A Fast Semi-direct Method for the Numerical Solution of Non-separable Elliptic Equations in Irregular Domains
We investigate new algorithms for the solution of nonseparable elliptic equations in irregular domains. Such equations arise frequently in fluid dynamics and other branches of continuum mechanics. We show that the combined use of a fast iteration (involving the use of fast Poisson solvers (FPS) in rectangular domains) and the capacitance matrix method can lead to algorithms which are several times faster than traditional methods of successive over relaxation (SOR), even when the latter are vectorized. We also show that use of a certain acceleration procedure enables problems in irregular domains to be solved with only slightly more computational effort than in regular domains.