An adaptive fast multipole boundary element method for three-dimensional acoustic wave problems based on the Burton–Miller formulation

Abstract

The high solution costs and non-uniqueness difficulties in the boundary element method (BEM) based on the conventional boundary integral equation (CBIE) formulation are two main weaknesses in the BEM for solving exterior acoustic wave problems. To tackle these two weaknesses, an adaptive fast multi- pole boundary element method (FMBEM) based on the Burton-Miller formulation for 3-D acoustics is presented in this paper. In this adaptive FMBEM, the Burton-Miller formulation using a linear combination oftheCBIEandhypersingularBIE(HBIE)isappliedto overcome the non-uniqueness difficulties. The iterative solver generalized minimal residual (GMRES) and fast multipole method (FMM) are adopted to improve the overallcomputationalefficiency.ThisadaptiveFMBEM for acoustics is an extension of the adaptive FMBEM for 3-D potential problems developed by the authors recently. Several examples on large-scale acoustic radi- ationandscatteringproblemsarepresentedinthispaper which show that the developed adaptive FMBEM can be several times faster than the non-adaptive FMBEM while maintaining the accuracies of the BEM.