• Ronny Ramlau, Lothar Reichel (Hg.)

ETNA - Electronic Transactions on Numerical Analysis

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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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ETNA - Electronic Transactions on Numerical Analysis



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Verlag der Österreichischen Akademie der Wissenschaften
Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2,
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400
https://verlag.oeaw.ac.at, e-mail: bestellung.verlag@oeaw.ac.at
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Robust BDDC algorithms for finite volume element methods

    Yanru Su, Xuemin Tu, Yingxiang Xu

ETNA - Electronic Transactions on Numerical Analysis, pp. 66-83, 2022/11/16

doi: 10.1553/etna_vol58s66

doi: 10.1553/etna_vol58s66


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doi:10.1553/etna_vol58s66



doi:10.1553/etna_vol58s66

Abstract

The balancing domain decomposition by constraints (BDDC) method is applied to the linear system arising from the finite volume element method (FVEM) discretization of a scalar elliptic equation. The FVEMs share nice features of both finite element and finite volume methods and are flexible for complicated geometries with good conservation properties. However, the resulting linear system usually is asymmetric. The generalized minimal residual (GMRES) method is used to accelerate convergence. The proposed BDDC methods allow for jumps of the coefficient across subdomain interfaces. When jumps of the coefficient appear inside subdomains, the BDDC algorithms adaptively choose the primal variables deriving from the eigenvectors of some local generalized eigenvalue problems. The adaptive BDDC algorithms with advanced deluxe scaling can ensure good performance with highly discontinuous coefficients. A convergence analysis of the BDDC method with a preconditioned GMRES iteration is provided, and several numerical experiments confirm the theoretical estimate.

Keywords: finite volume element methods, domain decomposition, BDDC, deluxe scaling