A multigrid method for Helmholtz transmission eigenvalue problems

Xia Ji; Jiguang Sun; Hehu Xie

doi:10.1007/s10915-013-9794-9

A multigrid method for Helmholtz transmission eigenvalue problems

Xia Ji, Jiguang Sun, Hehu Xie^*

^*Corresponding author for this work

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

59 Citations (Scopus)

Abstract

In this paper, we analyze the convergence of a finite element method for the computation of transmission eigenvalues and corresponding eigenfunctions. Based on the obtained error estimate results, we propose a multigrid method to solve the Helmholtz transmission eigenvalue problem. This new method needs only linear computational work. Numerical results are provided to validate the efficiency of the proposed method.

Original language	English
Pages (from-to)	276-294
Number of pages	19
Journal	Journal of Scientific Computing
Volume	60
Issue number	2
DOIs	https://doi.org/10.1007/s10915-013-9794-9
Publication status	Published - Aug 2014
Externally published	Yes

Keywords

Finite element method
Multigrid method
Transmission eigenvalue

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10.1007/s10915-013-9794-9

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title = "A multigrid method for Helmholtz transmission eigenvalue problems",

abstract = "In this paper, we analyze the convergence of a finite element method for the computation of transmission eigenvalues and corresponding eigenfunctions. Based on the obtained error estimate results, we propose a multigrid method to solve the Helmholtz transmission eigenvalue problem. This new method needs only linear computational work. Numerical results are provided to validate the efficiency of the proposed method.",

keywords = "Finite element method, Multigrid method, Transmission eigenvalue",

author = "Xia Ji and Jiguang Sun and Hehu Xie",

year = "2014",

month = aug,

doi = "10.1007/s10915-013-9794-9",

language = "English",

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T1 - A multigrid method for Helmholtz transmission eigenvalue problems

AU - Ji, Xia

AU - Sun, Jiguang

AU - Xie, Hehu

PY - 2014/8

Y1 - 2014/8

N2 - In this paper, we analyze the convergence of a finite element method for the computation of transmission eigenvalues and corresponding eigenfunctions. Based on the obtained error estimate results, we propose a multigrid method to solve the Helmholtz transmission eigenvalue problem. This new method needs only linear computational work. Numerical results are provided to validate the efficiency of the proposed method.

AB - In this paper, we analyze the convergence of a finite element method for the computation of transmission eigenvalues and corresponding eigenfunctions. Based on the obtained error estimate results, we propose a multigrid method to solve the Helmholtz transmission eigenvalue problem. This new method needs only linear computational work. Numerical results are provided to validate the efficiency of the proposed method.

KW - Finite element method

KW - Multigrid method

KW - Transmission eigenvalue

UR - http://www.scopus.com/inward/record.url?scp=84904249278&partnerID=8YFLogxK

U2 - 10.1007/s10915-013-9794-9

DO - 10.1007/s10915-013-9794-9

M3 - Article

AN - SCOPUS:84904249278

SN - 0885-7474

VL - 60

SP - 276

EP - 294

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

IS - 2

ER -

A multigrid method for Helmholtz transmission eigenvalue problems

Abstract

Keywords

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