Domain Decomposition and Preconditioning Method for Linear Partial Differential Equations Systems

This talk concerns a preconditioning method of AMLI type [3] for the solution of linear partial differential equations systems. An earlier idea of this study was proposed in [2] for scalar case. In this work we want to make some further extension of the study done in [1], in particular we propose to give a robust preconditioning iterative schemes using domain decomposition methods. Based on a special approximation of the Schur complement blocks corresponding to the new nodes after a proper step of static condensation at every discretization level we propose a robust preconditioner. The robustness is in the sense that the condition number is independent of both problem and discretization parameters.