Direct solutions for Poisson's equation in three dimensions

摘要: Abstract Two-dimensional Poisson problems are commonly solved by one of three direct methods: cyclic reduction (CR), Fourier analysis (FA), or a combination FA and CR (FACR). It has been shown that FACR requires the least amount computation most. All these methods employ one-dimensional solvers embedded in algorithms for solving two-dimensional problem. These can be used to solve three-dimensional systems if solver is replaced with solver. In dimensions require almost same number operations FACR. Further, using much larger comparison any other approaches considered. This information illustrated staggered grid Neumann boundary conditions. The operation counts this problem derived so they applicable even mesh points direction small. FFT algorithm required when presented. simpler code than A run times between (using systems) given several sizes. results agree count comparisons. Some input-output considerations coding which auxiliary storage also discussed.