A Fast-high Order Algorithm for Three-dimensional Poisson Equations

Abstract

The three-dimensional Poisson equations widely exist in many physical or engineering problems. We proposed a fourth-order fast algorithm for solving the three-dimensional Poisson equation. By the fast Fourier transform, block tridiagonal structure can be generated, and the original problem can be easily decomposed into small independent systems. Fourier operators accelerate the process of solving numerical solutions and greatly reduce the computation time. The accuracy and efficiency of the method are verified by several numerical experiments.