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High-order finite elements for the solution of Helmholtz problems.

Christodoulou, K. and Laghrouche, O. and Mohamed, M.S. and Trevelyan, J. (2017) 'High-order finite elements for the solution of Helmholtz problems.', Computers and structures., 191 . pp. 129-139.


In this paper, two high-order finite element models are investigated for the solution of two-dimensional wave problems governed by the Helmholtz equation. Plane wave enriched finite elements, developed in the Partition of Unity Finite Element Method (PUFEM), and high-order Lagrangian-polynomial based finite elements are considered. In the latter model, the Chebyshev-Gauss-Lobatto nodal distribution is adopted and the approach is often referred to as the Spectral Element Method (SEM). The two strategies, PUFEM and SEM, were developed separately and the current study provides data on how they compare for solving short wave problems, in which the characteristic dimension is a multiple of the wavelength. The considered test examples include wave scattering by a rigid circular cylinder, evanescent wave cases and propagation of waves in a duct with rigid walls. The two approaches are assessed in terms of accuracy for increasing SEM order and PUFEM enrichment. The conditioning, discretization level, total number of storage locations and total number of non-zero entries are also compared.

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Publisher statement:Creative Commons Attribution License (CC BY) This article is available under the terms of the Creative Commons Attribution License (CC BY). You may copy and distribute the article, create extracts, abstracts and new works from the article, alter and revise the article, text or data mine the article and otherwise reuse the article commercially (including reuse and/or resale of the article) without permission from Elsevier. You must give appropriate credit to the original work, together with a link to the formal publication through the relevant DOI and a link to the Creative Commons user license above. You must indicate if any changes are made but not in any way that suggests the licensor endorses you or your use of the work.
Date accepted:16 June 2017
Date deposited:20 June 2017
Date of first online publication:30 June 2017
Date first made open access:No date available

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