Parallel Performance of Some Two-Level ASPIN Algorithms
In this paper we study the parallel performance of some nonlinear additive Schwarz preconditioned inexact Newton methods for solving large sparse system of nonlinear equations arising from the discretization of partial differential equations. The main idea of nonlinear preconditioning is to replace an ill-conditioned nonlinear system by an equivalent nonlinear system that has more balanced nonlinearities. In addition to balance the nonlinearities through nonlinear preconditioning, we also need to make sure that the multilayered iterative solver is scalable with respect to the number of processors. We focus on some two-level nonlinear additive Schwarz preconditioners, and show numerically that these two-level methods can reduce the nonlinearities and at the same time maintain the parallel scalability. Parallel numerical results for some high Reynolds number incompressible Navier-Stokes equations will be presented.
KeywordsInitial Guess Coarse Grid Parallel Performance Coarse Solver Domain Decomposition Method
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