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On perfectly matched layers for discontinuous Petrov–Galerkin methods

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Abstract

In this article, several discontinuous Petrov–Galerkin (DPG) methods with perfectly matched layers (PMLs) are derived along with their quasi-optimal graph test norms. Ultimately, two different complex coordinate stretching strategies are considered in these derivations. Unlike with classical formulations used by Bubnov–Galerkin methods, with so-called ultraweak variational formulations, these two strategies in fact deliver different formulations in the PML region. One of the strategies, which is argued to be more physically natural, is employed for numerically solving two- and three-dimensional time-harmonic acoustic, elastic, and electromagnetic wave propagation problems, defined in unbounded domains. Through these numerical experiments, efficacy of the new DPG methods with PMLs is verified.

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Acknowledgements

This work was partially supported with grants by NSF (DMS-1418822), AFOSR (FA9550-12-1-0484), and ONR (N00014-15-1-2496). The first author was also supported in part by the 2016 Peter O’Donnell, Jr. Postdoctoral Fellowship from The Institute for Computational Engineering and Sciences at The University of Texas at Austin. The second author was also supported in part by the 2017 Graduate School University Graduate Continuing Fellowship at The University of Texas at Austin.

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  1. The Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin, 201 E 24th St, Austin, TX, 78712, USA

    Ali Vaziri Astaneh, Brendan Keith & Leszek Demkowicz

  2. MSC Software Corporation, Newport Beach, CA, 92660, USA

    Ali Vaziri Astaneh

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  1. Ali Vaziri Astaneh
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Correspondence to Ali Vaziri Astaneh.

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Vaziri Astaneh, A., Keith, B. & Demkowicz, L. On perfectly matched layers for discontinuous Petrov–Galerkin methods. Comput Mech 63, 1131–1145 (2019). https://doi.org/10.1007/s00466-018-1640-3

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