| Issue |
ESAIM: M2AN
Volume 46, Number 1, January-February 2012
|
|
|---|---|---|
| Page(s) | 39 - 57 | |
| DOI | https://doi.org/10.1051/m2an/2011017 | |
| Published online | 22 July 2011 | |
A numerical minimization scheme for the complex Helmholtz equation
1
Department of Mathematics, Michigan State University, East Lansing, 48824 Michigan, USA. richins@math.msu.edu
2
Department of Mathematics, University of Utah, Salt Lake City, 84112 Utah, USA. dobson@math.utah.edu
Received:
28
July
2010
Revised:
20
April
2011
We use the work of Milton, Seppecher, and Bouchitté on variational principles for waves in lossy media to formulate a finite element method for solving the complex Helmholtz equation that is based entirely on minimization. In particular, this method results in a finite element matrix that is symmetric positive-definite and therefore simple iterative descent methods and preconditioning can be used to solve the resulting system of equations. We also derive an error bound for the method and illustrate the method with numerical experiments.
Mathematics Subject Classification: 65N30 / 35A15
Key words: Variational methods / Helmholtz equation / finite element methods
© EDP Sciences, SMAI, 2011
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