Analysis of interior and exterior sound fields using iterative boundary element solvers

Abstract

The boundary element method (BEM) is an efficient tool for the calculation of interior and exterior sound fields. However, the discretization of the Helmholtz integral equation often leads to large, unsymmetrical, and fully populated systems of linear equations. Such systems can be solved by means of various iterative solvers. Three examples are considered: First, a preconditioned version of the generalized minimum residual method (GMRES) is used for calculating the high-frequency acoustic scattering from cylinderlike structures. Second, the sound field in a passenger compartment is analyzed by using five different iterative solvers: GMRES, the conjugate gradient squared algorithm (CGS), the quasiminimal residual approximation (QMR), the biconjugate gradient stabilized algorithm (BICGSTAB), and the conjugate gradient iteration on the normal equations (CGNR). These methods and a Gaussian elimination are compared with respect to their numerical performance and speed of convergence. Third, scattering and radiation of a nonconvex structure is investigated. This structure—called ‘‘cat’s eye’’—consists of a sphere, where the positive octant is cut out. The efficiency and accuracy of the above mentioned five iterative methods are studied for the vibrating cat’s eye. By means of the preconditioned GMRES, scattering cat’s eyes of several thousand boundary elements can be treated on personal computers.