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Algebraic Adaptive Multipreconditioning Applied to Restricted Additive Schwarz

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Book cover Domain Decomposition Methods in Science and Engineering XXIII

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 116))

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Abstract

In 2006 the Multipreconditioned Conjugate Gradient (MPCG) algorithm was introduced by Bridson and Greif. It is an iterative linear solver, adapted from the Preconditioned Conjugate Gradient (PCG) algorithm which can be used in cases where several preconditioners are available or the usual preconditioner is a sum of contributions. There, it was already pointed out that Domain Decomposition algorithms are ideal candidates to benefit from MPCG. The question posed by this work is whether an adaptive MPCG algorithm can be developed for Restricted Additive Schwarz. The goal is to design an adaptive algorithm that is robust at a minimal cost. One great feature of Additive Schwarz is that it is algebraic (all the components in the preconditioner can be computed from the knowledge of the matrix) and we will aim to preserve this property.

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Authors and Affiliations

  1. CMAP, Ecole polytechnique, CNRS, Université Paris-Saclay, 91128, Palaiseau, France

    Nicole Spillane

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  1. Nicole Spillane
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Correspondence to Nicole Spillane .

Editor information

Editors and Affiliations

  1. Dept. of Mathematical Sciences, KAIST, Daejeon, Korea (Republic of)

    Chang-Ock Lee

  2. Dept. of Computer Science, University of Colorado, Boulder, Colorado, USA

    Xiao-Chuan Cai

  3. Applied Math & Computational Science, KAUST, Thuwal, Saudi Arabia

    David E. Keyes

  4. Dept. of Applied Mathematics, Kyung Hee University, Yongin, Korea (Republic of)

    Hyea Hyun Kim

  5. Mathematisches Institut, Universität zu Köln, Köln, Germany

    Axel Klawonn

  6. Dept. of Computational Science & Engineering, Yonsei University, Seoul, Korea (Republic of)

    Eun-Jae Park

  7. Courant Institute of Mathematical Sciences, New York University, New York, New York, USA

    Olof B. Widlund

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Spillane, N. (2017). Algebraic Adaptive Multipreconditioning Applied to Restricted Additive Schwarz. In: Lee, CO., et al. Domain Decomposition Methods in Science and Engineering XXIII. Lecture Notes in Computational Science and Engineering, vol 116. Springer, Cham. https://doi.org/10.1007/978-3-319-52389-7_8

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