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Explicit computational wave propagation in micro-heterogeneous media

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Abstract

Explicit time stepping schemes are popular for linear acoustic and elastic wave propagation due to their simple nature which does not require sophisticated solvers for the inversion of the stiffness matrices. However, explicit schemes are only stable if the time step size is bounded by the mesh size in space subject to the so-called CFL condition. In micro-heterogeneous media, this condition is typically prohibitively restrictive because spatial oscillations of the medium need to be resolved by the discretization in space. This paper presents a way to reduce the spatial complexity in such a setting and, hence, to enable a relaxation of the CFL condition. This is done using the Localized orthogonal decomposition method as a tool for numerical homogenization. A complete convergence analysis is presented with appropriate, weak regularity assumptions on the initial data.

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Acknowledgements

The authors acknowledge support by Deutsche Forschungsgemeinschaft in the Priority Program 1748 Reliable simulation techniques in solid mechanics (PE2143/2-2). The authors thank the Hausdorff Institute for Mathematics in Bonn for the kind hospitality during the trimester program on multiscale problems in 2017.

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  1. Institut für Mathematik, Universität Augsburg, Universitätsstraße 14, D-86159, Augsburg, Germany

    Roland Maier & Daniel Peterseim

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  1. Roland Maier
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  2. Daniel Peterseim
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Correspondence to Roland Maier.

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Communicated by Jan Hesthaven.

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Maier, R., Peterseim, D. Explicit computational wave propagation in micro-heterogeneous media. Bit Numer Math 59, 443–462 (2019). https://doi.org/10.1007/s10543-018-0735-8

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  • DOI: https://doi.org/10.1007/s10543-018-0735-8

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