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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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Efficient inversion of the Galerkin matrix of general second-order elliptic operators with nonsmooth coefficients
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by Mario Bebendorf PDF
Math. Comp. 74 (2005), 1179-1199 Request permission

Abstract:

This article deals with the efficient (approximate) inversion of finite element stiffness matrices of general second-order elliptic operators with $L^\infty$-coefficients. It will be shown that the inverse stiffness matrix can be approximated by hierarchical matrices ($\mathcal {H}$-matrices). Furthermore, numerical results will demonstrate that it is possible to compute an approximate inverse with almost linear complexity.
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Additional Information
  • Mario Bebendorf
  • Affiliation: Fakultät für Mathematik und Informatik, Universität Leipzig, Augustusplatz 10/11, D-04109 Leipzig, Germany
  • MR Author ID: 656638
  • Email: bebendorf@math.uni-leipzig.de
  • Received by editor(s): June 4, 2003
  • Received by editor(s) in revised form: January 15, 2004
  • Published electronically: September 17, 2004
  • Additional Notes: This work was supported by the DFG priority program SPP 1146 “Modellierung inkrementeller Umformverfahren”
  • © Copyright 2004 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 1179-1199
  • MSC (2000): Primary 35C20, 65F05, 65F50, 65N30
  • DOI: https://doi.org/10.1090/S0025-5718-04-01716-8
  • MathSciNet review: 2136998