# A numerical minimization scheme for the complex Helmholtz equation

Russell B. Richins; David C. Dobson

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

- Volume: 46, Issue: 1, page 39-57
- ISSN: 0764-583X

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topRichins, Russell B., and Dobson, David C.. "A numerical minimization scheme for the complex Helmholtz equation." ESAIM: Mathematical Modelling and Numerical Analysis 46.1 (2011): 39-57. <http://eudml.org/doc/222121>.

@article{Richins2011,

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.
},

author = {Richins, Russell B., Dobson, David C.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Variational methods; Helmholtz equation; finite element methods; variational methods; error bound; numerical experiments},

language = {eng},

month = {7},

number = {1},

pages = {39-57},

publisher = {EDP Sciences},

title = {A numerical minimization scheme for the complex Helmholtz equation},

url = {http://eudml.org/doc/222121},

volume = {46},

year = {2011},

}

TY - JOUR

AU - Richins, Russell B.

AU - Dobson, David C.

TI - A numerical minimization scheme for the complex Helmholtz equation

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2011/7//

PB - EDP Sciences

VL - 46

IS - 1

SP - 39

EP - 57

AB -
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.

LA - eng

KW - Variational methods; Helmholtz equation; finite element methods; variational methods; error bound; numerical experiments

UR - http://eudml.org/doc/222121

ER -

## References

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