Modelling of short wave diffraction problems using approximating systems of plane waves

By Omar Laghrouche, P. Bettess, R. Astley. 2002

137 citations recorded by the source corpus.

This paper describes a finite element model for the solution of Helmholtz problems at higher frequencies that offers the possibility of computing many wavelengths in a single finite element. The approach is based on partition of unity isoparametric elements. At each finite element node the potential is expanded in a discrete series of planar waves, each propagating at a specified angle. These angles can be uniformly distributed or may be carefully chosen. They can also be the same for all nodes of the studied mesh or may vary from one node to another. The implemented approach is used to solve a few practical problems such as the diffraction of plane waves by cylinders and spheres. The wave number is increased and the mesh remains unchanged until a single finite element contains many wavelengths in each spatial direction and therefore the dimension of the whole problem is greatly reduced. Issues related to the integration and the conditioning are also discussed. Copyright © 2002 John Wiley & Sons, Ltd.

Subfields: Atomic and Molecular Physics, and Optics, Mechanics of Materials, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/26920a10ffe2351d69dc9155161a79fc315ade5a

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In Atomic and Molecular Physics, and Optics

In Mechanics of Materials

In Ocean Engineering

Citations in the corpus

A finite element method enriched for wave propagation problems (2012, methodology): “For time harmonic wave problems, the partition of unity finite element method has been proposed for the solution of Helmholtz problems at high frequencies [24] [25] [26] [27].”
A review of finite-element methods for time-harmonic acoustics (2006, methodology): “Another approach to reducing integration costs is given in [25, 118].”
PLANE WAVE DISCONTINUOUS GALERKIN METHODS: ANALYSIS OF THE h-VERSION ∗, ∗∗ (2009, methodology): “This has been attempted in the partition of unity (PUM) finite element method [3,20,25,26,28], the discontinuous enrichment approach [14,15,33], in the context of least squares approaches [27,32], and in the so-called “Variational Theory of Complex Rays” (VTCR) approach [29].”