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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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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 PDF
Math. Comp. 85 (2016), 119-152 Request permission

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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Additional Information
  • Markus Faustmann
  • Affiliation: Institute for Analysis and Scientific Computing (Inst. E 101), Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Wien, Austria
  • MR Author ID: 1123286
  • Email: markus.faustmann@tuwien.ac.at
  • Jens Markus Melenk
  • Affiliation: Institute for Analysis and Scientific Computing (Inst. E 101), Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Wien, Austria
  • MR Author ID: 613978
  • ORCID: 0000-0001-9024-6028
  • Email: melenk@tuwien.ac.at
  • Dirk Praetorius
  • Affiliation: Institute for Analysis and Scientific Computing (Inst. E 101), Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Wien, Austria
  • MR Author ID: 702616
  • ORCID: 0000-0002-1977-9830
  • Email: dirk.praetorius@tuwien.ac.at
  • Received by editor(s): November 20, 2013
  • Received by editor(s) in revised form: July 28, 2014, and August 11, 2014
  • Published electronically: June 18, 2015

  • Dedicated: Dedicated to Wolfgang Hackbusch on the occasion of his 65th birthday
  • © Copyright 2015 American Mathematical Society
  • Journal: Math. Comp. 85 (2016), 119-152
  • MSC (2010): Primary 65F05; Secondary 65N38, 65F30, 65F50
  • DOI: https://doi.org/10.1090/mcom/2990
  • MathSciNet review: 3404445