Summary
We present a new concept for the realization of finite element computations on parallel machines with distributed memory. The parallel programming model is based on a dynamic data structure addressed by points. All geometric objects (cells, faces, edges) are referenced by their midpoints, and all algebraic data structures (vectors and matrices) are tied to the nodal points of the finite elements. The parallel distribution of all objects is determined by processor lists assigned to the reference points.
Based on this new model for Distributed Point Objects (DPO) a first application to a geotechnical application with Taylor-Hood elements on hexahedra has been presented in Wieners et al. [2004]. Here, we consider the extension to parallel refinement, curved boundaries, and multigrid preconditioners. Finally, we present parallel results for a nonlinear model problem with isoparametric cubic elements.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S. Balay, W. D. Gropp, L. C. McInnes, and B. F. Smith. PETSc users manual. Technical Report ANL-95/11-Revision 2.1.1, Argonne National Laboratory, 2001.
R. E. Bank. PLTMG: A Software Package for Solving Elliptic Partial DifferentiaEquations, Users' Guide 8.0l, volume 5 of Software, Environments and Tools. SIAM, Philadelphia, 1998.
P. Bastian. Parallele adaptive Mehrgitterverfahren. Teubner Skripten zur Numerik. Teubner, Stuttgart, 1996.
P. Bastian, K. Birken, K. Johannsen, S. Lang, N. Neuß, H. Rentz-Reichert, and C. Wieners. UG — a flexible software toolbox for solving partial differential equations. Comp. Vis. Sci., 1:27–40, 1997.
P. Bastian, K. Birken, K. Johannsen, S. Lang, V. Reichenberger, H. Rentz-Reichert, C. Wieners, and G. Wittum. A parallel software-platform for solving problems of partial differential equations using unstructured grids and adaptive multigrid methods. In E. Krause and W. Jäger, editors, High Performance Computing in Science and Engineering '98, pages 326–339, Berlin, 1998. Springer-Verlag.
P. Bastian, M. Droske, C. Engwer, R. Klöfkorn, T. Neubauer, M. Ohlberger, and M. Rumpf. Towards a unified framework for scientific computing. In R. Kornhuber, O. Pironneau, R. Hoppe, J. Périaux, D. Keyes, and J. Xu, editors, Proc. Int. Conf. on Domain Decomposition Methods DD15, 2004.
P. Bastian, K. Johannsen, S. Lang, S. Nägele, V. Reichenberger, C. Wieners, G. Wittum, and C. Wrobel. Advances in high-performance computing: Multigrid methods for partial differential equations and its applications. In E. Krause and W. Jäger, editors, High Performance Computing in Science and Engineering '99, pages 506–519, Berlin, 1999. Springer-Verlag.
P. Bastian, K. Johannsen, S. Lang, V. Reichenberger, C. Wieners, G. Wittum, and C. Wrobel. Parallel solutions of partial differential equations with adaptive multigrid methods on unstructured grids. In E. Krause and W. Jäger, editors, High Performance Computing in Science and Engineering '00, pages 496–508, Berlin, 2000. Springer-Verlag.
S. Lang, C. Wieners, and G. Wittum. The application of adaptive parallel multigrid methods to problems in nonlinear solid mechanics. In E. Stein, editor, Error-Controlled Adaptive Finite Element Methods in Solid Mechanics, pages 347–384, New-York, 2002. Wiley.
P. L. Lions. On the existence of positive solutions of semilinear elliptic equations. SIAM Review, 24:441–467, 1982.
M. Plum and C. Wieners. New solutions of the Gelfand problem. J. Math. Anal. Appl., 269:588–606, 2002.
C. Wieners, M. Ammann, and W. Ehlers. Distributed point objects: A new concept for parallel finite elements applied to a geomechanical problem. Future Generation Computer Systems, 2004. to appear.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wieners, C. (2005). Distributed Point Objects. A New Concept for Parallel Finite Elements. In: Barth, T.J., et al. Domain Decomposition Methods in Science and Engineering. Lecture Notes in Computational Science and Engineering, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26825-1_14
Download citation
DOI: https://doi.org/10.1007/3-540-26825-1_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22523-2
Online ISBN: 978-3-540-26825-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)