Abstract
VECFEM is a black-box solver for the solution of a large class of nonlinear functional equations by finite element methods. It uses very robust solution methods for the linear FEM problem to compute reliably the Newton-Raphson correction and the error indicator. Kernel algorithms are conjugate gradient methods (CG) for the solution of the linear system. In this paper we present the optimal data structures on parallel computers for the matrix-vector multiplication, which is the key operation in the CG iteration, the principles of the element distribution onto the processors and the mounting of the global matrix over all processors as transformation of optimal data structures. VECFEM is portably implemented for message passing systems. Two examples with unstructured and structured grids will show the efficiency of the data structures.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
K.-J. Bathe. Finite Element Procedures in Engineering Analysis. Inc. Englewood Cliffs. Prentice Hall, New Jersey, 1982.
A. Geist, A. Beguelin, J. Dongarra, W. Jiang, R. Manchek, and V. Sunderam. PVM 3.0 User's Guide and Reference Manual, 1993.
N. Gibbs, W. Poole, and P. Stockmeyer. An algorithm for reducing the bandwidth and profile of a sparse matrix. SIAM J. Numer. Anal., 13(2), April 1976.
L. Groß, C. Roll, and W. Schönauer. A black-box-solver for the solution of general nonlinear functional equations by mixed fem. In M. Dekker, editor, FEM 50, The Finite Element Method: Fifty Years of the Courant Element, Finland, 1993.
L. Groß, C. Roll, and W. Schönauer. VECFEM for mixed finite elements. Internal report 50/93, University of Karlsruhe, Computing Center, 1993.
L. Groß, P. Sternecker, and W. Schönauer. Optimal data structures for an efficient vectorized finite element code. In H. Burkhardt, editor, CONPAR 90 — VAPP II, Lecture Notes of Computer Science. Springer Verlag Berlin, Heidelberg, New York, 1990.
L. Groß, P. Sternecker, and W. Schönauer. The finite element tool package VECFEM (version 1.1). Internal report 45/91, University of Karlsruhe, Computing Center, 1991.
I-DEAS, Solid Modeling, User's Guide. SDRC, 2000 Eastman Drive, Milford, Ohio 45150, USA, 1990.
PARAGON OSF/1 User's Guide, April 1993.
M. Schmauder and W. Schönauer. CADSOL-a fully vectorized black-box solver for 2-D and 3-D partial differential equations. In R. Vichnevetsky, D. Knight, and G. Richter, editors, Advances in Computer Methods for Partial Differential Equations VII, pages 639–645. IMACS, New Brunswik, 1992.
W. Schönauer. Scientific Computing on Vector Computers. North-Holland, Amsterdam, New York, Oxford, Tokyo, 1987.
R. Weiss. Convergence behavior of generalized conjugate gradient methods. Internal report 43/90, University of Karlsruhe, Computing Center, 1990.
R. Weiss and W. Schönauer. Black-box solvers for partial differential equations. In E. Küsters, E. Stein, and W. Werner, editors, Proceedings of the Conference on Mathematical Methods and Supercomputing in Nuclear Applications, Kernforschungszentrum Karlsruhe, Germany, volume 2, pages 29–40, 1993.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Grosz, L., Roll, C., Schönauer, W. (1994). Nonlinear finite element problems on parallel computers. In: Dongarra, J., Waśniewski, J. (eds) Parallel Scientific Computing. PARA 1994. Lecture Notes in Computer Science, vol 879. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030153
Download citation
DOI: https://doi.org/10.1007/BFb0030153
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58712-5
Online ISBN: 978-3-540-49050-0
eBook Packages: Springer Book Archive