We investigate time domain boundary element methods for the wave equation in R3,with a view towards sound emission problems in computational acoustics. The Neumann problem is reduced to a time dependent integral equation for the hypersingular operator,and we present a priori and a posteriori error estimates for conforming Galerkin approximations in the more general case of a screen. Numerical experiments validate the convergenc of our boundary element scheme and compare it with the numerical approximations obtainefrom an integral equation of the second kind. Computations in a half-space illustratthe influence of the reflection properties of a flat street.
Gimperlein, H., Oezdemir, C., & Stephan, E. P. (2018). Time domain boundary element methods for the Neumann problem: Error estimates and acoustic problems. Journal of Computational Mathematics, 36(1), 70-89. https://doi.org/10.4208/jcm.1610-m2016-0494