TWO-GRID METHODS FOR MAXWELL EIGENVALUE PROBLEMS

被引：58

作者：

Zhou, J. ^{[1
]}

Hu, X. ^{[2
]}

Zhong, L. ^{[3
]}

Shu, S. ^{[1
]}

Chen, L. ^{[4
]}

机构：

[1] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Peoples R China

[2] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[3] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

[4] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2014年 / 52卷 / 04期

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

two-grid method; Maxwell eigenvalue problem; edge element; FINITE-ELEMENT METHODS; INVERSE ITERATION; MULTILEVEL METHOD; CONVERGENCE; COMPUTATION; EQUATIONS; PRECONDITIONERS; APPROXIMATION; H(CURL); H(DIV);

D O I：

10.1137/130919921

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Two new two-grid algorithms are proposed for solving the Maxwell eigenvalue problem. The new methods are based on the two-grid methodology recently proposed by Xu and Zhou [Math. Comp., 70 (2001), pp. 17-25] and further developed by Hu and Cheng [Math. Comp., 80 (2011), pp. 1287-1301] for elliptic eigenvalue problems. The new two-grid schemes reduce the solution of the Maxwell eigenvalue problem on a fine grid to one linear indefinite Maxwell equation on the same fine grid and an original eigenvalue problem on a much coarser grid. The new schemes, therefore, save total computational cost. The error estimates reveals that the two-grid methods maintain asymptotically optimal accuracy, and the numerical experiments presented confirm the theoretical results.

引用

页码：2027 / 2047

页数：21