Preconditioners for iterative solutions of large-scale linear systems arising from Biot's consolidation equations

Abstract

The solution of the linear systems of equation is the most time-consuming part in large-scale finite element analysis. The development of fast preconditioned iterative solution methods are therefore of utmost importance to the field of scientific computing. The objective of this thesis was to investigate the efficient preconditioned iterative strategies as well as to develop robust preconditioning methods in conjunction with suitable iterative methods to solve very large symmetric or weakly nonsymmetric indefinite linear systems arising from the coupled Biot's consolidation equations. More specifically, the comparison study between a block constrained preconditioner (Pc) and a Generalized Jacobi (GJ) preconditioner was carried out and a new robust modified SSOR (MSSOR) preconditioner was proposed. Numerical examples showed that Pc can reduce CPU time about 40% compared to GJ, and MSSOR preconditioner may be extremely robust for large-scale consolidation problems with highly varied soil properties.