A parallel adaptive nonlinear elimination preconditioned inexact Newton method for transonic full potential equation

• New adaptive right nonlinear elimination preconditioner for inexact Newton algorithm proposed.
• Three major ingredients include: subspace correction, global update, and determination of partition.
• Key idea is to remove local nonlinearity before performing global Newton update.
• Intermediate solution used to select adaptively the to-be-eliminated components.
• Numerical examples used to demonstrate robustness and efficiency of the algorithm.

We propose and study a right-preconditioned inexact Newton method for the numerical solution of large sparse nonlinear system of equations. The target applications are nonlinear problems whose derivatives have some local discontinuities such that the traditional inexact Newton method suffers from slow or no convergence even with globalization techniques. The proposed adaptive nonlinear elimination preconditioned inexact Newton method consists of three major ingredients: a subspace correction, a global update, and an adaptive partitioning strategy. The key idea is to remove the local high nonlinearity before performing the global Newton update. The partition used to define the subspace nonlinear problem is chosen adaptively based on the information derived from the intermediate Newton solution. Some numerical experiments are presented to demonstrate the robustness and efficiency of the algorithm compared to the classical inexact Newton method. Some parallel performance results obtained on a cluster of PCs are reported.