Parallel adaptive FETI-DP using lightweight asynchronous dynamic load balancing

Abstract

A parallel FETI-DP domain decomposition method using an adaptive coarse space is presented. The implementation builds on a recently introduced adaptive FETI-DP approach for elliptic problems in three dimensions and uses small, local eigenvalue problems for faces and, additionally, for a small number of edges. The condition number of the preconditioned operator then satisfies a bound which is independent of coefficient heterogeneities in the problem. The computational cost of the local eigenvalue problems is not negligible, and also a significant load imbalance can be introduced. As a remedy, certain eigenvalue problems are discarded by a theory-guided heuristic strategy, based on the diagonal entries of the stiffness matrices. Additionally, a lightweight pairwise dynamic load balancing strategy is implemented for the eigenvalue problems. The load balancing is supervised by an orchestrating rank using asynchronous point-to-point communication. The resulting method shows good weak and strong scalability up to thousands of cores while fast convergence is obtained even for heterogeneous problems.