An iterative substructuring method for Raviart-Thomas vector fields in three dimensions

SIAM Journal on Numerical Analysis

Volumn 37, Issue 5, 2000, Pages 1657-1676

  Wohlmuth, Barbara I ^a   Toselli, Andrea ^b   Widlund, Olof B ^b  

^a UNIVERSITY OF AUGSBURG   (Germany)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

Domain decomposition; Iterative substructuring methods; Raviart Thomas finite elements

Indexed keywords

EID: 0013174621     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142998347310     Document Type: Article

References (27)

1. A. ALONSO AND A. VALLI, An optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations, Math. Comp., 68 (1998), pp. 607-631.
2. D. N. ARNOLD, R. S. FALK, AND R. WINTHER, Preconditioning in H(div) and applications, Math. Comp., 66 (1997), pp. 957-984.
3. D. N. ARNOLD, R. S. FALK, AND R. WINTHER, Multigrid in H(div) and H(curl), Technical Report 13 1997/98, Mittag-Leffler Institute, Djursholm, Sweden, 1998.
4. A. BEN ABDALLAH, F. BEN BELGACEM, AND Y. MADAY, Mortaring the two-dimensional "Nédélec" finite elements for the discretization of Maxwell equations, M2AN Math. Model. Numer. Anal., 2000, to appear.
5. 2 projection, Math. Comp., 56 (1991), pp. 463-476.
6. S. C. BRENNER, A multigrid algorithm for the lowest-order Raviart-Thomas mixed triangular finite element method, SIAM J. Numer. Anal., 29 (1992), pp. 647-678.
7. F. BREZZI AND M. FORTIN, Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991.
8. Z. CAI, R. R. PARASHKEVOV, T. F. RUSSEL, AND X. YE, Domain Decomposition for a Mixed Finite Element Method in Three Dimensions, Technical Report CCM-078, University of Colorado, Denver, Center for Computational Mathematics, 1997.
9. M. DAUGE, Elliptic Boundary Value Problems on Corner Domains, Lecture Notes in Math. 1341, Springer-Verlag, New York, 1988.
10. M. DRYJA, B. F. SMITH, AND O. B. WIDLUND, Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions, SIAM J. Numer. Anal., 31 (1994), pp. 1662-1694.
11. R. E. EWING AND J. WANG, Analysis of the Schwarz algorithm for mixed finite element methods, RAIRO Modél. Math. Anal. Numér., 26 (1992), pp. 739-756.
12. R. HIPTMAIR, Multilevel Preconditioning for Mixed Problems in Three Dimensions, Ph.D. thesis, Mathematisches Institut, Universität Augsburg, Germany, 1996.
13. R. HIPTMAIR AND A. TOSELLI, Overlapping and multilevel Schwarz methods for vector valued elliptic problems in three dimensions, in Parallel Solution of PDEs, P. Bjørstad and M. Luskin, eds., IMA Vol. Math. Appl. 120, Springer-Verlag, Berlin, 2000, pp. 181-208, to appear.
14. T. P. MATHEW, Schwarz alternating and iterative refinement methods for mixed formulations of elliptic problems, part I: Algorithms and numerical results, Numer. Math., 65 (1993), pp. 445-468.
15. T. P. MATHEW, Schwarz alternating and iterative refinement methods for mixed formulations of elliptic problems, part II: Theory, Numer. Math., 65 (1993), pp. 469-492.
16. J. NEČAS, Les méthodes directes en théorie des équations elliptiques, Academia, Prague, 1967.
17. D. P. O'LEARY AND O. B. WIDLUND, Capacitance matrix methods for the Helmholtz equation on general three dimensional regions, Math. Comp., 33 (1979), pp. 849-879.
18. A. QUARTERONI AND A. VALLI, Numerical Approximation of Partial Differential Equations, Springer-Verlag, Berlin, 1994.
19. M. V. SARKIS, Schwarz Preconditioners for Elliptic Problems with Discontinuous Coefficients Using Conforming and Non-Conforming Elements, Ph.D. thesis, Courant Institute, New York University, New York, NY, 1994.
20. M. V. SARKIS, Nonstandard coarse spaces and Schwarz methods for elliptic problems with discontinuous coefficients using non-conforming elements, Numer. Math., 77 (1997), pp. 383-406.
21. B. F. SMITH, P. E. BJØRSTAD, AND W. D. GROPP, Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations, Cambridge University Press, Cambridge, UK, 1996.
22. A. TOSELLI, Overlapping Schwarz methods for Maxwell's equations in three dimensions, Numer. Math., 1999, to appear.
23. A. TOSELLI, O. B. WIDLUND, AND B. I. WOHLMUTH, An Iterative Substructuring Method for Maxwell's Equations in Two Dimensions, Technical Report 768, Department of Computer Science, Courant Institute, New York University, New York, NY, 1998.
24. R. VERFÜRTH, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Teubner-Verlag, Stuttgart, 1996.
25. O. B. WIDLUND, Exotic coarse spaces for Schwarz methods for lower order and spectral finite elements, in Seventh International Conference of Domain Decomposition Methods in Scientific and Engineering Computing, D. E. Keyes and J. Xu, eds., Contemp. Math. 180, AMS, Providence, RI, 1994, pp. 131-136.
26. BARBARA I. WOHLMUTH, Adaptive Multilevel-Finite-Elemente Methoden zur Lösung elliptischer Randwertprobleme, Ph.D. thesis, TU München, Munich, Germany, 1995; also available from http://wwwhoppe.math.uni-augsburg.de/german/Wohlmuth/Wohlmuth_pub.html
27. BARABARA I. WOHLMUTH, The Discretization Methods and Iterative Solvers Based on Domain Decomposition Habilitation, thesis, University of Augsburg, Augsburg, Germany, 2000; also available from http://wwwhoppe.math.uni-augsburg.de/german/Wohlmuth/Wohlmuth_pub.html