Unstructured additive Schwarz-conjugate gradient method for elliptic problems with highly discontinuous coefficients

SIAM Journal of Scientific Computing

Volumn 20, Issue 6, 1999, Pages 2041-2066

  Graham, I G ^a   Hagger, M J ^a  

^a UNIVERSITY OF BATH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; GEOMETRY; MATHEMATICAL MODELS; PROBLEM SOLVING; STIFFNESS MATRIX;

ADDITIVE SCHWARZ; CONJUGATE GRADIENT METHOD; DIAGONAL SCALING; DISCONTINUOUS COEFFICIENT; DOMAIN DECOMPOSITION; ELLIPTIC PROBLEMS;

ITERATIVE METHODS;

EID: 0033295349     PISSN: 10648275     EISSN: None     Source Type: None    
DOI: 10.1137/S1064827596305593     Document Type: Article

References (29)

1. R. E. ALCOUFFE, A. BRANDT, J. E. DENDY, JR., AND J. W. PAINTER, The multi-grid method for the diffusion equation with strongly discontinuous coefficients, SIAM J. Sci. Statist. Comput., 2 (1981), pp. 430-454.
2. S. F. ASHBY, R. D. FALGOUT, S. G. SMITH, AND A. F. B. TOMPSON, A numerical solution of groundwater flow and contaminant transport on the CRAY T3D and C90 supercomputers, Int. J. High Perform. Comput. Appl., 13 (1999), pp. 80-93.
3. P. E. BJØRSTAD AND M. D. SKOGEN, Domain decomposition algorithms of Schwarz type, designed for massively parallel computers, in Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia, 1992, pp. 362-375.
4. J. H. BRAMBLE, J. E. PASCIAK, AND A. L. SCHATZ, The construction of preconditioners for elliptic problems by substructuring, Math. Comp., 47 (1986), pp. 103-134.
5. T. F. CHAN AND T. P. MATHEW, Domain decomposition algorithms, Acta Numerica, 1994, pp. 61-143.
6. T. F. CHAN, B. SMITH, AND J. ZOU, Overlapping Schwarz methods on unstructured meshes using non-matching coarse grids, Numer. Math., 73 (1996), pp. 149-167.
7. T. F. CHAN AND J. ZOU, Additive Schwarz domain decomposition methods for elliptic problems on unstructured meshes, Numer. Algorithms, 8 (1994), pp. 329 346.
8. R. K. COOMER AND I. G. GRAHAM, Domain decomposition methods for device modeling, in Domain Decomposition Methods in Science and Engineering, D. E. Keyes and J. Xu, eds., AMS Providence, RI, 1995, pp. 491-496.
9. R. K. COOMER AND I. G. GRAHAM, Massively parallel methods for semiconductor device modeling, Computing, 56 (1996), pp. 1-28.
10. M. DRYJA, M. V. SARKIS, AND O. B. WIDLUND, Multilevel schwarz methods for elliptic problems with discontinuous coefficients in three dimensions, Numer. Math., 72 (1996), pp. 313-348.
11. M. DRYJA AND O. B. WIDLUND, Some domain decomposition methods for elliptic problems, in Iterative Methods for Large Linear Systems, L. Hayes and D. Kincaid, eds., Academic Press, San Diego, 1989, pp. 273-291.
12. G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 2nd ed., Johns Hopkins University Press, Baltimore, MD, 1989.
13. I. G. GRAHAM AND M. J. HAGGER, Additive Schwarz, CG and discontinuous coefficients, in Domain Decomposition Methods in Sciences and Engineering, Domain Decomposition Press, Bergen, 1998, pp. 113-120.
14. A. GREENBAUM, C. LI, AND H. Z. CHAO, Parallising PCG algorithms, Comput. Phys. Comm., 53 (1989), pp. 295-309.
15. W. HACKBUSCH, Iterative Solution of Large Sparse Systems of Equations, Springer-Verlag, Berlin, 1994.
16. M. J. HAGGER, Iterative Solution of Large, Sparse Systems of Equations, Arising in Groundwater Flow Models, Ph.D. thesis, Department of Mathematical Sciences, University of Bath, Bath, UK, 1995.
17. B. HEISE, Parallel solvers for fem-bem equations with applications to non-linear magnetic field problems, in Numerical Treatment of Coupled Systems, Notes on Numerical Fluid Dynamics 51, W. Hackbusch and G. Wittum, eds., Vieweg, Braunschweig, 1995, pp. 73-85.
18. B. HEISE AND M. KUHN, Parallel Solves for Linear and Non-linear Exterior Magnetic Field Problems Based upon Coupled FE/BE Formulations, Computing, 56 (1996), pp. 1527-1544.
19. M. C. HILL, Solving groundwater flow problems by conjugate-gradient methods and the strongly implicit procedure, Water Resources Res., 26 (1990), pp. 1961-1969.
20. T. KATO, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1976.
21. B. N. KHOROMSKIJ, G. E. MAZURKEVICH, AND G. WITTUM, Robust iterative methods with highly varying coefficients in thin substructures: Applications in skin modeling, in Proceedings of the First European Conference on Numerical Mathematics and Advanced Applications, GAMNI/SMAI, Paris, France, 1995.
22. P. LETALLEC, Y.-H. DE ROECK, AND M. VIDRASCU, Domain decomposition methods for large linearly elliptic three-dimensional problems, J. Comput. Appl. Math., 34 (1991), pp. 93-117.
23. J. MANDEL, Balancing domain decomposition, Comm. Numer. Methods Engrg., 9 (1992) pp. 233-241.
24. S. V. NEPOMNYASCHIKH, Domain decomposition and Schwarz methods in a subspace for the approximate solution of elliptic boundary value problems, Research report, Computing Center of the Siberian Branch of the USSR Academy of Sciences, Novosibirsk, Russia, 1996.
25. A. RAMAGE AND A. J. WATHEN, On preconditioning for finite element equations on irregular grids, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 909-921.
26. B. F. SMITH, A domain decomposition method for elliptic problems in three dimensions, Numer. Math., 60 (1991), pp. 219-234.
27. C. WALSHAW, M. CROSS, AND M. G. EVERETT, A localised algorithm for optimising unstructured mesh partitions, Internat. J. Supercomputer Appl. High Perform. Comput., 9 (1995), pp. 280-295.
28. A. J. WATHEN, Realistic eigenvalue bounds for the Galerkin mass matrix, IMA J. Numer. Anal., 7 (1987), pp. 449-457.
29. J. XU, Iterative methods by space decomposition and subspace correction, SIAM Rev., 34 (1992), pp. 581-613.