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We describe a numerical method for the solution of acoustic exteriorscattering problems based on the time-domain boundary integral representationof the solution. As the spatial discretization of the resulting time-domainboundary integral equation we use either the method of fundamental solutions(MFS) or the Galerkin boundary element method (BEM). In time we apply either astandard convolution quadrature (CQ) based on an A-stable linear multistepmethod or a modified CQ scheme. It is well-known that the standard low-order CQschemes for hyperbolic problems suffer from strong dissipation and dispersionproperties. The modified scheme is designed to avoid these properties. We givea careful description of the modified scheme and its implementation withdifferences due to different spatial discretizations highlighted. Numerousnumerical experiments illustrate the effectiveness of the modified scheme anddramatic improvement with errors up to two orders of magnitude smaller incomparison with the standard scheme

A modified convolution quadrature combined with the method of fundamental solutions and Galerkin BEM for acoustic scattering