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

Laghrouche, O; Bettess, P; Astley, R.J.

Abstract

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 isoparamettic 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.

Citation

Laghrouche, O., Bettess, P., & Astley, R. (2002). Modelling of short wave diffraction problems using approximating systems of plane waves. International Journal for Numerical Methods in Engineering, 54(10), 1501-1533. https://doi.org/10.1002/nme.478

• Journal Article Type: Article
• Publication Date: 2002-08
• Deposit Date: Jan 23, 2007
• Journal: International Journal for Numerical Methods in Engineering
• Print ISSN: 0029-5981
• Electronic ISSN: 1097-0207
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 54
• Issue: 10
• Pages: 1501-1533
• DOI: https://doi.org/10.1002/nme.478
• Keywords: Short waves, Finite elements, Approximating plane waves, Wave diffraction, Economic modelling.