A sweeping preconditioner for time-harmonic Maxwell's equations with finite elements

被引：21

作者：

Tsuji, Paul ^{[1
]}

Engquist, Bjorn ^{[1
,2
]}

Ying, Lexing ^{[1
,2
]}

机构：

[1] Univ Texas Austin, ICES, Austin, TX 78712 USA

[2] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2012年 / 231卷 / 09期

关键词：

Maxwell's equations; Frequency domain; Finite element methods; Preconditioners; Fast solvers; Perfectly matched layers; Block LDLt factorization; High-frequency waves; HELMHOLTZ-EQUATION;

D O I：

10.1016/j.jcp.2012.01.025

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

This paper is concerned with preconditioning the stiffness matrix resulting from finite element discretizations of Maxwell's equations in the high frequency regime. The moving PML sweeping preconditioner, first introduced for the Helmholtz equation on a Cartesian finite difference grid, is generalized to an unstructured mesh with finite elements. The method dramatically reduces the number of GMRES iterations necessary for convergence, resulting in an almost linear complexity solver. Numerical examples including electromagnetic cloaking simulations are presented to demonstrate the efficiency of the proposed method. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：3770 / 3783

页数：14

共 18 条

[1] A fully asynchronous multifrontal solver using distributed dynamic scheduling [J].

Amestoy, PR ;

Duff, IS ;

L'Excellent, JY ;

Koster, J .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2001, 23 (01) :15-41

[2]

Babuska IM, 2000, SIAM REV, V42, P451

[3] AN ITERATIVE METHOD FOR THE HELMHOLTZ-EQUATION [J].

BAYLISS, A ;

GOLDSTEIN, CI ;

TURKEL, E .

JOURNAL OF COMPUTATIONAL PHYSICS, 1983, 49 (03) :443-457

[4] A PERFECTLY MATCHED LAYER FOR THE ABSORPTION OF ELECTROMAGNETIC-WAVES [J].

BERENGER, JP .

JOURNAL OF COMPUTATIONAL PHYSICS, 1994, 114 (02) :185-200

[5] A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation [J].

Boubendir, Y. ;

Antoine, X. ;

Geuzaine, C. .

JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 231 (02) :262-280

[6] A 3D PERFECTLY MATCHED MEDIUM FROM MODIFIED MAXWELLS EQUATIONS WITH STRETCHED COORDINATES [J].

CHEW, WC ;

WEEDON, WH .

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, 1994, 7 (13) :599-604

[7] Domain decomposition method for harmonic wave propagation: a general presentation [J].

Collino, F ;

Ghanemi, S ;

Joly, P .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2000, 184 (2-4) :171-211

[8] SWEEPING PRECONDITIONER FOR THE HELMHOLTZ EQUATION: MOVING PERFECTLY MATCHED LAYERS [J].

Engquist, Bjoern ;

Ying, Lexing .

MULTISCALE MODELING & SIMULATION, 2011, 9 (02) :686-710

[9] Sweeping Preconditioner for the Helmholtz Equation: Hierarchical Matrix Representation [J].

Engquist, Bjoern ;

Ying, Lexing .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2011, 64 (05) :697-735

[10] Comparison of multigrid and incomplete LU shifted-Laplace preconditioners for the inhomogeneous Helmholtz equation [J].

Erlangga, YA ;

Vuik, C ;

Oosterlee, CW .

APPLIED NUMERICAL MATHEMATICS, 2006, 56 (05) :648-666

← 1 2 →