Solving acoustic scattering problems by the isogeometric boundary element method

Abstract

We solve acoustic scattering problems by means of the isogeometric boundary integral equation method. In order to avoid spurious modes, we apply the combined field integral equations for either sound-hard scatterers or sound-soft scatterers. These integral equations are discretized by Galerkin’s method, which especially enables the mathematically correct regularization of the hypersingular integral operator. In order to circumvent densely populated system matrices, we employ the isogeometric embedded fast multipole method, which is based on interpolation of the kernel function under consideration on the reference domain, rather than in space. To overcome the prohibitive cost of the potential evaluation in case of many evaluation points, we also accelerate the potential evaluation by a fast multipole method which interpolates in space. The result is a frequency stable algorithm that scales essentially linear in the number of degrees of freedom and potential points. Numerical experiments are performed which show the feasibility and the performance of the approach.