Parallel Adaptive Mesh Generation and Decomposition

Engineering with Computers, Springer-Verlag, Vol 12, pp.155-167, December 1996

MESHING
RESEARCH
CORNER

Department of Computer Science, Purdue University, Indiana, USA

Abstract
An important class of methodologies for the parallel processing of computational models defined on some discrete geometric data structures (i.e. meshes, grids) is the so called geometry decomposition or splitting approach. Compared to the sequential processing of such models, the geometry splitting parallel methodology requires an additional computational phase. It consists of the decomposition of the associated geometric data structure into a number of balanced subdomains that satisfy a number of conditions that ensure the load balancing and minimum communication requirement of the underlying computations on a parallel hardware platform. It is well known that the implementation of the mesh decomposition phase requires the solution of a computationally intensive problem. For this reason several fast heuristics have been proposed. In this paper we explore a decomposition approach which is part of a parallel adaptive finite element mesh procedure. The proposed integrated approach consists of five steps. It starts with a coarse background mesh that is optimally decomposed by applying well known heuristics. Then. the initial mesh is refined in each subdomain after linking the new boundaries introduced by its decomposition. Finally the decomposition of the new refined mesh is improved so that it satisfies the objectives and conditions of the mesh decomposition problem. Extensive experimentation indicates the effectiveness and efficiency of the proposed parallel mesh and decomposition approach.