# Inexact Newton Methods with Restricted Additive Schwarz Based Nonlinear Elimination for Problems with High Local Nonlinearity

@article{Cai2011InexactNM, title={Inexact Newton Methods with Restricted Additive Schwarz Based Nonlinear Elimination for Problems with High Local Nonlinearity}, author={Xiao-Chuan Cai and Xuefeng Li}, journal={SIAM J. Sci. Comput.}, year={2011}, volume={33}, pages={746-762} }

The classical inexact Newton algorithm is an efficient and popular technique for solving large sparse nonlinear systems of equations. When the nonlinearities in the system are well balanced, a near quadratic convergence is often observed; however, if some of the equations are much more nonlinear than the others in the system, the convergence is much slower. The slow convergence (or sometimes divergence) is often determined by the small number of equations in the system with the highest…

## 42 Citations

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Strategies for combining Newton and ASPEN to accelerate the nonlinear solution process are presented and the computational runtime can be reduced by adaptively switching to regular Newton's method when nonlinearities are balanced throughout the physical domain and the local solves provide little benefit relative to their computational cost.

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