Parallel adaptive FETI‐DP using lightweight asynchronous dynamic load balancing

Abstract

SummaryA 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 that 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.