the finite-difference algorithm known as symmetric successive over-relaxation (SSOR) to solve the three-dimensional second-order elliptic partial differential equation ∇2V(x,y,z) F(x,y,z), which includes the Laplace (F ≡ 0) and Poisson (F ≠ 0) equations. After a brief review of other solution techniques, the program is described and a variety of sample usages is given. Recent enhancements were made in the use of various grid stencils (molecules), graphics facilities, and portability to UNIX systems. The dependence of errors on grid spacing, stencils, and machine precision are presented. The investigation of higher-order relaxation formulae (stencils) has shown promising results. Using a 27-point stencil, the solution accuracy can be dramatically improved with only a modest increase in execution time. (author)