Abstract
This article describes the displacement decomposition and its benefits for the parallelization of the preconditioned conjugate gradient method for finite element elasticity problems. It deals with both the fixed and variable preconditioning based on this decomposition. Numerical efficiency of the parallel algorithms is demonstrated on an academic benchmark and real-life modelling problem.
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
Axelsson, O., Gustafsson, I.: Iterative Methods for the solution of the Navier equations of elasticity. Computer Methods in Applied Mechanics and Engineering, 15 (1978), 241–258
Blaheta, R.: Displacement decomposition-incomplete factorization preconditioning techniques for linear elasticity problems. Numerical Linear Algebra with Applications, 1 (1994), 107–128
Blaheta, R.: GPCG-generalized preconditioned CG method and its use with nonlinear and nonsymmetric displacement decomposition preconditioners. TR-DAM-2001/3, Institute of Geonics Cz. Acad. Sci., Ostrava (2001), submitted
Blaheta, R.: Parallel iterative methods. Lecture notes, VŠB-Technical University, Ostrava (2000)
Blaheta, R.: Space decomposition methods: Displacement decomposition, composite grid finite elements and overlapping domain decomposition. In: Modern mathematical methods in engineering. VSB-Technical University, Ostrava (2000) 7–16
Blaheta, R., Byczanski, P., Jakl, O., Starý, J.: Space decomposition preconditioners and their application in geomechanics. TR-DAM-2001/4, Institute of Geonics Cz. Acad. Sci., Ostrava (2001), submitted
Blaheta, R., Jakl, O., Starý, J.: Large-scale FE Modelling in Geomechanics: a Case Study in Parallelization. In: Dongarra, J., Luque, E., Margalef, T. (eds.): Recent Advances in Parallel Virtual Machine and Message Passing Interface. LNCS, Vol. 1697. Springer-Verlag, Berlin (1999) 299–306
Dongarra, J. J.: Performance of various computers using standard linear equations software (18/01/01). http://www.netlib.org/benchmark/performance.ps
Dongarra, J. J., Duff, I. S., Sorensen, D. C., van der Vorst, H.: Numerical linear algebra for high-performance computers. SIAM, Philadelphia (1998)
Notay, Y.: Flexible conjugate gradients. SIAM J. Sci. Comp., Vol. 22 (2000), 1444–1460
Smith, B. F., Bjørstad, P. E., Gropp, W. D.: Domain Decomposition. Parallel multilevel methods for elliptic partial differential equations. Cambridge University Press (1996)
The Standard Performance Evaluation Corp. http://www.spec.org/ (25/01/01)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Blaheta, R., Jakl, O., Starý, J. (2002). Parallel Displacement Decomposition Solvers for Elasticity Problems. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2001. Lecture Notes in Computer Science, vol 2328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48086-2_44
Download citation
DOI: https://doi.org/10.1007/3-540-48086-2_44
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43792-5
Online ISBN: 978-3-540-48086-0
eBook Packages: Springer Book Archive