A Galerkin BEM for transient acoustic scattering by an absorbing obstacle

This paper deals with the numerical resolution of the so‐called time‐domain boundary integral equations. The scattering problem by an absorbing obstacle serves as the model for this discussion. A new system of retarded potential boundary integral equations (RPBIE) is set up to solve the problem. Using an energy identity, we are able to prove the unconditional stability for standard conforming Galerkin approximation of the RPBIE. The actual space–time boundary elements are described in some detail, and their implementation has confirmed that stability in a wide range of situations and for large run times never reached before.