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

A 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.