A Shifted-Inverse Adaptive Multigrid Method for the Elastic Eigenvalue Problem

被引：17

作者：

Gong, Bo ^{[1
]}

Han, Jiayu ^{[2
]}

Sun, Jiguang ^{[3
]}

Zhang, Zhimin ^{[1
,4
]}

机构：

[1] Beijing Computat Sci Res Ctr, Beijing 100193, Peoples R China

[2] Guizhou Normal Univ, Sch Math Sci, Guiyang 550025, Guizhou, Peoples R China

[3] Michigan Technol Univ, Dept Math Sci, Houghton, MI 49931 USA

[4] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

来源：

COMMUNICATIONS IN COMPUTATIONAL PHYSICS | 2020年 / 27卷 / 01期

基金：

美国国家科学基金会; 中国国家自然科学基金;

关键词：

Elastic eigenvalue problem; shifted-inverse iteration; adaptive multigrid method; FINITE-ELEMENT-METHOD; A-POSTERIORI; APPROXIMATION; DISCRETIZATIONS; SCHEME;

D O I：

10.4208/cicp.OA-2018-0293

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A shifted-inverse iteration is proposed for the finite element discretization of the elastic eigenvalue problem. The method integrates the multigrid scheme and adaptive algorithm to achieve high efficiency and accuracy. Error estimates and optimal convergence for the proposed method are proved. Numerical examples show that the proposed method inherits the advantages of both ingredients and can compute low regularity eigenfunctions effectively.

引用

页码：251 / 273

页数：23

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