Boundary element methods for the wave equation based on hierarchical matrices and adaptive cross approximation

Abstract Time-domain Boundary Element Methods (BEM) have been successfully used in acoustics, optics and elastodynamics to solve transient problems numerically. However, the storage requirements are immense, since fully populated system matrices be computed for a large number of time steps or frequencies. In this article, we propose new approximation scheme Convolution Quadrature Method powered BEM, which apply scattering governed by wave equation. We use $${\mathscr {H}}^2$$ H 2 -matrix compression spatial domain employ an adaptive cross algorithm frequency domain. way, computational costs reduced significantly, while accuracy method is preserved.