Abstract
We present a new parallelizable preconditioner that is used as the local component of a two-level preconditioner similar to BPS. On 2D model problems that exhibit either high anisotropy or discontinuity, we demonstrate its attractive numerical behaviour and compare it with the regular BPS. To alleviate the construction cost of this new preconditioner, that requires the computation of the local Schur complements, we propose a cheap alternative based on Incomplete Cholesky factorization, that reduces the computational cost but retains the good numerical features of the preconditioner.
Chapter PDF
Keywords
- Domain Decomposition
- Conjugate Gradient Method
- Diagonal Block
- Interpolation Operator
- Preconditioned Conjugate Gradient Method
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
M. Benzi, C.D. Meyer, and M. TŮma A sparse approximate inverse preconditioner for the conjugate gradient method. SIAM J. Sci. Comput., 17(5):1135–1149, 1996.
J.H. Bramble, J.E. Pasciak, and A.H. Schatz. The construction of preconditioners for elliptic problems by substructuring I. Math. Comp., 47(175):103–134, 1986.
L. Carvalho, L. Giraud, and P. Le Tallec. Algebraic two-level preconditioners for the Schur complement method. Tech. Rep. TR/PA/98/18, CERFACS, Toulouse, France, 1998. Submitted to SIAM J. Scientific Computing.
L.M. Carvalho and L. Giraud. Block diagonal preconditioners for the Schur complement method. In M. Papadrakakis and B.H.V. Topping, editors, Innovative computational methods for structural mechanics, pages 61–82, Edinburgh, UK, 1999. Saxe-Coburg publications.
T.F. Chan and T.P. Mathew. Domain Decomposition Algorithms, volume 3 of Acta Numerica, pages 61–143. Cambridge University Press, Cambridge, 1994.
Y.-H. De Roeck and P. Le Tallec. Analysis and test of a local domain decomposition preconditioner. In R. Glowinski, Y. Kuznetsov, G. Meurant, J. Périaux, and O. Widlund, editors, Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations, pages 112–128. SIAM, Philadelphia, PA, 1991.
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(6):1662–1694, 1993.
C. Farhat and F.-X. Roux. A method of finite element tearing and interconnecting and its parallel solution algorithm. Int. J. Numer. Meth. Engng., 32:1205–1227, 1991.
M. Grote and T. Huckle. Parallel preconditioning with sparse approximate inverses. SIAM J. Sci. Comput., 18:838–853, 1997.
P. Le Tallec. Domain decomposition methods in computational mechanics, volume 1 of Computational Mechanics Advances, pages 121–220. North-Holland, 1994.
J. Mandel. Balancing domain decomposition. Communications in Numerical Methods in Engineering, 9:233–241, 1993.
T.A. Manteuffel. Shifted incomplete Cholesky factorization. In I.S. Duff and G.W. Stewart, editors, Sparse Matrix Proceedings 1978, Philadelphia, PA, 1979. SIAM Publications.
B.F. Smith. Domain Decomposition Algorithms for the Partial Differential Equations of Linear Elasticity. PhD thesis, Courant Institute of Mathematical Sciences, September 1990. Tech. Rep. 517, Department of Computer Science, Courant Institute.
B.F. Smith, P. Bjørstad, and W. Gropp. Domain Decomposition, Parallel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge University Press, New York, 1st edition, 1996.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Carvalho⋆, L.M., Giraud, L. (1999). Parallel Subdomain-Based Preconditioner for the Schur Complement. In: Amestoy, P., et al. Euro-Par’99 Parallel Processing. Euro-Par 1999. Lecture Notes in Computer Science, vol 1685. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48311-X_144
Download citation
DOI: https://doi.org/10.1007/3-540-48311-X_144
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66443-7
Online ISBN: 978-3-540-48311-3
eBook Packages: Springer Book Archive