Acoustic Scattering Problems with Convolution Quadrature and the Method of Fundamental Solutions

Abstract

Time domain acoustic scattering problems in two and three dimensions are studied. The numerical scheme consists in the use of Convolution Quadrature method to reduce the time domain problem to solve frequency domain Helmholtz equations with complex wavenumbers. These equations are solved with the method of fundamental solutions (MFS), which approximates the solution by a linear combination of fundamental solutions defined at source points inside (outside) the scatterer for exterior (interior) problems. Numerical results show that the coupling of both methods works efficiently and accurately for multistep and multistage based CQ.