A family of efficient numerical solvers of time domain boundary integral equations

When applicable, boundary integral equation (BIE) methods are an elegant way to transform a differential equation posed on (often unbounded) domainfi Rn to a BIE on the (often bounded) n-1 dimensional boundary = @ In the frequency domain, this approach has been very successful for the numerical solution of acoustic and electromagnetic scattering problems. In time domain acoustics, numerical methods for boundary integral equations (TDBIE) have until recently received less attention. Nevertheless, good methods do exist and promising results have been achieved in producing eficient and stable numerical solutions. In this talk, we describe a generalization of convolution quadrature, a method that can be used to solve TDBIE numerically. Recently the first author has been involved in proving convergence and stability of high-order Runge-Kutta convolution quadratures and in developing eficient algorithms for their implementation. Here, we extend these results to a family of related methods that are potentially more eficient in situations where high accuracy is not essential, but good (low) dispersion and dissipation properties of the numerical solution are paramount. First numerical experiments with the new method are promising.