Fast and Accurate Time Domain Solver Based on the Exact Calculation of Matrix Entries in Boundary Element Method for Scalar Wave Scattering

In this work we present a first application of a novel integration strategy for the calculation of matrix entries in space-time Galerkin discretization of time domain boundary integral equations for wave scattering problems. The strategy is based on using an all-analytical formula for self-interaction and close interaction terms, while a semi-analytical method is chosen for geometrically distant elements. The exact formula is based on a dimensionality reduction procedure of the interaction integrals adapted to the time domain case. Nevertheless, interaction be-tween distant triangle pairs often present challenging geometrical configurations where cancellations between big numbers occur. Hence, a semi-analytical method is preferable in such cases. This hybrid strategy is applied within a marching-on in time algorithm for a scalar wave scattering problem. Computation time resulted to be similar to the full semi-analytical strategy while obtaining a better precision for the interaction elements.