Adaptive refinement for hp-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem

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 ad...

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Main Authors: Congreve, Scott, Houston, Paul, Perugia, Ilaria
Format: Article
Published: Springer 2018
Online Access:https://eprints.nottingham.ac.uk/52555/
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author Congreve, Scott
Houston, Paul
Perugia, Ilaria
author_facet Congreve, Scott
Houston, Paul
Perugia, Ilaria
author_sort Congreve, Scott
building Nottingham Research Data Repository
collection Online Access
description 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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spelling nottingham-525552020-05-04T19:46:31Z https://eprints.nottingham.ac.uk/52555/ Adaptive refinement for hp-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem Congreve, Scott Houston, Paul Perugia, Ilaria 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. Springer 2018-07-16 Article PeerReviewed Congreve, Scott, Houston, Paul and Perugia, Ilaria (2018) Adaptive refinement for hp-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem. Advances in Computational Mathematics . ISSN 1572-9044 (In Press) https://link.springer.com/article/10.1007/s10444-018-9621-9 doi:10.1007/s10444-018-9621-9 doi:10.1007/s10444-018-9621-9
spellingShingle Congreve, Scott
Houston, Paul
Perugia, Ilaria
Adaptive refinement for hp-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem
title Adaptive refinement for hp-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem
title_full Adaptive refinement for hp-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem
title_fullStr Adaptive refinement for hp-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem
title_full_unstemmed Adaptive refinement for hp-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem
title_short Adaptive refinement for hp-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem
title_sort adaptive refinement for hp-version trefftz discontinuous galerkin methods for the homogeneous helmholtz problem
url https://eprints.nottingham.ac.uk/52555/
https://eprints.nottingham.ac.uk/52555/
https://eprints.nottingham.ac.uk/52555/