Shape-optimized mesh partitioning and load balancing for parallel adaptiveFEM

We present a dynamic distributed load balancing algorithm for parallel, ada ptive Finite Element simulations in which we use preconditioned Conjugate G radient solvers based on domain-decomposition. The load balancing is design ed to maintain good partition aspect ratio and we show that cut size is not always the appropriate measure in load balancing. Furthermore, we attempt to answer the question why the aspect ratio of partitions plays an importan t role for certain solvers. We define and rate different kinds of aspect ra tio and present a new center-based partitioning method of calculating the i nitial distribution which implicitly optimizes this measure. During the ada ptive simulation, the load balancer calculates a balancing how using differ ent versions of the diffusion algorithm and a variant of breadth first sear ch. Elements to be migrated are chosen according to a cost function aiming at the optimization of subdomain shapes. Experimental results for Bramble's preconditioner and comparisons to state-of-the-art load balancers show the benefits of the construction. (C) 2000 Elsevier Science B.V. All rights re served.