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A least-squares method for the Helmholtz equation

✍ Scribed by P. Monk; Da-Qing Wang

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 871 KB
Volume: 175
Category: Article
ISSN: 0045-7825
DOI: 10.1016/s0045-7825(98)00326-0

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✦ Synopsis

We investigate the use of least-squares methods to approximate the Helmholtz equation. The basis used in the discrete method consists of st lutions of the Helmholtz equation (either consisting of plane waves or Bessel functions) on each element of a finite element grid. Unlike p~evious methods of this type, we do not use polynomial based finite elements. The use of small elements (and relatively few basis functions per element) allows us to prove convergence theorems for the method and, to some extent, control the conditioning of the resulting linear s} ~tem. Numerical results show the efficiency of the new method and suggest that it may be possible to obtain accurate results with a coarser grid than is usual for standard finite element methods.

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