A shape optimizing load distribution heuristic for parallel adaptive FEM computations

Abstract

Load balancing plays an important role in parallel numerical simulations. To address this problem, some general purpose libraries as well as a number of more specific approaches have been developed. Many of them base on vertex exchange operations like the Kerninghan-Lin heuristic which, due to their sequential nature, are hard to parallelize. Furthermore, libraries like Metis and Jostle primarily minimize the edge-cut and cannot obey constraints like connectivity and straight partition boundaries, which are important for some numerical solvers. In this paper we present a new approach to address the load balancing problem. In contrast to existing heuristics, we are able to guarantee connectivity and the resulting partitions are usually well shaped. Furthermore, our experiments indicate that we can outperform the two parallel state-of-the-art libraries Metis and Jostle also according to the classic metrics like edge-cut and boundary length. The proposed algorithm thereby contains a high degree of natural parallelism, while its drawback is the long run-time, especially if the parallelism is not exploited. © Springer-Verlag Berlin Heidelberg 2005.