Distributed Point Objects. A New Concept for Parallel Finite Elements
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. . 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.
KeywordsHigh Performance Computing Multigrid Method Domain Decomposition Method Parallel Distribution Parallel Programming Model
Unable to display preview. Download preview PDF.
- 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.Google Scholar
- 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.Google Scholar
- P. Bastian. Parallele adaptive Mehrgitterverfahren. Teubner Skripten zur Numerik. Teubner, Stuttgart, 1996.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- 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.Google Scholar