Analysis of two-level domain decomposition preconditioners based on aggregation

Mathematical Modelling and Numerical Analysis

Volumn 38, Issue 5, 2004, Pages 765-780

  Sala, Marzio ^a  

^a EPFL   (Switzerland)

Author keywords

Aggregation coarse corrections; Domain decomposition; Elliptic equations; Schwarz methods

Indexed keywords

EID: 10044287213     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:2004038     Document Type: Article

References (23)

1. M. Brezina, Robust iterative method on unstructured meshes. Ph.D. Thesis, University of Colorado at Denver (1997).
2. M. Brezina and P. Vaněk, A black-box iterative solver based on a two-level Schwarz method. Computing 63 (1999) 233-263.
3. O. Broeker, M.J. Grote, C. Mayer and A. Reusken, Robust parallel smoothing for multigrid via sparse approximate inverses. SIAM J. Sci. Comput. 23 (2001) 1396-1417.
4. M. Dryja and O.B. Widlund, Domain decomposition algorithms with small overlap. SIAM J. Sci. Comput. 15 (1994) 604-620.
5. M. Dryja and O.B. Widlund, Schwarz methods of Neumann-Neumann type for three-dimensional elliptic finite element problems. Comm. Pure Appl. Math. 48 (1995) 121-155.
6. L. Formaggia, A. Scheinine and A. Quarteroni, A numerical investigation of Schwarz domain decomposition techniques for elliptic problems on unstructured grids. Math. Comput. Simulations 44 (1994) 313-330.
7. |7] G.H. Golub and C.F. van Loan, Matrix Computations. The Johns Hopkins University Press, Baltimore, Maryland (1983).
8. L. Jenkins, T. Kelley, C.T. Miller and C.E. Kees, An aggregation-based domain decomposition preconditioner for groundwater flow. Technical Report TR00-13, Department of Mathematics, North Carolina State University (2000).
9. C.E. Kees, C.T. Miller, E.W. Jenkins and C.T. Kelley, Versatile multilevel Schwarz preconditioners for multiphase flow. Technical Report CRSC-TR01-32, Center for Research-in Scientific Computation, North Carolina State University (2001).
10. C. Lasser and A. Toselli, An overlapping domain decomposition preconditioner for a class of discontinuous Galerkin approximations of advection-diffusion problems. Technical Report 810, Dept. of Computer Science, Courant Institute (2000). Math. Comput. 72 (2003) 1215-1238.
11. C. Lasser and A. Toselli, Convergence of some two-level overlapping domain decomposition preconditioners with smoothed aggregation coarse spaces. Technical Report TUM-M0109, Technische Universität München (2001).
12. W. Leontief, The structure of the American Economy. Oxford University Press, New York (1951).
13. J. Mandel and B. Sekerka, A local convergence proof for the iterative aggregation method. Linear Algebra Appl. 51 (1983) 163-172.
14. L. Paglieri, A. Scheinine, L. Formaggia and A. Quarteroni, Parallel conjugate gradient with Schwarz preconditioner applied to fluid dynamics problems, in Parallel Computational Fluid Dynamics, Algorithms and Results using Advanced Computer, Proceedings of Parallel CFD'96, P. Schiano et al., Eds. (1997) 21-30.
15. A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations. Springer-Verlag, Berlin (1994).
16. A. Quarteroni and A. Valli, Domain Decomposition Methods for Partial Differential Equations. Oxford University Press, Oxford (1999).
17. M. Sala and L. Formaggia, Parallel Schur and Schwarz based preconditioners and agglomeration coarse corrections for CFD problems. Technical Report 15, DMA-EPFL (2001).
18. M. Sala and L. Formaggia, Algebraic coarse grid operators for domain decomposition based preconditioners, in Parallel Computational Fluid Dynamics - Practice and Theory, P. Wilders, A. Ecer, J. Periaux, N. Satofuka and P. Fox, Eds., Elsevier Science, The Netherlands (2002) 119-126.
19. B.F. Smith, P. Bjorstad and W.D. Gropp, Parallel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge University Press, Cambrige (1996).
20. [20) P. Le Tallec, Domain decomposition methods in computational mechanics, in Computational Mechanics Advances, J.T. Oden, Ed., North-Holland 1 (1994) 121-220.
21. R.S. Tuminaro and C. Tong, Parallel smoothed aggregation multigrid: Aggregation strategies on massively parallel machines, in SuperComputing 2000 Proceedings, J. Donnelley, Ed. (2000).
22. P. Vanek, M. Brezina and R. Tezaur, Two-grid method for linear elasticity on unstructured meshes. SIAM J. Sci. Comput. 21 (1999) 900-923.
23. P. Vanek, M. Brezina and J. Mandel, Convergence of algebraic multigrid based on smoothed aggregation. Numer. Math. 88 (2001) 559-579.