A mixed parallel strategy for the solution of coupled multi-scale problems at finite strains

A mixed parallel strategy for the solution of homogenization-based multi-scale constitutive problems undergoing finite strains is proposed. The approach aims to reduce the computational time and memory requirements of non-linear coupled simulations that use finite element discretization at both scales (FE 2 ). In the first level of the algorithm, a non-conforming domain decomposition technique, based on the FETI method combined with a mortar discretization at the interface of macroscopic subdomains, is employed. A master–slave scheme, which distributes tasks by macroscopic element and adopts dynamic scheduling, is then used for each macroscopic subdomain composing the second level of the algorithm. This strategy allows the parallelization of FE 2 simulations in computers with either shared memory or distributed memory architectures. The proposed strategy preserves the quadratic rates of asymptotic convergence that characterize the Newton–Raphson scheme. Several examples are presented to demonstrate the robustness and efficiency of the proposed parallel strategy.