High-order finite elements for the solution of Helmholtz problems

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

Abstract

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.

Citation

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. https://doi.org/10.1016/j.compstruc.2017.06.010

• 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
• Electronic ISSN: 1879-2243
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 191
• Pages: 129-139
• DOI: https://doi.org/10.1016/j.compstruc.2017.06.010
• Public URL: https://durham-repository.worktribe.com/output/1376894