Existence of ℋ-matrix approximants to the inverses of BEM matrices: The simple-layer operator

Faustmann, Markus; Melenk, Jens; Praetorius, Dirk

doi:10.1090/mcom/2990

Existence of $\mathcal {H}$-matrix approximants to the inverses of BEM matrices: The simple-layer operator
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by Markus Faustmann, Jens Markus Melenk and Dirk Praetorius;

Math. Comp. 85 (2016), 119-152

DOI: https://doi.org/10.1090/mcom/2990

Published electronically: June 18, 2015

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Abstract:

We consider the question of approximating the inverse $\mathbf W = \mathbf V^{-1}$ of the Galerkin stiffness matrix $\mathbf V$ obtained by discretizing the simple-layer operator $V$ with piecewise constant functions. The block partitioning of $\mathbf W$ is assumed to satisfy any one of several standard admissibility criteria that are employed in connection with clustering algorithms to approximate the discrete BEM operator $\mathbf V$. We show that $\mathbf W$ can be approximated by blockwise low-rank matrices such that the error decays exponentially in the block rank employed. Similar exponential approximability results are shown for the Cholesky factorization of $\mathbf V$.

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