A general preconditioning framework for coupled multiphysics problems with application to contact- and poro-mechanics

This work discusses a general approach for preconditioning the block Jacobian matrix arising from the discretization and linearization of coupled multiphysics problem. The objective is to provide a fully algebraic framework that can be employed as a starting point for the development of specialized algorithms exploiting unique features of the specific problem at hand. The basic idea relies on approximately computing an operator able to decouple the different processes, which can then be solved independently one from the other. In this work, the decoupling operator is computed by extending the theory of block sparse approximate inverses. The proposed approach is implemented for two multiphysics applications, namely the simulation of a coupled poromechanical system and the mechanics of fractured media. The numerical results obtained in experiments taken from real-world examples are used to analyze and discuss the properties of the preconditioner.