Adaptive boundary element method of time-harmonic exterior acoustics in two dimensions

Abstract

In this paper we carry out boundary element computations of the Helmholtz equation in two dimensions, in the context of time-harmonic exterior acoustics. The purpose is to demonstrate cost savings engendered through adaptivity for propagating solutions at moderate wave numbers. The computation are performed on meshes of constant boundary elements, and are adapted to the solution by locally changing element sizes (h-version). Burton and Miller approach is employed to solve the exterior problems for all wave numbers. Two error indicators obtained from the dual integral equations in conjunction with the exact error indicator are used for local error estimation, which are essential ingredients for all adaptive mesh schemes in BEM. Computational experiments are performed for the two-dimensional exterior acoustics. The three error tracking curves are in good agreement with their shapes. Three examples show that the adaptive mesh based on the error indicators converge to the exact solution more efficiently using the same number of elements than does uniform mesh discretization.