Abstract
We describe and compare some recent domain decomposition algorithms of Schwarz type with respect to parallel performance. A new, robust domain decomposition algorithm — Additive Average Schwarz is compared with a classical overlapping Schwarz code. Complexity estimates are given in both two and three dimensions and actual implementations are compared on a Paragon machine as well as on a cluster of modern workstations
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
P. E. Bjørstad, M. Dryja, and E. Vainikko, Additive Schwarz methods without subdomain overlap and with new coarse spaces, in Domain Decomposition Methods in Sciences and Engineering, R. Glowinski, J. Périaux, Z. Shi, and O. B. Widlund, eds., John Wiley & Sons, 1996. Proceedings from the Eight International Conference on Domain Dec omposition Metods, May 1995, Beijing.
P. E. Bjørstad and T. Kårstad, Domain decomposition, parallel computing and petroleum engineering, in Domain-Based Parallelism and Problem Decomposition Methods in Computational Science and Engineering, D. E. Keyes, Y. Saad, and D. G. Truhlar, eds., SIAM, 1995, ch. 3, pp. 39–56.
P. E. Bjørstad, R. Moe, and M. Skogen, Parallel domain decomposition and iterative refinement algorithms, in Parallel Algorithms for Partial Differential Equations, W. Hackbusch, ed., Braunschweig, Germany, 1991, VIEWEG, pp. 28–46. Notes on Numerical Fluid Mechanics, Vol 31, Proceedings of the sixth GAMM-Seminar, Kiel, January 19–21 1990.
P. E. Bjørstad and M. D. Skogen, Domain decomposition algorithms of Schwarz type, designed for massively parallel computers, in Domain Decomposition Methods for Partial Differential Equations, D. E. Keyes, T. F. Chan, G. Meurant, J. S. Scroggs, and R. G. Voigt, eds., SIAM, 1992, pp. 362–375. In the proceedings from the Fifth International Symposium on Domain Decomposition Methods, Norfolk, Virginia 1991.
J. H. Bramble and J. Xu, Some estimates for a weighted L2projection, Math. Comp., 56 (1991), pp. 463–476.
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.
W. D. Gropp, E. Lusk, and A. Skjellum, Using MPI: Portable Parallel Programming with the Message-Passing Interface, MIT Press, 1994.
W. D. Gropp and B. F. Smith, Experiences with domain decomposition in three dimensions: Overlapping Schwarz methods, Contemporary Mathematics, (1991).
B. Hendrickson and R. Leland, The Chaco user's guide, version 2.0, Tech. Report SAND 94-2692, Sandia National Laboratories, July 1995.
D. E. Keyes and W. D. Gropp, A comparison of domain decomposition techniques for elliptic partial differential equations and their parallel implementation, SIAM J. Sci. Stat. Comput., 8 (1987), pp. 166–202.
P. Oswald, On the robustness of the BPX-preconditioner with respect to jumps in the coefficients, tech. report, Dept. of Math. Texas A&M University, College Station, TX 77843-3368, 1995.
B. F. Smith, P. E. Bjørstad, and W. D. Gropp, Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations, Cambridge University Press, 1996.
J. Xu, Counter examples concerning a weighted L2projection, Math. Comp., 57 (1991), pp. 563–568.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bjørstad, P.E., Dryja, M., Vainikko, E. (1996). Parallel implementation of a Schwarz domain decomposition algorithm. In: Waśniewski, J., Dongarra, J., Madsen, K., Olesen, D. (eds) Applied Parallel Computing Industrial Computation and Optimization. PARA 1996. Lecture Notes in Computer Science, vol 1184. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62095-8_6
Download citation
DOI: https://doi.org/10.1007/3-540-62095-8_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62095-2
Online ISBN: 978-3-540-49643-4
eBook Packages: Springer Book Archive