A parallel fast multipole boundary element method for acoustic problems in moving flows

Abstract

The boundary element method (BEM) has emerged as a powerful computational method for acoustic problems with a quiescent medium. However, the BEM is still in its infancy for large-scale acoustic problems in moving flows. In this paper, the convected BEM based on the direct convected boundary integral equation (BIE) is developed to solve the acoustic problems in a subsonic uniform flow. The fast multipole method (FMM) is implemented to overcome the inherent flaws of the conventional BEM (CBEM). In addition, the parallel computation technique is adopted to accelerate the solution of FMBEM further by taking advantage of modern computers with multicore CPUs. The parallel scheme is implemented with the wellknown OpenMP parallelization standard. Both the parallel schemes of the CBEM and FMBEM are introduced. For the CBEM, the construction of the coefficient matrix, as well as solving process, are drastically accelerated by utilizing a simple columnwise distribution scheme. For the FMBEM, the parallel GMRES iteration including the upward and downward passes is accelerated by distributing the threads to all cells at each level. The developed parallelization scheme for the FMM does not demand much extra memory storage. To illustrate the merits of the proposed method, several numerical examples are performed to validate the accuracy and efficiency of the developed parallel convected BEM.