Modul: MAT870 Zurich Colloquium in Applied and Computational Mathematics

## A new approach to Space-Time Boundary Integral Equations for the Wave Equation

Dr. Carolina Urzua Torres talk

**Date:** 02.10.19 **Time:** 16.15 - 17.45 **Room:** ETH HG E 1.2

Space-time discretization methods are becoming increasingly popular, since they allow adaptivity in space and time simultaneously, and can use parallel iterative solution strategies for time-dependent problems. However, in order to exploit these advantages, one needs to have a complete numerical analysis of the corresponding Galerkin methods. Different strategies have been used to derive variational methods for the time domain boundary integral equations for the wave equation. The more established and succesful ones include weak formulations based on the Laplace transform, and also time-space energetic variational formulations. However, their corresponding numerical analyses are still incomplete and present difficulties that are hard to overcome, if possible at all. As an alternative, we pursue a new approach to formulate the boundary integral equations for the wave equation, which aims to provide the missing mathematical analysis for space-time boundary element methods. In this talk, I will give a short introduction to boundary element methods; briefly explain the current formulations for the wave equation; and discuss the new approach and our preliminary results.