Abstract
The parallel properties of three fast direct solution methods for linear systems with separable blocktridiagonal matrices and a related C/MPI code are studied. Fast algorithm for separation of variables and two new variants of the generalized marching algorithm are first summarized. The results from numerical tests performed on two coarse-grained parallel architectures are then reported. The obtained speed-up and efficiency coefficients are compared. The presented results confirm that not always the best sequential solver has the best parallel performance.
Supported in part by the USA National Science Foundation under Grant DMS 9973328, by the Bulgarian Ministry of Education and Science under Grant MU-I-901/99 and by the Center of Excellence BIS-21 Grant ICA1-2000-70016.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bank, R.: Marching Algorithms for Elliptic Boundary Value Problems. II: The Variable Coefficient Case. SIAM J. Numer. Anal. 14, 950–970 (1977)
Bank, R., Rose, D.: Marching Algorithms for Elliptic Boundary Value Problems. I: The Constant Coefficient Case. SIAM J. Numer. Anal. 14, 792–829 (1977)
Bencheva, G.: Comparative Analysis of Marching Algorithms for Separable Elliptic Problems. In: Vulkov, L.G., Waśniewski, J., Yalamov, P. (eds.) NAA 2000. LNCS, vol. 1988, pp. 76–83. Springer, Heidelberg (2001)
Bencheva, G.: MPI Parallel Implementation of a Fast Separable Solver. In: Margenov, S., Waśniewski, J., Yalamov, P. (eds.) LSSC 2001. LNCS, vol. 2179, pp. 454–461. Springer, Heidelberg (2001)
Kuznetsov, Y.: Block relaxation methods in subspaces, their optimization and application. Sov. J. Numer. Anal. Math. Model. 4, 433–452 (1989)
Petrova, S.: Parallel implementation of fast elliptic solver. Parallel Computing 23, 1113–1128 (1997)
Rossi, T., Toivanen, J.: A parallel fast direct solver for block tridiagonal systems with separable matrices of arbitrary dimension. SIAM J. Sci. Comput. 20(5), 1778–1796 (1999)
Vassilevski, P.S.: An Optimal Stabilization of Marching Algorithm. Compt. rend. de l’Acad. bulg. Sci. 41(7), 29–32 (1988)
Vassilevski, P.S.: Fast Algorithm for Solving a Linear Algebraic Problem with Separable Variables. Compt. rend. de l’Acad. bulg. Sci. 37(3), 305–308 (1984)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bencheva, G. (2004). Parallel Performance Comparison of Three Direct Separable Elliptic Solvers. In: Lirkov, I., Margenov, S., Waśniewski, J., Yalamov, P. (eds) Large-Scale Scientific Computing. LSSC 2003. Lecture Notes in Computer Science, vol 2907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24588-9_48
Download citation
DOI: https://doi.org/10.1007/978-3-540-24588-9_48
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21090-0
Online ISBN: 978-3-540-24588-9
eBook Packages: Springer Book Archive