A Modified Convolution Quadrature Combined with the Method of Fundamental Solutions and Galerkin BEM for Acoustic Scattering (Communications in Computational Physics, 2025)
We describe a numerical method for the solution of acoustic exterior scattering problems based on the time-domain boundary integral representation of the solution. As the spatial discretization of the resulting time-domain boundary integral equation we use either the method of fundamental solutions (MFS) or the Galerkin boundary element method (BEM). In time we apply either a standard convolution quadrature (CQ) based on an A-stable linear multistep method or a modified CQ scheme. Itis well-known that the standard low-order CQ schemes for hyperbolic problems sufferfrom strong dissipation and dispersion properties. The modified scheme is designedto avoid these properties. We give a careful description of the modified scheme and itsimplementation with differences due to different spatial discretizations highlighted.Numerous numerical experiments illustrate the effectiveness of the modified schemeand dramatic improvement with errors up to two orders of magnitude smaller in comparison with the standard scheme.
Keywords: Acoustic wave scattering; convolution quadrature; modified convolution quadrature; method of fundamental solutions; boundary integral equation.