Article in Proceedings INPROC-2002-32

BibliographyBader, Michael; Bungartz, Hans-Joachim; Frank, Anton; Mundani, Ralf-Peter: Space Tree Structures for PDE Software.
In: Sloot, P.M.A. (ed.); Kenneth Tan, C.J. (ed.); Dongarra, J.J.; Hoekstra, A.G. (ed.): Proceedings of the 2002 International Conference on Computational Science: ICCS 2002; Amsterdam, The Netherlands, April 21-24, 2002.
University of Stuttgart, Faculty of Computer Science, Electrical Engineering, and Information Technology.
Lecture Notes in Computer Science; 2331, pp. 662-671, english.
Springer-Verlag, April 2002.
ISBN: 3-540-43594-8.
Article in Proceedings (Conference Paper).
CR-SchemaE.1 (Data Structures)
E.4 (Data Coding and Information Theory)
G.1.8 (Partial Differential Equations)
I.3.5 (Computational Geometry and Object Modeling)
Keywordsoctrees; hierarchical data structures; partial differential equations; multigrid
Abstract

In this paper, we study the potential of space trees (boundary extended octrees for an arbitrary number of dimensions) in the context of software for the numerical solution of PDEs. The main advantage of the approach presented is the fact that the underlying geometry's resolution can be decoupled from the computational grid's resolution, although both are organized within the same data structure. This allows us to solve the PDE on a quite coarse orthogonal grid at an accuracy corresponding to a much finer resolution. We show how fast (multigrid) solvers based on the nested dissection principle can be directly implemented on a space tree. Furthermore, we discuss the use of this hierarchical concept as the common data basis for the partitioned solution of coupled problems like fluid-structure interactions, e.g., and we address its suitability for an integration of simulation software.

ContactHans-Joachim Bungartz bungartz@ipvs.uni-stuttgart.de
Department(s)University of Stuttgart, Institute of Parallel and Distributed Systems, Simulation of Large Systems
Entry dateOctober 20, 2004
   Publ. Department   Publ. Institute   Publ. Computer Science