ℋ^2-matrices for translation-invariant kernel functions

10/29/2022

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by   Steffen Börm, et al.

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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 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.