Load Balancing and Communication Optimization for Parallel Adaptive Finite Element Methods

This paper describes predictive load balancing schemes designed for use with parallel adaptive finite element methods. We provide an overview of data structures suitable for distributed storage of finite element mesh data as well as software designed for mesh adaptation and load balancing. During the course of a parallel computation, processor load imbalances are introduced at adaptive enrichment steps. The predictive load balancing methods described here use a priori estimates of work load for adaptive refinement and subsequent computation to improve enrichment efficiency and reduce total balancing time. An analysis code developed with these components for solving compressible flow problems is used to obtain predictive load balancing results on an IBM SP2 computer. Our test problem involves the transient solution of the threedimensional Euler equations of compressible flow inside a perforated shock tube. We also present a message passing library extension in development which allows for automated packing of messages to improve communication efficiency.