Novel and efficient implementation of multi-level fast multipole indirect BEM for industrial Helmholtz problems

Abstract

Fast multipole boundary element methods (FMBEM) have been successfully applied to solve ultra-large acoustic problems. In practice, there are still a large number of industrial applications where model sizes are well below a million Degrees of freedom. Thus, it is of practical importance to further improve the solver’s efficiency for such applications. This paper presents a novel formulation of the multi-level fast multipole indirect BEM, which relies on redesigning a conventional FMBEM with considerations from several aspects. A new flexible partition algorithm is proposed to generate a flexible and efficient multi-level structure for fast multipole calculations, which also allows the explicit calculation of the far field contributions. A hybrid and efficient regularization approach for hypersingular integral is investigated and implemented, which significantly reduces the iterative solving time. The use of efficient sparse approximate inverse preconditioners is key for fast convergence. Two strategies for constructing the sparsity pattern are implemented and evaluated. Numerical results show that by bringing the aforementioned techniques all together in one package, the new flexible multi-level fast multipole indirect BEM (f-FMBEM) provides significant improvements on actual simulation time over the conventional BEM and FMBEM solvers for industrial size problems (with a non-dimensional Helmholtz number up to kA∼323) on a modern workstation. To efficiently address larger problems, a more efficient multipole translation should be considered.