An iterative GMRES-based boundary element solver for acoustic scattering

摘要

High-frequency scattering of complex structures is studied using a new variant of the generalized minimum residual method (GMRES) along with an appropriate preconditioning, which was originally developed for iterative solutions in electrodynamics [Comparison of GMRES and CG Iterations on the Normal Form of Magnetic Field Integral Equation, submitted]. The starting point is a self-adjoint formulation of the Helmholtz integral equation for scattering. Three iterative methods, the Jacobi iteration with overrelaxation and two variants of the GMRES are presented, and the advantages of the improved GMRES are discussed. The GMRES is applied to the scattering of a plane wave from a cylinder-like, rigid structure comprising several ten thousands of boundary elements. Fast convergence of the iteration process is observed for all investigated cases. The relative error decreases rapidly and becomes smaller than the discretization error after a few iteration steps. The GMRES solver is only weakly affected by internal resonances, but could be combined with a dual-layer CHIEF approach. All computations are carried out on regular personal computers, even for the boundary element model with about 48,000 elements.