Affiliation:
1. School of Engineering, University of Durham, Durham DH1 3LE, UK
Abstract
The solutions to the Helmholtz equation in the plane are approximated by systems of plane waves. The aim is to develop finite elements capable of containing many wavelengths and therefore simulating problems with large wave numbers without refining the mesh to satisfy the traditional requirement of about ten nodal points per wavelength. At each node of the meshed domain, the wave potential is written as a combination of plane waves propagating in many possible directions. The resulting element matrices contain oscillatory functions and are evaluated using high order Gauss-Legendre integration. These finite elements are used to solve wave problems such as a diffracted potential from a cylinder. Many wavelengths are contained in a single finite element and the number of parameters in the problem is greatly reduced.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Acoustics and Ultrasonics
Cited by
98 articles.
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