
Frequency extraction for BEMmatrices arising from the 3D scalar Helmholtz equation
The discretisation of boundary integral equations for the scalar Helmhol...
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Approximation of boundary element matrices using GPGPUs and nested cross approximation
The efficiency of boundary element methods depends crucially on the time...
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The numerical approximation of the Schrödinger equation with concentrated potential
We present a family of algorithms for the numerical approximation of the...
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An extended Filon–Clenshaw–Curtis method for highfrequency wave scattering problems in two dimensions
We study the efficient approximation of integrals involving Hankel funct...
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The surrogate matrix methodology: Accelerating isogeometric analysis of waves
The surrogate matrix methodology delivers lowcost approximations of mat...
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A frequencydependent padaptive technique for spectral methods
When using spectral methods, a question arises as how to determine the e...
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The Time Domain Linear Sampling Method for Determining the Shape of a Scatterer using Electromagnetic Waves
The time domain linear sampling method (TDLSM) solves inverse scatterin...
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Boundary Element Methods for the Wave Equation based on Hierarchical Matrices and Adaptive Cross Approximation
Timedomain 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 ℋ^2matrix 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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