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Efficient inversion of the Galerkin matrix of general second-order elliptic operators with nonsmooth coefficients


Author: Mario Bebendorf
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
Published electronically: September 17, 2004
MathSciNet review: 2136998
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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
Email: bebendorf@math.uni-leipzig.de

DOI: https://doi.org/10.1090/S0025-5718-04-01716-8
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”
Article copyright: © Copyright 2004 American Mathematical Society

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