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

• Published in: Computers & structures Vol. 88; no. 3; pp. 178 - 188
• Main Author: Charmpis, Dimos C.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.02.2010; Elsevier
• Subjects: Computational techniques; Conjugate gradient method; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Incomplete factorization; Iterative solution; Mathematical methods in physics; Monte Carlo simulation; Physics; Preconditioner; Solid mechanics; Stochastic Finite Element; Structural and continuum mechanics; Conjugate gradient method; Incomplete factorization; Stochastic Finite Element; Iterative solution; Preconditioner; Monte Carlo simulation; Monte Carlo method; Probabilistic approach; Iterative method; Factorization; Scale model; Modeling; Finite element method; Scaling law; Preconditioning; Structural analysis; Stochastic equation
• ISSN: 0045-7949; 1879-2243
• DOI: 10.1016/j.compstruc.2009.09.010

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.