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Convolution quadrature (CQ) methods have enjoyed tremendous interest inrecent years as an efficient tool for solving time-domain wave problems inunbounded domains via boundary integral equation techniques. In this paper weconsider CQ type formulations for the parallel space-time evaluation ofmultistep or stiffly accurate Runge-Kutta rules for the wave equation. Inparticular, we decouple the number of Laplace domain solves from the number oftime steps. This allows to overresolve in the Laplace domain by computing moreLaplace domain solutions solutions than there are time steps. We use techniquesfrom complex approximation theory to analyse the error of the CQ approximationof the underlying time-stepping rule when overresolving in the Laplace domainand show that the performance is intimately linked to the location of the polesof the solution operator. Several examples using boundary integral equationformulations in the Laplace domain are presented to illustrate the mainresults.

Overresolving in the Laplace domain for convolution quadrature methods