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

收藏

页码：71 / 88

页数：18

相关论文

共 50 条

[41] Energy-minimizing coarse spaces for two-level Schwarz methods for multiscale PDEs [J].

Van Lent, Jan ;

Scheichl, Robert ;

Graham, Ivan G. .

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2009, 16 (10) :775-799

[42] A two-level linearized compact ADI scheme for two-dimensional nonlinear reaction-diffusion equations [J].

Wu, Fengyan ;

Cheng, Xiujun ;

Li, Dongfang ;

Duan, Jinqiao .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2018, 75 (08) :2835-2850

[43] Nonlinear localization strategies for domain decomposition methods: Application to post-buckling analyses [J].

Cresta, Philippe ;

Allix, Olivier ;

Rey, Christian ;

Guinard, Stephane .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2007, 196 (08) :1436-1446

[44] A matrix-free parallel two-level deflation preconditioner for two-dimensional heterogeneous Helmholtz problems [J].

Chen, Jinqiang ;

Dwarka, Vandana ;

Vuik, Cornelis .

JOURNAL OF COMPUTATIONAL PHYSICS, 2024, 514

[45] Optimized Algebraic Interface Conditions in Domain Decomposition Methods for Strongly Heterogeneous Unsymmetric Problems [J].

Dipartimento di Matematica, Università di Trento, Italy ;

不详 .

Lect. Notes Comput. Sci. Eng., 2007, (189-196) :189-196

[46] Substructured two-grid and multi-grid domain decomposition methods [J].

Ciaramella, G. ;

Vanzan, T. .

NUMERICAL ALGORITHMS, 2022, 91 (01) :413-448

[47] Substructured two-grid and multi-grid domain decomposition methods [J].

G. Ciaramella ;

T. Vanzan .

Numerical Algorithms, 2022, 91 :413-448

[48] Recent advances in domain decomposition methods for large-scale saddle point problems [J].

Nataf, Frederic ;

Tournier, Pierre-Henri .

COMPTES RENDUS MECANIQUE, 2022, 350

[49] Two kinds of Conjugate Gradient Methods for Solving NonLinear Complementarity Problems [J].

Chu, Ajie ;

Du, Shouqiang ;

Su, Yixiao .

2015 CHINESE AUTOMATION CONGRESS (CAC), 2015, :108-114

[50] Stability and convergence of two-level iterative methods for the stationary incompressible magnetohydrodynamics with different Reynolds numbers [J].

Tao, ZhenZhen ;

Zhang, Tong .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 428 (01) :627-652

← 1 2 3 4 5 →