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Implementation and computational aspects of a 3D elastic wave modelling by PUFEM.

Mahmood, M.S. and Laghrouche, O. and Trevelyan, J. and El Kacimi, A. (2017) 'Implementation and computational aspects of a 3D elastic wave modelling by PUFEM.', Applied mathematical modelling., 49 . pp. 568-586.

Abstract

This paper presents an enriched finite element model for three dimensional elastic wave problems, in the frequency domain, capable of containing many wavelengths per nodal spacing. This is achieved by applying the plane wave basis decomposition to the three-dimensional (3D) elastic wave equation and expressing the displacement field as a sum of both pressure (P) and shear (S) plane waves. The implementation of this model in 3D presents a number of issues in comparison to its 2D counterpart, especially regarding how S-waves are used in the basis at each node and how to choose the balance between P and S-waves in the approximation space. Various proposed techniques that could be used for the selection of wave directions in 3D are also summarised and used. The developed elements allow us to relax the traditional requirement which consists to consider many nodal points per wavelength, used with low order polynomial based finite elements, and therefore solve elastic wave problems without refining the mesh of the computational domain at each frequency. The effectiveness of the proposed technique is determined by comparing solutions for selected problems with available analytical models or to high resolution numerical results using conventional finite elements, by considering the effect of the mesh size and the number of enriching 3D plane waves. Both balanced and unbalanced choices of plane wave directions in space on structured mesh grids are investigated for assessing the accuracy and conditioning of this 3D PUFEM model for elastic waves.

Item Type:Article
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.apm.2017.05.013
Publisher statement: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. Permission is not required for this type of reuse.
Date accepted:07 May 2017
Date deposited:17 May 2017
Date of first online publication:12 May 2017
Date first made open access:No date available

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