A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation

被引：88

作者：

Boubendir, Y. ^{[1
,2
]}

Antoine, X. ^{[3
]}

Geuzaine, C. ^{[4
]}

机构：

[1] Univ Heights, Dept Math Sci, Newark, NJ 07102 USA

[2] Univ Heights, NJIT, Ctr Appl Math & Stat, Newark, NJ 07102 USA

[3] Nancy Univ, INRIA Corida Team, IECN, F-54506 Vandoeuvre Les Nancy, France

[4] Univ Liege, Dept Elect Engn & Comp Sci, Inst Montefiore, B-4000 Liege, Belgium

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2012年 / 231卷 / 02期

基金：

美国国家科学基金会;

关键词：

Helmholtz equation; Domain decomposition methods; Finite elements; Pade approximants; PERFECTLY MATCHED LAYER; FINITE-ELEMENT METHODS; ITERATIVE SOLUTION; BOUNDARY-CONDITIONS; INTEGRAL-EQUATIONS;

D O I：

10.1016/j.jcp.2011.08.007

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

This paper presents a new non-overlapping domain decomposition method for the Helmholtz equation, whose effective convergence is quasi-optimal. These improved properties result from a combination of an appropriate choice of transmission conditions and a suitable approximation of the Dirichlet to Neumann operator. A convergence theorem of the algorithm is established and numerical results validating the new approach are presented in both two and three dimensions. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：262 / 280

页数：19

共 45 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]

[Anonymous], 1996, Iterative Methods for Sparse Linear Systems

[3] Alternative integral equations for the iterative solution of acoustic scattering problems [J].

Antoine, X ;

Darbas, M .

QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 2005, 58 :107-128

[4] Bayliss-Turkel-lilte radiation conditions on surfaces of arbitrary shape [J].

Antoine, X ;

Barucq, H .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 229 (01) :184-211

[5]

ANTOINE X, INTEGRAL EQ IN PRESS

[6] Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation [J].

Antoine, Xavier ;

Darbas, Marion .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2007, 41 (01) :147-167

[7] An improved surface radiation condition for high-frequency acoustic scattering problems [J].

Antoine, Xavier ;

Darbas, Marion ;

Lu, Ya Yan .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2006, 195 (33-36) :4060-4074

[8] Phase reduction models for improving the accuracy of the finite element solution of time-harmonic scattering problems I: General approach and low-order models [J].

Antoine, Xavier ;

Geuzaine, Christophe .

JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 228 (08) :3114-3136

[9] BOUNDARY-CONDITIONS FOR THE NUMERICAL-SOLUTION OF ELLIPTIC-EQUATIONS IN EXTERIOR REGIONS [J].

BAYLISS, A ;

GUNZBURGER, M ;

TURKEL, E .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1982, 42 (02) :430-451

[10] RADIATION BOUNDARY-CONDITIONS FOR WAVE-LIKE EQUATIONS [J].

BAYLISS, A ;

TURKEL, E .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1980, 33 (06) :707-725

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