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Adaptive refinement for hp–Version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem

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Abstract

In this article, we develop an hp-adaptive refinement procedure for Trefftz discontinuous Galerkin methods applied to the homogeneous Helmholtz problem. Our approach combines not only mesh subdivision (h–refinement) and local basis enrichment (p–refinement), but also incorporates local directional adaptivity, whereby the elementwise plane wave basis is aligned with the dominant scattering direction. Numerical experiments based on employing an empirical a posteriori error indicator clearly highlight the efficiency of the proposed approach for various examples.

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Funding

S. Congreve and I. Perugia have been funded by the Austrian Science Fund (FWF) through the project P29197-N32. I. Perugia has also been funded by the FWF through the project F 65.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria

    Scott Congreve & Ilaria Perugia

  2. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK

    Paul Houston

Authors
  1. Scott Congreve
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  2. Paul Houston
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  3. Ilaria Perugia
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Correspondence to Scott Congreve.

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Communicated by: Jan Hesthaven

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Congreve, S., Houston, P. & Perugia, I. Adaptive refinement for hp–Version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem. Adv Comput Math 45, 361–393 (2019). https://doi.org/10.1007/s10444-018-9621-9

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  • DOI: https://doi.org/10.1007/s10444-018-9621-9

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