A numerical minimization scheme for the complex Helmholtz equation
Richins, Russell B. ; Dobson, David C.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 46 (2012), p. 39-57 / Harvested from Numdam
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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.

Publié le : 2012-01-01
DOI : https://doi.org/10.1051/m2an/2011017
Classification:  65N30,  35A15 
@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},
     volume = {46},
     year = {2012},
     pages = {39-57},
     doi = {10.1051/m2an/2011017},
     mrnumber = {2846366},
     zbl = {1272.65095},
     language = {en},
     url = {http://dml.mathdoc.fr/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, Tome 46 (2012) pp. 39-57. doi : 10.1051/m2an/2011017. http://gdmltest.u-ga.fr/item/M2AN_2012__46_1_39_0/

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