Parallel dynamic load-balancing for adaptive unstructured meshes

This chapter describes a parallel optimization technique that incorporates a distributed load-balancing algorithm and provides an extremely fast solution to the problem of load-balancing adaptive unstructured meshes. Moreover, a parallel graph contraction technique can be employed to enhance the partition quality and the resulting strategy outperforms or matches results from existing state-of-the-art static mesh partitioning algorithms. The strategy can also be applied to static partitioning problems. Dynamic procedures have been found to be much faster than static techniques, to provide partitions of similar or higher quality and, in comparison, involve the migration of a fraction of the data. The method employs a new iterative optimization technique that balances the workload and attempts to minimize the interprocessor communications overhead. Experiments on a series of adaptively refined meshes indicate that the algorithm provides partitions of an equivalent or higher quality to static partitioners (which do not reuse the existing partition) and much more quickly. The dynamic evolution of load has three major influences on possible partitioning techniques; cost, reuse, and parallelism. The unstructured mesh may be modified every few time-steps and so the load-balancing must have a low cost relative to that of the solution algorithm in between remeshing.

Quality balancing for parallel adaptive FEM

We present a dynamic distributed load balancing algorithm for parallel, adaptive finite element simulations using preconditioned conjugate gradient solvers based on domain-decomposition. The load balancer is designed to maintain good partition aspect ratios. It can calculate a balancing flow using different versions of diffusion and a variant of breadth first search. Elements to be migrated are chosen according to a cost function aiming at the optimization of subdomain shapes. We show how to use information from the second step to guide the first. Experimental results using Bramble's preconditioner and comparisons to existing state-ot-the-art load balancers show the benefits of the construction.

Load balancing for parallel adaptive FEM

We present a dynamic distributed load balancing algorithm for parallel, adaptive finite element simulations using preconditioned conjugate gradient solvers based on domain-decomposition. The load balancer is designed to maintain good partition aspect ratios. It calculates a balancing flow using different versions of diffusion and a variant of breadth first search. Elements to be migrated are chosen according to a cost function aiming at the optimization of subdomain shapes. We show how to use information from the second step to guide the first. Experimental results using Bramble's preconditioner and comparisons to existing state-of-the-art balancers show the benefits of the construction.

A Distributed algorithm for 1-D non-linear heat conduction with an unknown point source

Abstract not available