Distributed fast boundary element methods for Helmholtz problems

Abstract

We present an approach for a distributed memory parallelization of the boundary element method. The given mesh is decomposed into submeshes and the respective matrix blocks are distributed among computational nodes (processes). The distribution which takes care of the load balancing during the system matrix assembly and matrix-vector multiplication is based on the cyclic graph decomposition. Moreover, since the individual matrix blocks are approximated using the adaptive cross approximation method, we describe its modification capable of dealing with zero blocks in the double-layer operator matrix since these are usually problematic when using the original adaptive cross approximation algorithm. Convergence and scalability of the method are demonstrated on the half- and full-space sound scattering problems modeled by the Helmholtz equation.