One- and Two-Level Domain Decomposition Methods for Nonlinear Problems

被引：0

作者：

Badea, L. ^{[1
]}

机构：

[1] Romanian Acad, Inst Math, Bucharest, Romania

来源：

PROCEEDINGS OF THE FIRST INTERNATIONAL CONFERENCE ON PARALLEL, DISTRIBUTED AND GRID COMPUTING FOR ENGINEERING | 2009年 / 90期

关键词：

domain decomposition methods; nonlinear variational inequalities; fixed-point problems; quasi-variational inequalities; multigrid and multilevel methods; contact problems with friction; nonlinear obstacle problems; SCHWARZ ALTERNATING METHODS; MONOTONE MULTIGRID METHODS; VARIATIONAL-INEQUALITIES; CONVERGENCE;

D O I：

暂无

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this paper we synthesize the results in [1] - [6] concerning the convergence rate of the one- and two-level methods for some nonlinear problems: nonlinear variational inequalities, inequalities with contraction operators, variational inequalities of the second kind and quasi-variational inequalities. Also, we verify that the convergence rates obtained by numerical tests are really in concordance with the theoretical ones. We comparatively illustrate the convergence rates of the one- and two-level methods by numerical experiments for the solution of the two-obstacle problem of a nonlinear elastic membrane.

引用

页码：71 / 88

页数：18

共 50 条

[21] TWO-LEVEL METHODS FOR VARIATIONAL INEQUALITIES OF THE SECOND KIND AND QUASI-VARIATIONAL INEQUALITIES [J].

Badea, Lori .

REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES, 2018, 63 (04) :315-338

[22] Homogeneous and heterogeneous domain decomposition methods for plate bending problems [J].

Gervasio, P .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2005, 194 (42-44) :4321-4343

[23] A two-level method for mimetic finite difference discretizations of elliptic problems [J].

Antonietti, Paola F. ;

Verani, Marco ;

Zikatanov, Ludmil .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2015, 70 (11) :2674-2687

[24] An Adapted Coarse Space for Balancing Domain Decomposition Methods in Nonlinear Elastodynamics [J].

University of Perpignan, 52 Avenue Paul-Alduy, Perpignan, 66860, France .

Lect. Notes Comput. Sci. Eng., 2007, (481-488) :481-488

[25] Differential-Difference Iterative Domain Decomposition Methods for the Problems of Contact of Elastic Bodies with Nonlinear Winkler Surface Layers [J].

Prokopyshyn І.І. ;

Shakhno S.M. .

Journal of Mathematical Sciences, 2022, 261 (1) :41-58

[26] Domain decomposition algorithms for mixed methods for second order elliptic problems [J].

Chen, ZX ;

Ewing, RE ;

Lazarov, R .

MATHEMATICS OF COMPUTATION, 1996, 65 (214) :467-490

[27] Schur complement domain decomposition methods for the solution of multiple scattering problems [J].

Pedneault, Michael ;

Turc, Catalin ;

Boubendir, Andyassine .

IMA JOURNAL OF APPLIED MATHEMATICS, 2017, 82 (05) :1104-1134

[28] Domain decomposition methods for parallel solution of shape sensitivity analysis problems [J].

Papadrakakis, M ;

Tsompanakis, Y .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1999, 44 (02) :281-303

[29] An efficient two-level preconditioner for multi-frequency wave propagation problems [J].

Baumann, Manuel ;

van Gijzen, Martin B. .

APPLIED NUMERICAL MATHEMATICS, 2019, 135 :316-332

[30] A CONSERVATIVE DOMAIN DECOMPOSITION PROCEDURE FOR NONLINEAR DIFFUSION PROBLEMS ON ARBITRARY QUADRILATERAL GRIDS [J].

Yuan, Guangwei ;

Yao, Yanzhong ;

Yin, Li .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2011, 33 (03) :1352-1368

← 1 2 3 4 5 →