A Space Decomposition Method for Parabolic Equations

Numerical Methods for Partial Differential Equations

Volumn 14, Issue 1, 1998, Pages 27-46

  Tai, Xue Cheng ^a  

^a UNIVERSITY OF BERGEN   (Norway)

Author keywords

Domain decomposition; Parabolic equation; Parallel; Space decomposition

Indexed keywords

EID: 0040367079     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2426(199801)14:1<27::AID-NUM2>3.0.CO;2-N     Document Type: Article

References (31)

1. J. C. Xu, "Iterative methods by space decomposition and subspace correction," SIAM Review 34, 581-613 (1992).
2. X.-C. Tai, "Parallel function decomposition and space decomposition methods with applications to optimization, splitting and domain decomposition," Preprint No. 231-1992, Institut für Mathematik, Technische Universität Graz (http: //www.mi.uib.no/~tai) (1992).
3. P. Bjørstad and O. Widlund, "Iterative methods for the solution of elliptic problems on regions portioned into substructuring," SIAM J. Numer. Anal. 23, 1097-1120 (1986).
4. o Comput. Meth. Appl. Mech. Eng. 67, 149-159 (1988).
5. o Math. Comp. 47, 103-134 (1986).
6. o Math. Comp. 49, 1-16 (1987).
7. o Math. Comp. 55, 1-21 (1990).
8. o SIAM J. Sci. Comp. 15, 587-604 (1994).
9. o Domain Decomposition Methods for Partial Differential Equations, R. Glowinski, G. H. Golub, G. A. Meurant, and J. Periaux, Eds., SIAM, Philadelphia, 1988, pp. 1-42.
10. o Numer. Math. 60, 41-62 (1991).
11. o Fourth international symposium on Domain decomposition methods for partial differential equations, R. Glowinski, Yuri Kuznetsov, G. A. Meurant, J. Periaux, O. Widlund, Eds., SIAM, Philadelphia, 1991, pp. 264-271.
12. o preprint (1992).
13. R. Ewing and R. D. Lazarov, J. E. Pasciak, and P. S. Vassilevski, "Domain decomposition type iterative techniques for parabolic problems on locally refined grids," SIAM J. Numer. Anal. 30, 1357-1557 (1993).
14. o Sov. J. Numer. Anal. Math. Modelling 3, 99-114 (1988).
15. o University of Bergen, Department of Mathematics, Report No. 102 (1996).
16. o Proceedings of the 9th domain decomposition conference, D. Keyes, P. Bjørstad, and M. Espedal, Eds., John Wiley and Sons, to appear.
17. o Domain decomposition methods in Sciences and Engineering, proceedings of the 8th International Conference on Domain Decomposition Methods, China, R. Glowinski, J. Periaux, Z-C. Shi, and O. Widlund, Eds., John Wiley and Sons, 1997, pp. 317-324.
18. o Computing 49, 11-23 (1992).
19. o Finite element methods, fifty years of the courant element, Lecture notes in pure and applied mathematics, 164, 1994, pp. 367-380.
20. o Technical report of IBM Germany, Heidelberg scientific centre, 1992.
21. o Math, Comp. 57, 63-71 (1991).
22. o Math. Comp. 58, 21-34 (1992).
23. o Lecture notes in mathematics, 1054, Springer, Berlin, 1984.
24. P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.
25. o Beijing Math. 1, 104-134 (1995).
26. o Beijing Math. 1, 135-152 (1995).
27. o Finite element methods, fifty years of the courant element, P. Neittaanmäki, Ed., Lecture notes in pure and applied mathematics, 164, Marcel Dekker, 1994, pp. 421-432.
28. o Domain decomposition methods in scientific and engineering computing, D. Keyes and J. Xu, Eds., Proc. of the 7th international conference on domain decomposition, Penn. State University, 1993, American Mathematical Society, 1995, pp. 355-360.
29. o Proceedings of the 9th domain decomposition conference, D. Keyes, P. Bjørstad and M. Espedal, Eds., John Wiley and Sons, to appear.
30. o SIAM J. Numer. Anal., to appear.
31. o East-west J. Numer. Math. 2, 151-174 (1994).