Parallel Implementation of Direct Solution Strategies for the Coarse Grid Solvers in 2-level FETI Method

The FETI method is based on introducing Lagrange multipliers along interfaces between subdomain to enforce continuity of local solutions [4]. It has been demonstrated to be numerically scalable in the case of second-order problems, thanks to a built-in “coarse grid” projection [3]. For high-order problems, especially with plate or shell finite element models in structural analysis, a two-level preconditioning technique for the FETI method has been introduced [2]. Computing the preconditioned gradient requires the solution of a coarse grid problem that is of the same kind as the original FETI problem, but is associated with a small subset of Lagrange multipliers enforcing continuity at cross-points. This preconditioner gives optimal convergence property for plate or shell finite element models [5]. This approach has been recently generalized to various local or partial continuity requirements in order to derive a general methodology for building second-level preconditioners [1]. For a sake of simplicity, the first method advocated for solving the coarse grid problems in distributed memory environment has been the same projected gradient as for the first-level FETI method [6] [7]. But with the increased complexity of the generalized 2-level FETI method, this approach leads to poor performance on machines with high performance compute nodes. In the present paper this new preconditioning technique is reinterpreted in a simple algebraic form, in order to derive algorithms based on direct solution techniques to solve efficiently the coarse grid problems in distributed memory environment. Performance results for real-life applications are given.