Performance of Neumann Expansion Preconditioners for Iterative Methods with Geotechnical Elastoplastic Applications

Because most geotechnical analyses may involve elastoplastic geomaterials, a robust solution scheme is of critical importance to the efficiency of the entire finite-element (FE) computation. To accelerate the Krylov subspace iterative methods, some preconditioning techniques have been developed based on the factorization of elastic stiffness. However, the idea of constructing a preconditioner based on elastic stiffness is heuristic. In this study, a class of Neumann expansion preconditioners constructed from the constant (elastic) partition and varying (plastic) partition of the elastoplastic stiffness matrix was proposed. Based on two numerical examples, the performances of truncated Neumann expansion preconditioners were examined with associated and nonassociated soil plasticity considered, respectively. It is interesting to note that the convergence behaviors of truncated Neumann expansion preconditioners closely depended on the approximation to the elastic stiffness part as well as the truncat...