A generalized plane-wave numerical method for smooth nonconstant coefficients

Lise Marie Imbert-Gérard; Bruno Després

doi:10.1093/imanum/drt030

A generalized plane-wave numerical method for smooth nonconstant coefficients

Lise Marie Imbert-Gérard, Bruno Després

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

We propose an original method based on generalized plane waves and approximated coefficients for the numerical approximation of the Helmholtz equation with a smooth nonconstant coefficient. This is justified by a high-order convergence estimate rate. Our motivation stems from Maxwell's equations with Hermitian dielectric tensor ε which are used to model reflectometry in fusion plasma. Simplified models split them into two different propagation modes. Some numerical results are presented in dimensions 1 and 2.

Original language	English (US)
Pages (from-to)	1072-1103
Number of pages	32
Journal	IMA Journal of Numerical Analysis
Volume	34
Issue number	3
DOIs	https://doi.org/10.1093/imanum/drt030
State	Published - Jul 2014
Externally published	Yes

Keywords

generalized plane waves
high order
wave equations

ASJC Scopus subject areas

General Mathematics
Computational Mathematics
Applied Mathematics

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10.1093/imanum/drt030

Cite this

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abstract = "We propose an original method based on generalized plane waves and approximated coefficients for the numerical approximation of the Helmholtz equation with a smooth nonconstant coefficient. This is justified by a high-order convergence estimate rate. Our motivation stems from Maxwell's equations with Hermitian dielectric tensor ε which are used to model reflectometry in fusion plasma. Simplified models split them into two different propagation modes. Some numerical results are presented in dimensions 1 and 2.",

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AU - Després, Bruno

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AB - We propose an original method based on generalized plane waves and approximated coefficients for the numerical approximation of the Helmholtz equation with a smooth nonconstant coefficient. This is justified by a high-order convergence estimate rate. Our motivation stems from Maxwell's equations with Hermitian dielectric tensor ε which are used to model reflectometry in fusion plasma. Simplified models split them into two different propagation modes. Some numerical results are presented in dimensions 1 and 2.

KW - generalized plane waves

KW - high order

KW - wave equations

UR - https://www.scopus.com/pages/publications/84904153204

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DO - 10.1093/imanum/drt030

M3 - Article

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ER -

A generalized plane-wave numerical method for smooth nonconstant coefficients

Abstract

Keywords

ASJC Scopus subject areas

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