Boundary Element Methods for the Wave Equation based on Hierarchical Matrices and Adaptive Cross Approximation

2020/06/09 by Daniel Seibel, Seibel, Daniel
Engineering · Physics and Astronomy · #65N30 #65N38 #65N50 #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2006.05186

openalex publication_date 2020/06/09 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

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 (CQM) powered BEM, which we apply to scattering problems governed by the wave equation. We use H²-matrix compression in the spatial domain and employ an adaptive cross approximation (ACA) algorithm in the frequency domain. In this way, the storage and computational costs are reduced significantly, while the accuracy of the method is preserved.

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