Grid solution of problem with unilateral constraints

被引:6
作者
Chau, M. [1 ]
Laouar, A. [2 ]
Garcia, T. [3 ,4 ]
Spiteri, P. [3 ]
机构
[1] IRT SystemX, 8 Ave Vauve, F-91120 Palaiseau, France
[2] Univ Annaba, Fac Sci, Lab LANOS, Dept Math, BP 12, Annaba 23000, Algeria
[3] UMR CNRS 5505, IRIT ENSEEIHT, 2 Rue Camichel BP 7122, F-31071 Toulouse, France
[4] UVSQ PRISM, 45 Ave Etats Unis, F-78035 Versailles, France
关键词
Variational inequality; Parallel iterative algorithms; Asynchronous iterations; Unilateral constraints problem; Grid computing; Fluid mechanics; MULTISPLITTING METHODS; ITERATIVE METHODS; SCHWARZ; ALGORITHMS; JACOBI;
D O I
10.1007/s11075-016-0224-6
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The present study deals with the solution of a problem, defined in a three-dimensional domain, arising in fluid mechanics. Such problem is modelled with unilateral constraints on the boundary. Then, the problem to solve consists in minimizing a functional in a closed convex set. The characterization of the solution leads to solve a time-dependent variational inequality. An implicit scheme is used for the discretization of the time-dependent part of the operator and so we have to solve a sequence of stationary elliptic problems. For the solution of each stationary problem, an equivalent form of a minimization problem is formulated as the solution of a multivalued equation, obtained by the perturbation of the previous stationary elliptic operator by a diagonal monotone maximal multivalued operator. The spatial discretization of such problem by appropriate scheme leads to the solution of large scale algebraic systems. According to the size of these systems, parallel iterative asynchronous and synchronous methods are carried out on distributed architectures; in the present study, methods without and with overlapping like Schwarz alternating methods are considered. The convergence of the parallel iterative algorithms is analysed by contraction approaches. Finally, the parallel experiments are presented.
引用
收藏
页码:879 / 908
页数:30
相关论文
共 47 条
  • [1] [Anonymous], 1976, ANAL NUMERIQUE INEQU
  • [2] [Anonymous], 1962, Matrix Iterative Analysis
  • [3] [Anonymous], 1972, CAHIER IRIA, V2, P11
  • [4] [Anonymous], 1969, Linear algebra and its applications, DOI DOI 10.1016/0024-3795(69)90028-7
  • [5] Axelson O., 1984, Finite Element Solution of Boundary Value Problems
  • [6] Badea L, 2000, MATH COMPUT, V69, P1341, DOI 10.1090/S0025-5718-99-01164-3
  • [7] Badea L, 2003, SIAM J NUMER ANAL, V41, P1052, DOI [10.1137/S0036142901393607, 10.1137/S0036l42901393607]
  • [8] Chaotic iterative methods for the linear complementarity problems
    Bai, ZZ
    Evans, DJ
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1998, 96 (02) : 127 - 138
  • [9] Matrix multisplitting methods with applications to linear complementarity problems: Parallel asynchronous methods
    Bai, ZZ
    Evans, DJ
    [J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2002, 79 (02) : 205 - 232
  • [10] BARBU V., 1976, Editura Academiei Republicii Socialiste Romania