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 the fully populated system matrices have to be computed for a large number of time steps or frequencies. In this article, we propose a new approximation scheme for the Convolution Quadrature Method powered BEM, which we apply to scattering problems governed by the wave equation. We use {mathscr {H}}^2-matrix compression in the spatial domain and employ an adaptive cross approximation algorithm in the frequency domain. In this way, the storage and computational costs are reduced significantly, while the accuracy of the method is preserved.
Highlights
The numerical solution of wave propagation problems is a crucial task in computational mathematics and its applications
In contrast to Finite Element or Difference Methods, Boundary Element Methods (BEM) are based on boundary integral equations posed in terms of the traces of the solution
Since the boundary data is only given on ΓD or ΓN, we derive a system of boundary integral equations for its unknown parts
Summary
The numerical solution of wave propagation problems is a crucial task in computational mathematics and its applications. In this context, BEM play a special role, since they only require the discretisation of the boundary instead of the whole domain. BEM are favourable in situations where the domain is unbounded, as it is often the case for scattering problems. In contrast to Finite Element or Difference Methods, BEM are based on boundary integral equations posed in terms of the traces of the solution. For the classical example of the scalar wave equation, the occurring integral operators take the form of so called “retarded potentials” related to Huygen’s principle. In [2], Bamberger and Ha
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