Implementation of the efficient communication layer for the highly parallel total FETI and hybrid total FETI solvers

Abstract

This paper describes the implementation, performance, and scalability of our communica- tion layer developed for Total FETI (TFETI) and Hybrid Total FETI (HTFETI) solvers. HTFETI is based on our variant of the Finite Element Tearing and Interconnecting (FETI) type do- main decomposition method. In this approach a small number of neighboring subdomains is aggregated into clusters, which results in a smaller coarse problem. To solve the origi- nal problem TFETI method is applied twice: to the clusters and then to the subdomains in each cluster. The current implementation of the solver is focused on the performance optimization of the main CG iteration loop, including: implementation of communication hiding and avoid- ing techniques for global communications; optimization of the nearest neighbor commu- nication - multiplication with a global gluing matrix; and optimization of the parallel CG algorithm to iterate over local Lagrange multipliers only. The performance is demonstrated on a linear elasticity 3D cube and real world bench- marks.