Frequency-robust preconditioning of boundary integral equations for acoustic transmission

Abstract

The scattering and transmission of harmonic acoustic waves at a penetrable material are commonly modelled by a set of Helmholtz equations. This system of partial differential equations can be rewritten into boundary integral equations defined at the surface of the objects and solved with the boundary element method (BEM). High frequencies or geometrical details require a fine surface mesh, which increases the number of degrees of freedom in the weak formulation. Then, matrix compression techniques need to be combined with iterative linear solvers to limit the computational footprint. Moreover, the convergence of the iterative linear solvers often depends on the frequency of the wave field and the objects' characteristic size. Here, the robust PMCHWT formulation is used to solve the acoustic transmission problem. An operator preconditioner based on on-surface radiation conditions (OSRC) is designed that yields frequency-robust convergence characteristics. Computational benchmarks compare the performance of this novel preconditioned formulation with other preconditioners and boundary integral formulations. The OSRC preconditioned PMCHWT formulation effectively simulates large-scale problems of engineering interest, such as focused ultrasound treatment of osteoid osteoma