Rate of convergence of some space decomposition methods for linear and nonlinear problems

SIAM Journal on Numerical Analysis

Volumn 35, Issue 4, 1998, Pages 1558-1570

  Tai, Xue Cheng ^a   Espedal, Magne ^a  

^a UNIVERSITY OF BERGEN   (Norway)

Author keywords

Domain decomposition; Elliptic equation; Nonlinear; Parallel; Space decomposition

Indexed keywords

EID: 0000986730     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142996297461     Document Type: Article

References (16)

1. J. CEA, Optimisation - théorie et algorithmes, Dunod, Paris, 1971.
2. M. DRYJA AND W. HACKBUSCH, On the Nonlinear Domain Decomposition Method, Report 95-5, Christian-Albrechts-Universität zu Kiel, November 1995.
3. M. DRYJA AND O. B. WIDLUND, Domain decomposition algorithms with small overlap, SIAM J. Sci. Comput., 15 (1994), pp. 604-620.
4. I. EKELAND AND R. TEMAM, Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976.
5. W. HACKBUSCH, Iterative Methods for Large Sparse Linear Systems, Springer, Heidelberg, 1993.
6. B. F. SMITH, P. E. BJØRSTAD, AND W. D. GROPP, Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations, Cambridge University Press, Cambridge, 1996.
7. X.-C. TAI, Parallel Function Decomposition and Space Decomposition Methods with Applications to Optimisation, Splitting and Domain Decomposition, Preprint 231-1992, Institut für Mathematik, Technische Universität Graz, 1992; see also http://www.mi.uib.no/̃tai.
8. X.-C. TAI, Parallel function and space decomposition methods, in Finite Element Methods, Fifty Years of the Courant Element, Lecture Notes in Pure and Appl. Math. 164, P. Neittaanmäki, ed., Marcel Dekker, New York, 1994, pp. 421-432.
9. X.-C. TAI, Domain decomposition for linear and nonlinear elliptic problems via function or space decomposition, in Domain Decomposition Methods in Scientific and Engineering Computing, Proc. of the 7th International Conference on Domain Decomposition, Pennsylvania State University, 1993, D. Keyes and J. Xu, eds., American Mathematical Society, Providence, RI, 1995, pp. 355-360.
10. X.-C. TAI, Parallel function and space decomposition methods - Part I. Function decomposition, Beijing Math., 1 (1995), pp. 104-134.
11. X.-C. TAI, Parallel function and space decomposition methods - Part II. Space decomposition, Beijing Math., 1 (1995), pp. 135-152.
12. X.-C. TAI, A space decomposition method for parabolic problems, Numer. Methods Partial Differential Equations, 14 (1998), pp. 27-46.
13. X.-C. TAI AND M. ESPEDAL, Rate of Convergence of a Space Decomposition Method and Applications to Linear and Nonlinear Elliptic Problems, Report 103, Mathematics Department, University of Bergen, 1996; see also http://www.mi.uib.no/̃tai.
14. X.-C. TAI AND M. ESPEDAL, A space decomposition method for minimization problems, in Proc. of the 9th Domain Decomposition Conference, June 3-8, 1996, Ullensvang, Norway, P. Bjørstad, M. Espedal, and D. Keyes, eds., John Wiley and Sons, to appear; see also http://www.mi.uib.no/̃tai.
15. O. WIDLUND, Some Schwartz methods for symmetric and nonsymmetric elliptic problems, in Proc. 5th International Symposium on Domain Decomposition Methods for Partial Differential Equations, Norfolk, VA, May 1991, SIAM, Philadelphia, 1992.
16. J. C. Xu, Iteration methods by space decomposition and subspace correction, SIAM Rev., 34 (1992), pp. 581-613.