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自由边界问题的线性互补投影迭代算法 被引量：7

On Linear Complementarity-Projection Iterative Algorithm for Seepage with Free Boundary Problem
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摘要 对一类自由边界问题,提出了基于线性互补问题的投影迭代算法.用有限差分对微分模型离散化后得到一个正定线性互补问题,然后导出与之等价的不动点问题,从而提出求解线性互补问题的投影迭代算法.利用投影原理,证明了该算法的收敛性.数值结果表明了算法的可行性和有效性. The projection iterative algorithm based on linear complementarity problem for solving the free boundary problem has been presented in this paper. When the finite differential method is used to discrete the problem, a positive definite linear complementarity problem which is equivalent to a fixed point prob- lem have been obtained, and a projection iterative algorithm deduced. With positive definiteness and pro- jection principle, the convergence of the algorithm has been proved. The process of the iterative algorithm has been provided, and the numerical results presented to illustrate the feasibility and effectiveness of this algorithm.
作者 张守贵
机构地区 重庆师范大学数学学院
出处 《西南师范大学学报（自然科学版）》 CAS CSCD 北大核心 2013年第7期15-19,共5页 Journal of Southwest China Normal University(Natural Science Edition)
基金 国家自然科学基金资助项目(11101454) 重庆师范大学科研项目(13XL001)
关键词 自由边界问题 有限差分 线性互补 不动点 投影迭代 free boundary problem finite difference linear complementarity fixed point projection iterative
分类号 O241.182 [理学—计算数学]
  • 相关文献

参考文献11

  • 1余颖禾,孙鹰,郭小明.具有自由边界的二维渗流问题[J].应用数学和力学,1996,17(6):523-527. 被引量：4
  • 2JIANG B, BRUCH J C, SLOSS J M. A Non-Overlapping Domain Decomposition Method for Variational Inequalities Derived from Free Boundary Problems [J]. Numer Meth Part D E, 2006, 22(1): 1-17.
  • 3PIERMATEI FILHO O, LEONTIEV A. An Optimization Approach for Unconfined Seepage Problem with Semipermea hie Conditions [J]. Struct Multidiscip Optim, 2009, 39(6): 581-588.
  • 4LIN Y, CRYER C W. An Alternating Direction Implicit Algorithm for the Solution of Linear Complementarity Problems Arising from Free Boundary Problems [J]. Appl Math Optim, 1985, 13(1) : 1-17.
  • 5CHAIYO K, RATTANADECHO P, CHANTASIRIWAN S. The Method of Fundamental Solutions for Solving Free Boundary Saturated Seepage Problem [J]. Int Commun Heat Mass, 2011, 38(2) : 249-254.
  • 6YUAN D M, CHENG X L. A Meshless Method for Solving the Free Boundary Problem Associated with Unilateral Obstacle[J]. J Comput Math, 2012, 89(1): 90-97.
  • 7NOOR M A, NOOR K I, HUANG Z Y, et al. Implicit Schemes for Solving Extended General Nonconvex Variational Inequalities[J]. J ApplMath, 2012(1): 1-10.
  • 8李胜坤.对称正定线性互补问题的一种广义模方法(英文)[J].西南大学学报（自然科学版）,2010,32(9):68-71. 被引量：2
  • 9龚黔芬,闻道君.非凸变分不等式和Wiener-Hopf方程的逼近方法[J].西南师范大学学报（自然科学版）,2012,37(2):34-37. 被引量：4
  • 10ITO K R, KUNISCH K G. Semi-Smooth Newton Methods for the Signorini Problem[J]. Appl Math, 2008, 53(5) : 455-468.

二级参考文献20

  • 1Cottle R, Pang J S, Stone R. The Linear Complementarity Problem [M]. San Diego: Academic Press, 1992.
  • 2Li Y T, Dai P F. Generalized AOR Methods for Linear Complementarity Problem [J]. Appl Math Comput, 2007, 188(1) : 7 -- 18.
  • 3Van Bokhoven W. Piecewise-Linear Modelling and Analysis [M]. Proefschrift: Eindhoven, 1981.
  • 4Schafur U. On the Modulus Algorithm for the Linear Complementarity Problem [J]. Oper Res Lett, 2004, 32 (4): 350 -- 354.
  • 5Dong J L, Jiang M Q. A Modified Modulus Method for Symmetric Positive-Definite Linear Complementarity Problems [J]. Numer Linear Algebra Appl, 2009, 16(2): 129--143.
  • 6Bai Z Z, Golub G, Ng M. Herimitian and Skew Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems [J]. SIAMJ Matrix AnalAppl, 2003, 24(3): 603--626.
  • 7CLARKE F H,LEDYAEV Y S,WOLENSKI P R.Nonsmooth Analysis and Control Theory[M].Berlin:Springer,1998.
  • 8POLIQUIN R A,ROCKAFELLAR R T,THIBAULT L.Local Differentiability of Distance Functions[J].Trans Am Math Soc,2000,352:5231-5249.
  • 9NOOR M A.Projection Methods for Nonconvex Variational Inequalities[J].Optim Lett,2009(3):411-418.
  • 10NOOR M A.Some Iterative Methods for Nonconvex Variational Inequalities[J].Comput Math Model,2010,21(1):97-108.

共引文献6

同被引文献24

  • 1王传伟.一个求解变分不等式问题的投影算法[J].重庆师范大学学报（自然科学版）,2005,22(1):6-10. 被引量：4
  • 2孙洪春,孙敏,李国成.广义变分不等式的一个投影型算法及收敛速度[J].重庆师范大学学报（自然科学版）,2005,22(3):53-57. 被引量：1
  • 3LIN Y, CRYER C W. An Alternating Direction Implicit Algorithm for the Solution of Linear Complementarity Problems Arising from Free Boundary Problems [J]. Appl Math Optim, 1985, 13(1): 1-17.
  • 4FAN C M, LIU C S, YEI H W, et al. The Scalar Homotopy Method for Solving Non-Linear Obstacle Problem [J]. Comput Mater Con, 2010, 15(1): 67-86.
  • 5ZHANG Y M. Multilevel Proiection Algorithm for Solving Obstacle Problems [J]. Comput Math Appl, 2001, 41(12): 1505-1513.
  • 6XUE L, CHANG X L. An Algorithm for Solving the Obstacle Problems [J]. Comput Math Appl, 2004, 48(10-11): 1651-1657.
  • 7PIERMATEI FILHO O, LEONT1EV A. An Optimization Approach for Unconfined Seepage Problem with Semipermea- ble Conditions [J]. Struct Multidisc Optim, 2009, 39(6): 581-588.
  • 8CHAIYO K, RATTANADECHO P, CHANTASIRIWAN S. The Method of Fundamental Solutions for Solving Free Boundary Saturated Seepage Problem [J]. Int Commun Heat Mass, 2011, 38(2): 249-254.
  • 9YUAN D M, CHENG X L. A Meshless Method for Solving the Free Boundary Problem Associated with Unilateral Ob- stacle [J]. J Comput Math, 2012, 89(1): 90-97.
  • 10HE B S. Improvements of some Projection Methods for Monotone Nonlinear Variational Inequalities [J]. J Optimiz The- ory App, 2002, 112(1): 111-128.

引证文献7

二级引证文献8

西南师范大学学报（自然科学版）
2013年 第7期

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