“Causal” shape functions in the time domain boundary element method

Since failing to respect the causality condition has been identified as one of the main sources of inaccuracies in the time domain boundary element method for elastodynamics and scalar wave propagation problems, in this contribution new shape functions are investigated, which permit a more accurate simulation of the continuous propagation of wave fronts. The performance of these shape functions in 2D scalar wave propagation problems is tested both for the potential (displacement) and for the time gradient (velocity) equations. Analytical time integrations are developed and numerical results are presented.