A Numerical Minimization Scheme for the Complex Helmholtz Equation

Details A Numerical Minimization Scheme for the Complex Helmholtz Equation A Numerical Minimization Scheme for the Complex Helmholtz Equation

2010-07-29

arxiv.org/abs/1007.5319v1

Mathematics

Numerical Analysis

18 pages, 4 figures

Scientific paper

We use the work of Milton, Seppecher, and Bouchitt\'{e} 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.

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