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...
| Main Authors: | , , |
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| Format: | Article |
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Springer
2018
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| Online Access: | https://eprints.nottingham.ac.uk/52555/ |
| _version_ | 1848798753140506624 |
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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. |
| first_indexed | 2025-11-14T20:24:47Z |
| format | Article |
| id | nottingham-52555 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:24:47Z |
| publishDate | 2018 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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/ |