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A Nonlinear ParaExp Algorithm

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Book cover Domain Decomposition Methods in Science and Engineering XXIV (DD 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 125))

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Abstract

We derive and analyze a nonlinear variant of the ParaExp algorithm introduced in Gander and Güttel (SIAM J Sci Comput 35(2):C123–C142, 2013) for linear evolution problems. We show that the nonlinear ParaExp algorithm converges in a finite number of steps, and that it can be interpreted as a parareal algorithm where the coarse integrator solves the linear part of the evolution problem. We also provide a numerical example illustrating the efficiency of the new algorithm.

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Author information

Authors and Affiliations

  1. Université de Genève, Genève, Switzerland

    Martin J. Gander

  2. School of Mathematics, The University of Manchester, Manchester, UK

    Stefan Güttel

  3. Laboratoire de Mathématiques, Université de Poitiers, Poitiers, France

    Madalina Petcu

  4. The Institute of Statistics and Applied Mathematics of the Romanian Academy, Bucharest, Romania

    Madalina Petcu

  5. The Institute of Mathematics of the Romanian Academy, Bucharest, Romania

    Madalina Petcu

Authors
  1. Martin J. Gander
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  2. Stefan Güttel
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  3. Madalina Petcu
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Corresponding authors

Correspondence to Martin J. Gander , Stefan Güttel or Madalina Petcu .

Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Petter E. Bjørstad

  2. Department of Mathematics, Louisana State University, Baton Rouge, LA, USA

    Susanne C. Brenner

  3. Laboratoire Analyse, Géométrie et Applications, Université Paris 13, Villetaneuse, France

    Lawrence Halpern

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

    Hyea Hyun Kim

  5. FB Mathematik und Informatik, Freie Universität Berlin, Berlin, Germany

    Ralf Kornhuber

  6. Western Norway University of Applied Sciences, Bergen, Norway

    Talal Rahman

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

    Olof B. Widlund

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Gander, M.J., Güttel, S., Petcu, M. (2018). A Nonlinear ParaExp Algorithm. In: Bjørstad, P., et al. Domain Decomposition Methods in Science and Engineering XXIV . DD 2017. Lecture Notes in Computational Science and Engineering, vol 125. Springer, Cham. https://doi.org/10.1007/978-3-319-93873-8_24

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