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

Congreve, Scott; Houston, Paul; Perugia, Ilaria

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.

Citation

Congreve, S., Houston, P., & Perugia, I. (2019). Adaptive refinement for hp-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem. Advances in Computational Mathematics, 45(1), 361-393. https://doi.org/10.1007/s10444-018-9621-9

• Journal Article Type: Article
• Acceptance Date: Jun 19, 2018
• Online Publication Date: Jul 16, 2018
• Publication Date: Feb 28, 2019
• Deposit Date: Jun 22, 2018
• Publicly Available Date: Jul 17, 2019
• Journal: Advances in Computational Mathematics
• Print ISSN: 1019-7168
• Electronic ISSN: 1572-9044
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 45
• Issue: 1
• Pages: 361-393
• DOI: https://doi.org/10.1007/s10444-018-9621-9
• Public URL: https://nottingham-repository.worktribe.com/output/946924
• Publisher URL: https://link.springer.com/article/10.1007/s10444-018-9621-9
• Contract Date: Jun 22, 2018