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A numerical minimization scheme for the complex Helmholtz equation

Published online by Cambridge University Press:  22 July 2011

Russell B. Richins  and
David C. Dobson
Russell B. Richins
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, 48824 Michigan, USA. richins@math.msu.edu
David C. Dobson
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, 84112 Utah, USA. dobson@math.utah.edu
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Abstract

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.

Keywords

Variational methodsHelmholtz equationfinite element methods
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 1 , January 2012 , pp. 39 - 57
Copyright
© EDP Sciences, SMAI, 2011

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