Asynchronous Partial Update of Domain Decomposition Preconditioners to Solve Nonlinear CFD Problems

In this paper, we propose a numerical strategy to speed up the implicit solution of unsteady nonlinear problems arising from fluid dynamics. This strategy consists in a partial update of a domain decomposition preconditioner used in the Newton-Krylov method that solves the nonlinear problem of each time step. The underlying principle of the proposed method is that, usually, there is only slight changes between two consecutive Jacobian matrices. Consequently, it is possible to use the same preconditioner for few Newton iterations, or, even better, to partially update it. We propose to add some processes dedicated to the asynchronous update of the subdomains parts of the preconditioner. Numerical results for the lid-driven cavity are provided, they show that this addition of processes can speed up the computation in a super linear way.