Martin J. Gander,
Lukáš Jakabčin,
Michal Outrata
S. 319 - 341
doi:
10.1553/etna_vol59s319
Verlag der Österreichischen Akademie der Wissenschaften
doi:
10.1553/etna_vol59s319
Abstract:
We show for a model problem that the truncation of an unbounded domain by an artificial Dirichlet boundary condition placed far away from the domain of interest is equivalent to a specific absorbing boundary condition placed closer to the domain of interest. This specific absorbing boundary condition can be implemented as a truncation layer terminated by a Dirichlet condition. We prove that the absorbing boundary condition thus obtained is a spectral Padé approximation about infinity of the transparent boundary condition. We also study numerically two improvements for this boundary condition, the truncation with an artificial Robin condition placed at the end of the truncation layer and a Padé approximation about a different point than infinity. Both of these give new and substantially better results compared to using the artificial Dirichlet boundary condition at the end of the truncation layer. We prove our results in the context of linear algebra, using spectral analysis of finite and infinite Schur complements, which we relate to continued fractions. We illustrate our results with numerical experiments.
domain truncation, ABC, Schur complement, continued fractions, Padé approximants
Published Online:
2024/01/23 09:39:16
Object Identifier:
0xc1aa5576 0x003ec78d
Rights:All rights reserved.For questions regarding copyright and copies please contact us by email.
Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.
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