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Abstract

We study on Restricted Additive Schwarz Preconditioned Exact Newton method (RASPEN), a nonlinear preconditioning of Newton's method for solving the nonlinear algebraic systems of equations which result from the discretisation of partial differential equations (PDEs). The preconditioned system is created by the help of additive Schwarz method to enable the parallel computation and is supposed to be more suitable for Newton’s method. We also propose the coarse grid correction for RASPEN due to the fact that the one-level scheme has a scalability concern when doing a large-scale computation. Adding the second level would remedy this drawback. Our coarse space is based on the idea of Nicolaides coarse space with some extensions. It does not need an explicit coarse mesh and can be constructed in the purely algebraic manner. Furthermore, the setup of the coarse problem can be done in parallel. We apply RASPEN on various scenarios in order to investigate the flexibility of RASPEN and the effectiveness of the two-level approach.