Convergence analysis of inexact LU-type preconditioners for indefinite problems arising in incompressible continuum analysis

Developing efficient solution methods for indefinite problems arising in constraint problems is an important issue in incompressible or nearly incompressible continuum analysis. In this paper, we first compare the convergence properties of two classical iterative approaches, namely the inexact block triangular algorithm and the inexact block LU algorithm. It is shown that the latter can be applied under more relaxed conditions than the former. We further analyze properties of the latter algorithm when applied as a preconditioner for Krylov subspace methods. Similar to the analysis of the inexact block LU preconditioner, we also analyze the properties of a fill-controlled incomplete LU preconditioner. The theoretical convergence estimates are validated and the performance of the two LU-type preconditioners are compared through numerical experiments with large deformation problems of a hyper-elastic material.