A multilevel FETI‐DP method and its performance for problems with billions of degrees of freedom

Abstract

SummaryA multilevel generalization of the dual‐primal finite element tearing and interconnecting (FETI‐DP) domain decomposition method is proposed for very large‐scale discrete problems to address the bottleneck associated with the solution of the coarse problems at such scales. This bottleneck destroys the parallel scalability of the original, two‐level FETI‐DP method when using more than a few thousand processor cores. In the multilevel formulation proposed here, the FETI‐DP method is applied recursively to solve all coarse problems but the smallest one. Crucially, this recursive application of the method is enabled by utilizing a new primal formulation of the augmentation/enrichment process of the coarse problems. The efficiency and scalability of the proposed approach are demonstrated for up to 32 768 processor cores, and large‐scale real‐world and benchmark problems with more than 21 billion degrees of freedom. The obtained performance results show that the three‐ and four‐level FETI‐DP methods exhibit a better scalability than the original two‐level FETI‐DP method.