Parallelized fast multipole BEM based on the convolution quadrature method for 3-D wave propagation problems in time-domain

Abstract

This paper presents a new time-domain boundary element method (BEM) using a convolution quadrature method (CQM) and a fast multipole method (FMM) in 3-D scalar wave propagation. In general, the use of direct time-domain BEM sometimes causes the numerical instability of time-stepping solutions and needs much computational time and memory. To overcome these difficulties, in this paper, the convolution quadrature method developed by Lubich is applied to establish the stability behavior of the time-stepping scheme. Moreover, the fast multipole method and parallelization techniques are adapted to improve the computational efficiency for large size problems. The formulation and numerical implementation of the new boundary element method, and the basic formulas for the fast multipole method such as the multipole expansion, the local expansion, and the translation relations of them in the fast multipole algorithm are presented. The accuracy, the computational efficiency and the applicability are checked by solving 3-D large scale wave scattering problems.