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High-order finite elements for the solution of Helmholtz problems

Christodoulou, K.; Laghrouche, O.; Mohamed, M.S.; Trevelyan, J.

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


K. Christodoulou

O. Laghrouche

M.S. Mohamed


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.


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

Journal Article Type Article
Acceptance Date Jun 16, 2017
Online Publication Date Jun 30, 2017
Publication Date Oct 15, 2017
Deposit Date Jun 16, 2017
Publicly Available Date Jun 20, 2017
Journal Computers and Structures
Print ISSN 0045-7949
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 191
Pages 129-139


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