Multilevel preconditioned iterative eigensolvers for Maxwell eigenvalue problems

被引：26

作者：

Arbenz, P ^{[1
]}

Geus, R ^{[1
]}

机构：

[1] ETH, Inst Computat Sci, CH-8092 Zurich, Switzerland

来源：

APPLIED NUMERICAL MATHEMATICS | 2005年 / 54卷 / 02期

关键词：

Maxwell equation; generalized eigenvalue problem; Jacobi-Davidson; LOBPCG; smoothed aggregation AMG preconditioner;

D O I：

10.1016/j.apnum.2004.09.026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate eigensolvers for computing a few of the smallest eigenvalues of a generalized eigenvalue problem resulting from the finite element discretization of the time independent Maxwell equation. Various multilevel preconditioners are employed to improve the convergence and memory consumption of the Jacobi-Davidson algorithm and of the locally optimal block preconditioned conjugate gradient (LOBPCG) method. We present numerical results of very large eigenvalue problems originating from the design of resonant cavities of particle accelerators. (c) 2004 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：107 / 121

页数：15

共 33 条

[21]

KIKUCHI F, 1987, COMPUT METHOD APPL M, V64, P509, DOI 10.1016/0045-7825(87)90053-3

[22] Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method [J].

Knyazev, AV .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2001, 23 (02) :517-541

[23]

Knyazev AV, 2003, ELECTRON T NUMER ANA, V15, P38

[24] A geometric theory for preconditioned inverse iteration III: A short and sharp convergence estimate for generalized eigenvalue problems [J].

Knyazev, AV ;

Neymeyr, K .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2003, 358 :95-114

[25] SIMULTANEOUS RAYLEIGH-QUOTIENT MINIMIZATION METHODS FOR AX=LAMBDA-BX [J].

LONGSINE, DE ;

MCCORMICK, SF .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1980, 34 (DEC) :195-234

[26]

PARLETT B. N., 1980, The Symmetric Eigenvalue Problem

[27] EXTREME EIGENVALUES OF LARGE SPARSE MATRICES BY RAYLEIGH QUOTIENT AND MODIFIED CONJUGATE GRADIENTS [J].

PERDON, A ;

GAMBOLATI, G .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1986, 56 (03) :251-264

[28] An algebraic multigrid method for finite element discretizations with edge elements [J].

Reitzinger, S ;

Schöberl, J .

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2002, 9 (03) :223-238

[29]

SIVLESTER PP, 1996, FINITE ELEMENTS ELEC

[30]

Sleijpen GLG, 1996, SIAM J MATRIX ANAL A, V17, P401, DOI [10.1137/S0895479894270427, 10.1137/S0036144599363084]

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