Comparison of conjugate gradient, SIP, and other iterative methods for the solution of Poisson's equation with irregular boundary conditions.

摘要

Several well known iterative methods for solving Poisson's equation, including Strongly Implicit Procedure and several preconditioned conjugate gradient methods are first applied to a problem with simple boundary conditions and a known solution. Then a problem with more complicated boundary conditions, similar to those encountered when modeling AVLIS plasmas, is solved. Differences in the solutions of the various methods are examined through the use of Fourier analysis. It was found that combinations of different iterative schemes will in some cases be the most efficient method of solution. 22 refs., 29 figs.