Nonlinear Schwarz iterations with reduced rank extrapolation

被引：9

作者：

Duminil, Sebastien ^{[1
]}

Sadok, Hassane ^{[1
]}

Szyld, Daniel B. ^{[2
]}

机构：

[1] Univ Littoral, Lab Math Pures & Appl, Ctr Univ Mi Voix, F-62228 Calais, France

[2] Temple Univ 038 16, Dept Math, Philadelphia, PA 19122 USA

来源：

APPLIED NUMERICAL MATHEMATICS | 2015年 / 94卷

基金：

美国国家科学基金会;

关键词：

Vector extrapolation; Schwarz methods; Domain decomposition; Iterative methods; Nonlinear problems; CONVERGENCE; ACCELERATION; EQUATIONS; SYSTEMS;

D O I：

10.1016/j.apnum.2015.04.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Extrapolation methods can be a very effective technique used for accelerating the convergence of vector sequences. In this paper, these methods are used to accelerate the convergence of Schwarz iterative methods for nonlinear problems. A new implementation of the reduced-rank-extrapolation (RRE) method is introduced. Some convergence analysis is presented, and it is shown numerically that certain extrapolation methods can indeed be very effective in accelerating the convergence of Schwarz methods. (C) 2015 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：209 / 221

页数：13

共 30 条

[1]

[Anonymous], 1965, METHOD MOMENTS APPL

[2]

[Anonymous], 2005, SPRINGER SER COMPUT

[3]

Brezinski C., 1975, Calcolo, V12, P317, DOI 10.1007/BF02575753

[4]

Brezinski C., 1991, Extrapolation Methods: Theory and Practice, V2

[5] THE SIMPLIFIED TOPOLOGICAL ε-ALGORITHMS FOR ACCELERATING SEQUENCES IN A VECTOR SPACE [J].

Brezinski, Claude ;

Redivo-Zaglia, Michela .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2014, 36 (05) :A2227-A2247

[6] POLYNOMIAL EXTRAPOLATION METHOD FOR FINDING LIMITS AND ANTI-LIMITS OF VECTOR SEQUENCES [J].

CABAY, S ;

JACKSON, LW .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1976, 13 (05) :734-752

[7]

Cai X.C., 2000, DOMAIN DECOMPOSITION, P343

[8] A restricted additive Schwarz preconditioner for general sparse linear systems [J].

Cai, XC ;

Sarkis, M .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1999, 21 (02) :792-797

[9]

CHEVALIER P., 1998, Domain Decomposition Methods, V10, P400

[10] THE OPTIMIZED SCHWARZ METHOD WITH A COARSE GRID CORRECTION [J].

Dubois, Olivier ;

Gander, Martin J. ;

Loisel, Sebastien ;

St-Cyr, Amik ;

Szyld, Daniel B. .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2012, 34 (01) :A421-A458

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