TY - JOUR
T1 - Time Domain Boundary Element Methods for the Neumann Problem: Error Estimates and Acoustic Problems
AU - Gimperlein , Heiko
AU - Özdemir , Ceyhun
AU - Stephan , Ernst P.
JO - Journal of Computational Mathematics
VL - 1
SP - 70
EP - 89
PY - 2018
DA - 2018/02
SN - 36
DO - http://doi.org/10.4208/jcm.1610-m2016-0494
UR - https://global-sci.org/intro/article_detail/jcm/10583.html
KW - Time domain boundary element method, Wave equation, Neumann problem, Error estimates, Sound radiation.
AB - <p style="text-align: justify;">We investigate time domain boundary element methods for the wave equation in $\mathbb{R}^3$, 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 convergence of our boundary element scheme and compare it with the numerical approximations obtained from an integral equation of the second kind. Computations in a half-space illustrate the influence of the reflection properties of a flat street.</p>