Incomplete factorization preconditioners for the iterative solution of Stochastic Finite Element equations

This work is focused on enhancing the computational efficiency in Monte Carlo simulation-based Stochastic Finite Element (SFE) analysis of large-scale structural models. Such analyses require the solution of successive systems of equations derived during simulations, which can be efficiently treated using customized versions of the iterative Preconditioned Conjugate Gradient (PCG) solution method. PCG-customization is localized at the preconditioning matrix employed to accelerate convergence. Thus, specialized preconditioners following the rationale of incomplete factorization are presented, which retain only essential numerical information during factorization. The resulting PCG-based solution schemes allow for computationally efficient SFE analyses with low storage demands in computer memory.