Stability of Galerkin and collocation time domain boundary element methods as applied to the scalar wave equation

The Galerkin method for time domain boundary element analysis is presented in this paper and used for the first time as an alternative procedure to improve the stability of BEM formulations applied to the scalar wave equation. The paper includes a short review of the classical time-stepping BEM formulation and the modifications required to implement a Galerkin approach. No mathematical proof is given here, concerning the stability improvement of the Galerkin formulation over the point collocation method. However, strong numerical evidence of such stability improvement is provided by the second example of this paper where the Galerkin approach has shown to be stable for rather small time steps.