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Space–time enriched finite elements for elastodynamic wave propagation

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Abstract

This article investigates a generalised finite-element method for time-dependent elastic wave propagation, based on plane-wave enrichments of the approximation space. The enrichment in both space and time allows good approximation of oscillatory solutions even on coarse mesh grids and for large time steps. The proposed method is based on a discontinuous Galerkin discretisation in time and conforming finite elements in space. Numerical experiments study the stability and accuracy and confirm significant reductions of the computational effort required to achieve engineering accuracy.

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Data availability

No data sets are used and the results are from solving the numerical method. Extensions to the code are being developed before making it publically available.

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Acknowledgements

The authors would like to thank Omar Laghrouche for the fruitful discussions on the topics of this article.

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Authors and Affiliations

  1. Engineering Mathematics, Leopold-Franzens-Universität Innsbruck, Technikerstraße 13, 6020, Innsbruck, Austria

    Kieran Quaine & Heiko Gimperlein

  2. Maxwell Institute for Mathematical Sciences and School of Mathematics, Edinburgh University, James Clerk Maxwell Building, Edinburgh, EH9 3FD, UK

    Kieran Quaine

  3. FEN Research GmbH, Technikerstraße 1/3, 6020, Innsbruck, Austria

    Kieran Quaine

  4. Department of Mathematical, Physical and Computer Sciences, University of Parma, Parco Area delle Scienze, 53/A, 43124, Parma, Italy

    Heiko Gimperlein

Authors
  1. Kieran Quaine
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  2. Heiko Gimperlein
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Correspondence to Kieran Quaine.

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Conflict of interest

The authors would like to thank The Maxwell Institute Graduate School in Analysis and its Applications, a Centre for Doctoral Training funded by the UK Engineering and Physical Sciences Research Council (Grant EP/L016508/01), Heriot-Watt University, University of Edinburgh and AWE (Contract No. PO30408299) for their sponsorship. The authors have no further competing interests to declare that are relevant to the content of this article.

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Quaine, K., Gimperlein, H. Space–time enriched finite elements for elastodynamic wave propagation. Engineering with Computers 39, 4077–4091 (2023). https://doi.org/10.1007/s00366-023-01874-z

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