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Time Parallelization for Nonlinear Problems Based on Diagonalization

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Domain Decomposition Methods in Science and Engineering XXIII

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

Abstract

The direct time parallelization method based on diagonalization is only applicable to linear problems. We propose here a new method based on diagonalization which permits the direct parallelization in time of a Newton iteration that works simultaneously over several time steps. We first explain the method for a scalar model problem, and then give a formulation for a nonlinear partial differential equation based on tensorization. We illustrate the methods with numerical experiments.

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Author information

Authors and Affiliations

  1. University of Geneva, Geneva, Switzerland

    Martin J. Gander

  2. University Paris 13, Paris, France

    Laurence Halpern

Authors
  1. Martin J. Gander
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  2. Laurence Halpern
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Corresponding author

Correspondence to Laurence Halpern .

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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Gander, M.J., Halpern, L. (2017). Time Parallelization for Nonlinear Problems Based on Diagonalization. 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_15

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