Table of Content

Open AccessOpen Access


Fast BEM Solvers for 3D Poisson-Type Equations

Xuefei He1, Kian-Meng Lim1,2,3, Siak-Piang Lim1,2

Singapore-MIT Alliance, E4-04-10, 4 Engineering Drive 3, Singapore 117576.
Department of Mechanical Engineering, National University of Singapore, Singapore 119260.
Corresponding author. Email:

Computer Modeling in Engineering & Sciences 2008, 35(1), 21-48.


The boundary element method (BEM) is known to have the advantage of reducing the dimension of problem by discretizing only the boundary of the domain. But it becomes less attractive for solving Poisson-type equations, due to the need to evaluate the domain integral which is computationally expensive. In this paper, we present the extension of a recently developed fast algorithm for Laplace equation, based on fast Fourier transform on multipoles (FFTM), to solve large scale 3D Poisson-type equations. We combined the Laplace solver with two fast methods for handling the domain integral based on fast Fourier transform (FFT). The first method uses the FFT on multipoles to accelerate the domain integral, while the second method solves the domain integral as a particular solution using FFT. The particular solution method is found to be faster and more accurate, and it is extended to solve non-linear Poisson-type equations. The algorithm is shown to be efficient when it is used in the inner loop of the iterative solver for the non-linear equations.


Cite This Article

He, X., Lim, K., Lim, S. (2008). Fast BEM Solvers for 3D Poisson-Type Equations. CMES-Computer Modeling in Engineering & Sciences, 35(1), 21–48.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
  • 925


  • 914


  • 0


Related articles

Share Link