Low-Rank Update of the Restricted Additive Schwarz Preconditioner for Nonlinear Systems

摘要

We presented a very simple procedure to update the RAS preconditioner without loss of parallelism. This update leads to a decrease of the number of Krylov iterations, especially for the time steps that requires the largest number of Newton iterations. However, further developments are needed to achieve an efficient method. This quasi-Newton update of the preconditioner should be used with a well-parametrized restarting procedure, since the efficiency of the preconditioner decreases from one iteration to another. A natural extension of this work is to use higher-rank updates, like the multisecant update. Techniques such as partial updates, or relaxed updates should also be investigated since they are expected to significantly improve the numerical efficiency of the updated preconditioner.