Accurate temporal discretization of time domain boundary integral equations

In this contribution, a novel temporal discretization scheme for time domain boundary integral equations is introduced. It distinguishes itself by (i) a new approach to the construction of higher order temporal basis functions, and (ii) the use of temporal Petrov-Galerkin testing as opposed to the widespread collocation in time method. The retarded potential boundary integral equation and its classic collocation in time discretization will be revisited. Next, the new temporal basis and testing functions will be introduced. The space-time Petrov-Galerkin discretization using these functions will be elucidated. Finally, numerical results are presented testifying to the improved accuracy of the novel scheme.