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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Bibliographic Details
Main Authors: Congreve, Scott, Houston, Paul, Perugia, Ilaria
Format: Article
Published: Springer 2018
Online Access:https://eprints.nottingham.ac.uk/52555/
Description
Summary: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.