Some issues in research on block preconditioning for coupled Biot´s linear system

Based on the recent developments of block preconditioning, a computational framework of block preconditioners is established for the coupled Biot´s linear system of equation. Within the computational framework, some issues which may significantly influence the performance of preconditioned Krylov subspace iterative method are discussed. Firstly, the issue about which scheme (i.e. a fully iterative scheme or a combined scheme) should be used for large-scale Biot´s linear system is raised and discussed. Next, when developing block preconditioners it is suggested that the recent or future efforts should be devoted to the practical nonlinear consolidation analysis in which significant material property contrast may be frequently encountered. The issues addressed are believed to be essential for fast iterative solutions of large-scale coupled Biot´s linear systems from practical point of view.