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^*

^*此作品的通讯作者

CAS - Academy of Mathematics and System Sciences
Michigan Technological University

科研成果: 期刊稿件 › 文章 › 同行评审

68 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	276-294
页数	19
期刊	Journal of Scientific Computing
卷	60
期	2
DOI	https://doi.org/10.1007/s10915-013-9794-9
出版状态	已出版 - 8月 2014
已对外发布	是

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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",

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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 - https://www.scopus.com/pages/publications/84904249278

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

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