A relevant problem in the computational simulation of (time-harmonic and transient) waves is the devising of the correct boundary conditions that allow us to cut-off the computational domain and, therefore, to use any of the common PDE solvers. The main issue arises from the fact that waves have to be allowed to scatter away but the artificial boundary has to avoid them bouncing back.

This problem is nowadays very well understood in the time-harmonic case, for the most relevant types of linear waves: acoustic, elastic, electromagnetic,... Much recent progress is occurring in the field of transient problems. Most possible approaches can be categorized in three classes (almost corresponding to tribal groups): ABC, PML and BIE. I will try to explain the advantages and disadvantages of some Absorbing Boundary Conditions and Perfectly Matched Layers for transient acoustic waves. I will then move to the realm of Boundary Integral Operators/Equations, explaining what they have to offer (exactness and arbitrary closeness to where "stuff happens") and what is the price to pay, both at the computational level and at the steep learning process they require.

The talk will be informative. There will be plenty of formulas and some pictures, but no theorems or Sobolev spaces.