Robust Algebraic Preconditioners for Large Scale Applications

Abstract. In this talk we discuss a robust algebraic preconditioner for solving sparse linear systems of equations involving symmetric and positive definite matrices. The preconditioner relies on a decomposition into subdomains and the approximation of a Schur complement that involves the factorization of a separator and a low rank correction obtained by solving a generalized eigenvalue problem. The preconditioner can be build and applied in parallel. Numerical results on a set of matrices arising from the discretization by the finite element method of linear elasticity models illustrate the robustness and the efficiency of our preconditioner.