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arXiv · 1311.5028

Existence of $\mathcal{H}$-matrix approximants to the inverses of BEM matrices: the simple-layer operator

Markus Faustmann·Jens Markus Melenk·Dirk Praetorius
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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 of the 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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Markus Faustmann, Jens Markus Melenk, Dirk Praetorius. 2013-11-20. Existence of $\mathcal{H}$-matrix approximants to the inverses of BEM matrices: the simple-layer operator. https://doi.org/10.1090/mcom%2F2990

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