The second generation FETI methods and their application to the parallel solution of large-scale linear and geometrically non-linear structural analysis problems Original Research Article

The FETI algorithms are a family of numerically scalable domain decomposition methods. They have been designed in the early 1990s for solving iteratively and on parallel machines, large-scale systems of equations arising from the finite element discretization of solid mechanics, structural engineering, structural dynamics, and acoustic scattering problems, and for analyzing complex structures obtained from the assembly of substructures with incompatible discrete interfaces. In this paper, we present the second generation of these methods that operate more efficiently on large numbers of subdomains, offer greater robustness, better performance, and more flexibility for implementation on a wider variety of computational platforms. We also report on the application and performance of these methods for the solution of geometrically non-linear structural analysis problems. We discuss key aspects of their implementation on shared and distributed memory parallel processors, benchmark them against optimized direct sparse solvers, and highlight their potential with the solution of large-scale structural mechanics problems with several million degrees of freedom.