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Efficient and High-Order Explicit Local Time Stepping on Moving DG Spectral Element Meshes

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Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 106))

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Abstract

We outline and extend results for an explicit local time stepping (LTS) strategy designed to operate with the discontinuous Galerkin spectral element method (DGSEM). The LTS procedure is derived from Adams-Bashforth multirate time integration methods. The new results of the LTS method focus on parallelization and reformulation of the LTS integrator to maintain conservation. Discussion is focused on a moving mesh implementation, but the procedures remain applicable to static meshes. In numerical tests, we demonstrate the strong scaling of a parallel, LTS implementation and compare the scaling properties to a parallel, global time stepping (GTS) Runge-Kutta implementation. We also present time-step refinement studies to show that the redesigned, conservative LTS approximations are spectrally accurate in space and have design temporal accuracy.

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Authors and Affiliations

  1. Department of Mathematics, The Florida State University, 208 Love Building, 1017 Academic Way, Tallahassee, FL, 32306, USA

    Andrew R. Winters & David A. Kopriva

Authors
  1. Andrew R. Winters
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  2. David A. Kopriva
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Correspondence to Andrew R. Winters .

Editor information

Editors and Affiliations

  1. School of Computing , University of Utah, Salt Lake City, Utah, USA

    Robert M. Kirby

  2. School of Computing, University of Utah, Salt Lake City, Utah, USA

    Martin Berzins

  3. EPFL-SB-MATHICSE-MCSS, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Jan S. Hesthaven

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Winters, A.R., Kopriva, D.A. (2015). Efficient and High-Order Explicit Local Time Stepping on Moving DG Spectral Element Meshes. In: Kirby, R., Berzins, M., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Lecture Notes in Computational Science and Engineering, vol 106. Springer, Cham. https://doi.org/10.1007/978-3-319-19800-2_48

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