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arXiv · 2210.16609

$\mathcal{H}^2$-matrices for translation-invariant kernel functions

Steffen Börm·Janne Henningsen
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Abstract

Boundary element methods for elliptic partial differential equations typically lead to boundary integral operators with translation-invariant kernel functions. Taking advantage of this property is fairly simple for particle methods, e.g., Nystrom-type discretizations, but more challenging if the supports of basis functions have to be taken into account. In this article, we present a modified construction for $\mathcal{H}^2$-matrices that uses translation-invariance to significantly reduce the storage requirements. Due to the uniformity of the boxes used for the construction, we need only a few uncomplicated assumptions to prove estimates for the resulting storage complexity.

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Steffen Börm, Janne Henningsen. 2022-10-29. $\mathcal{H}^2$-matrices for translation-invariant kernel functions. https://arxiv.org/abs/2210.16609

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