A Direct Solution of Poisson's Equation by Dimension Reduction Method

[摘要] This paper describes a direct solution of Poisson's equation where boundary values are prescribed on the perimeter of the rectangular domain. When the number of mesh points along a side of the rectangular domain is a power of 2, the Fast Fourier Transform Method proposed by Cooley and Tukey (1965) is applicable. The number of arithmetic operations required on a N × N mesh is 10 N2 log2 N. This is comparable with that required by Cooley's method (1966) with the Complex Fourier Series, and compares favorably with the best iterative method which would require 40 N2 (log N)2 operations.

[学科分类] 大气科学