Abstract

Abstract: Absorbing or transparent boundary conditions for transient waves can be accomplished in several ways, with Perfectly Matched Layers, with Surface Differential Operators or with Boundary Integral Equations. This last possibility (which is very well understood and quite widely employed in the frequency domain) has several advantages: no need of convexity for the cut-off boundary, possibility of having separate boundaries that transport information among computational domains as well as arbitrary proximity to sources, non-homogeneities, etc. In this talk I will show how to construct the simplest integral absorbing boundary condition for the acoustic wave equation and will give some pointers on its properties: unconditional stability after space-Galerkin discretization, energy conservation and possibility of time-stepping with convolution quadrature. I will also explain the challenges that time domain boundary integral equations have to overcome in the near future.