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Extrapolated Multirate Methods for Differential Equations with Multiple Time Scales

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Abstract

In this paper we construct extrapolated multirate discretization methods that allows one to efficiently solve problems that have components with different dynamics. This approach is suited for the time integration of multiscale ordinary and partial differential equations and provides highly accurate discretizations. We analyze the linear stability properties of the multirate explicit and linearly implicit extrapolated methods. Numerical results with multiscale ODEs illustrate the theoretical findings.

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Acknowledgements

We thank the reviewers for their constructive critique and suggestions, which made this into a better paper. We also thank Valeriu Savcenco for his help with the results reported in [31].

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Authors and Affiliations

  1. Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S Cass Avenue, Argonne, IL, 60439, USA

    Emil M. Constantinescu

  2. Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061, USA

    Adrian Sandu

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  1. Emil M. Constantinescu
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  2. Adrian Sandu
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Correspondence to Emil M. Constantinescu.

Additional information

Emil Constantinescu was supported in part by the Office of Advanced Scientific Computing Research, Office of Science, U.S. Department of Energy, under Contract DE-AC02-06CH11357, and by the National Science Foundation through award NSF CCF-0515170. The work of Adrian Sandu was supported in part by NSF through the awards NSF CCF-0515170, NSF OCI-0904397, NSF CCF-0916493, and NSF DMS-0915047.

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Constantinescu, E.M., Sandu, A. Extrapolated Multirate Methods for Differential Equations with Multiple Time Scales. J Sci Comput 56, 28–44 (2013). https://doi.org/10.1007/s10915-012-9662-z

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  • DOI: https://doi.org/10.1007/s10915-012-9662-z

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