Flexible multi-level fast multipole BEM with direct solver for industrial acoustic problems

Fast Multipole Boundary Element Method (FMBEM) for acoustics is a very powerful method to solve ultra large problems, which exploits iterative solvers. However, for Helmholtz problem iterative solvers may fail to converge in some cases. Whereas FMBEM provides a unique offering for ultra large problems, many industrial problems in fact can be solved with tens of thousands of Dofs and can be considered as medium to large size. For such problems, direct solvers are still viable and provide a good option in terms of stability and convenience for solving many right-hand sides, especially in light of recent many core architectures like GPU. In this paper, we present a flexible fast multipole accelerated indirect BEM for solving medium to large size acoustic problems. The assembly process of the indirect BEM is accelerated by a flexible multi-level fast multipole method. The system matrix is then solved by a direct solver. Numerical results show that this combination offers an efficient and robust approach, where medium to large size acoustic problems can be efficiently solved on a modern desktop computer.