A FAST NUMERICAL METHOD FOR SOLVING A REGULARIZED PROBLEM ASSOCIATED WITH OBSTACLE PROBLEMS

被引：2

作者：

Yuan, DaMing ^{[1
,2
]}

Li, Xi ^{[1
]}

Lei, ChengFeng ^{[1
]}

机构：

[1] Nanchang Hangkong Univ, Coll Math & Informat Sci, Nanchang 330063, Peoples R China

[2] Zhejiang Univ, Dept Math, Hangzhou 310027, Peoples R China

来源：

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2012年 / 49卷 / 05期

基金：

美国国家科学基金会;

关键词：

Rung-Kutta method; level set method; obstacle problem; ELLIPTIC VARIATIONAL-INEQUALITIES; MONOTONE MULTIGRID METHODS; SET METHODS; ALGORITHMS; EQUATIONS; FRONTS;

D O I：

10.4134/JKMS.2012.49.5.893

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Kirsi Majava and Xue-Cheng Tai [12] proposed a modified level set method for solving a free boundary problem associated with unilateral obstacle problems. The proximal bundle method and gradient method were applied to solve the nonsmooth minimization problems and the regularized problem, respectively. In this paper, we extend this approach to solve the bilateral obstacle problems and employ Rung-Kutta method to solve the initial value problem derived from the regularized problem. Numerical experiments are presented to verify the efficiency of the methods.

引用

页码：893 / 905

页数：13

共 23 条

[1] The fast construction of extension velocities in level set methods [J].

Adalsteinsson, D ;

Sethian, JA .

JOURNAL OF COMPUTATIONAL PHYSICS, 1999, 148 (01) :2-22

[2]

[Anonymous], 1984, Numerical Methods for Nonlinear Variational Problems

[3] ITERATIVE SOLUTION OF PIECEWISE LINEAR SYSTEMS [J].

Brugnano, Luigi ;

Casulli, Vincenzo .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2008, 30 (01) :463-472

[4] ON PARTIAL DIFFERENCE EQUATIONS OF MATHEMATICAL PHYSICS [J].

COURANT, R ;

FRIEDRICHS, K ;

LEWY, H .

IBM JOURNAL OF RESEARCH AND DEVELOPMENT, 1967, 11 (02) :215-+

[5]

Duvaut G., 1976, INEQUALITIES MECH PH, Vfirst, DOI [10.1007/978-3-642-66165-5, DOI 10.1007/978-3-642-66165-5]

[6] ADAPTIVE MULTILEVEL METHODS FOR OBSTACLE PROBLEMS [J].

HOPPE, RHW ;

KORNHUBER, R .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1994, 31 (02) :301-323

[7] MULTIGRID ALGORITHMS FOR VARIATIONAL-INEQUALITIES [J].

HOPPE, RHW .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1987, 24 (05) :1046-1065

[8]

Howison S, 1995, MATH FINANCIAL DERIV

[9] Augmented Lagrangian active set methods for obstacle problems [J].

Kärkkäinen, T ;

Kunisch, K ;

Tarvainen, P .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2003, 119 (03) :499-533

[10]

KORNHUBER R, 1994, NUMER MATH, V69, P167

← 1 2 3 →