Space tree structures for PDE software

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. © Springer-Verlag 2002.