Abstract
A parallel multigrid algorithm developed by Chan and Saad [4] is generalized by domain splitting for problems having a greater size than the system size. It is shown by complexity analysis how efficiently problems of this kind can run on hypercube multiprocessor systems. The maximum speedup of problems of size N is given by N/log N. Further, an algebraic expression for efficiency is developed that gives an approximate result for hypercube systems depending on system parameters such as operational speed and transfer capability. Some examples are given for different systems showing the accordance of simulated and algebraic results.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
K. Stüben and U. Trottenberg: Multigrid Methods: Fundamental Algorithms, Model Problem Analysis and Applications; in Hackbusch and Trottenberg (eds.): Multigrid Methods, Proc. of the Conf. in Köln-Porz, nov. 23–27, 1981; Lecture Notes in Mathematics, Springer, Berlin 1982.
A. Brandt: Multigrid Solvers on Parallel Computers; M. H. Schultz (ed): Elliptic Problem Solvers; Academic Press 1981.
T. F. Chan and R. Schreiber: Parallel Networks for Multigrid Algorithms: Architecture and Complexity, SIAM J. Scient. Stat. Comp., 3, 1985.
T. F. Chan and Y. Saad: Multigrid Algorithms on the Hypercube Multiprocessor; IEEE Trans. Comput., vol. C-35, pp. 969–977, 1986.
C.-A. Thole: Experiments with Multigrid Methods on the CalTech-Hypercube; GMD-Studien No. 103, GMD, St. Augustin, FRG, 1985.
O. Mc Bryan and E. Van de Velde, Hypercubes Algorithms and Implementations, SIAM J. Sci. Stat. Comput., 8, 227–287, 1987.
O. Kolp and H. Mierendorff: Efficient Multigrid Algorithms for locally Constrained Parallel Systems; AMC 19: 169–200 (1986), New York.
O. Kolp and H. Mierendorff: Bus Coupled Systems for Multigrid Algorithms; Proc. 2nd European Conf. on Multigrid Methods, Köln, oct. 1–4, 1985
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kolp, O. (1988). A Multigrid Algorithm on Hypercube Systems. In: Kastens, U., Rammig, F.J. (eds) Architektur und Betrieb von Rechensystemen. Informatik-Fachberichte, vol 168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73451-9_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-73451-9_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18994-7
Online ISBN: 978-3-642-73451-9
eBook Packages: Springer Book Archive