[1]曾玉平,陈金如.求解H(div)-椭圆问题的最优型区域分解算法(英文)[J].南京师大学报(自然科学版),2012,35(04):1-6.
 Zeng Yuping,Chen Jinru.Optimization-Based Domain Decomposition Methods for H(div)-Elliptic Problem[J].Journal of Nanjing Normal University(Natural Science Edition),2012,35(04):1-6.
点击复制

求解H(div)-椭圆问题的最优型区域分解算法(英文)()
分享到:

《南京师大学报(自然科学版)》[ISSN:1001-4616/CN:32-1239/N]

卷:
第35卷
期数:
2012年04期
页码:
1-6
栏目:
数学
出版日期:
2012-12-20

文章信息/Info

Title:
Optimization-Based Domain Decomposition Methods for H(div)-Elliptic Problem
作者:
曾玉平;陈金如;
南京师范大学数学科学学院,江苏省大规模复杂系统数值模拟重点实验室,江苏南京210023
Author(s):
Zeng YupingChen Jinru
Jiangsu Key Laboratory for NSLSCS,School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China
关键词:
最优型区域分解算法H( div) - 椭圆问题
Keywords:
optimization domain decomposition methodH( div) -elliptic problem
分类号:
O175
摘要:
本文提出了几种求解H(div)-椭圆问题的最优型区域分解算法,通过适当参数的选取,论证了算法的收敛性.数值实验验证了算法的有效性.
Abstract:
In this paper,we propose some optimization-based domain decomposition methods for H( div) -elliptic problem. Convergent properties are examined by choosing proper parameters. Some numerical testes are presented to demonstrate the effectiveness of the method.

参考文献/References:

[1] Smith B F,Bjorstad P,Gropp W D. Domain Decomposition: Parallel Multilevel Algorithms for Elliptic Partial Equations[M]. New York: Cambridge Univerdsity Press, 1996.
[2] Quarteroni A,Valli A. Domain Decomposition Methods for Partial Equations[M]. Oxfrod: Oxford University Press, 1999.
[3] Toselli A,Widlund O B. Domain Decomposition Methods—Algorithms and Theory[M]. Berlin: Springer-Verlag, 2005.
[4] Xu J,Zou J. Some nonoverlapping domain decomposition methods[J]. SIAM Rev, 1998, 40( 4) : 857-914.
[5] Du Q. Optimization based nonoverlapping domain decomposition algorithms and their convergence[J]. SIAM J Numer Anal, 2001, 39( 3) : 1 056-1 077.
[6] Du Q,Gunzburger M D. A gradient method approach to optimization based multidisciplinary simulations and nonoverlapping domain decomposition algorithms[J]. SIAM J Numer Anal, 2000, 37( 5) : 1 513-1 541.
[7] Gunzburger M D,Lee H K. An optimization-based domain decomposition method for the Navier-Stokes equations[J]. SIAM J Numer Anal, 2000, 37( 5) : 1 455-1 480.
[8] Gunzburger M D,Heikenschloss M,Lee H K. Solution of elliptic partial differential equations by an optimization-based domaind decompostion method[J]. Appl Math Comput, 2000, 113( 2) : 111-139.
[9] Gunzburger M D,Peterson J,Lee H K. An optimization based domain decomposition method for partial differential equations [J]. Comp Math Appl, 1999, 37( 10) : 77-93.
[10] Bresch D,Koko J. Oprator-splitting and lagranger multiplier domain decomposition methods for numerical simulation of two coupled Navier-Stokes fluids[J]. Int J Appl Math Comput Sci, 2006, 16( 16) : 419-429.
[11] Arnold D N,Falk R S,Winther R. Multigrid preconditioning in H( div) and application[J]. Math Comp, 1997, 66( 219) : 957- 984.
[12] Arnold D N,Falk R S,Winther R. Multigrid in H( div) and H( curl) [J]. Numer Math, 2000, 85( 2) : 197-217.
[13] Hiptmair R. Multigrid method for H( div) in three dimensions[J]. Electron Tran Numer Anal, 1997,6 : 133-152.
[14] Hiptmair R,Toselli A. Overlapping and multilevel Schwarz methods for vector valued elliptic problems in three dimensions, in Parallel Solution of PDEs[C]/ /IMA Volumes in Mathematics and its Applications. Berlin: Springer-Verlag, 2000.
[15] Wohlmuth B I,Toselli A,Widlund O B. An iterative substructuring method for Raviart-Thomas vector fileds in three dimensions [J]. SIAM J Numer Anal, 2000, 37( 5) : 1 657-1 676.
[16] Tosseli A. Neuman-Neuman methods for vector field problems[J]. Electron Tran Numer Anal, 2000, 11: 1-24.
[17] Raviart P A,Thomas J M. A mixed finite element method for second order elliptic problems[C]/ /Lecture Notes in Math. Berlin- Heidelberg,New York: Springer, 1977, 66: 292-315.
[18] Brezzi F,Fortin M. Mixed and Hybrid Finite Element Methods[M]. New York: Springer-Verlag, 1991.
[19] Ahusborde E,Aza¨lez M,Deville M O, et al. An iterative domain decomposition algorithm for the grad( div) operator[J]. Commun Comput Phys, 2009,5 ( 2 /4) : 391-397.

备注/Memo

备注/Memo:
Foundation item: Supported by NSFC( 11071124) . Corresponding author: Chen Jinru,professor,majored in numerical methods for partial equations. E-mail: jrchen@ njnu. edu. cn
更新日期/Last Update: 2013-03-11