A numerical minimization scheme for the complex Helmholtz equation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 1, p. 39-57

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.

DOI : https://doi.org/10.1051/m2an/2011017
Classification:  65N30,  35A15
Keywords: variational methods, Helmholtz equation, finite element methods
@article{M2AN_2012__46_1_39_0,
     author = {Richins, Russell B. and Dobson, David C.},
     title = {A numerical minimization scheme for the complex Helmholtz equation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {1},
     year = {2012},
     pages = {39-57},
     doi = {10.1051/m2an/2011017},
     zbl = {1272.65095},
     mrnumber = {2846366},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2012__46_1_39_0}
}
Richins, Russell B.; Dobson, David C. A numerical minimization scheme for the complex Helmholtz equation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 1, pp. 39-57. doi : 10.1051/m2an/2011017. http://www.numdam.org/item/M2AN_2012__46_1_39_0/

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