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Erschienen in:
2020 | OriginalPaper | Buchkapitel
Acceleration of Newton’s Method Using Nonlinear Jacobi Preconditioning
verfasst von : Konstantin Brenner
Erschienen in: Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples
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Abstract
For mildly nonlinear systems, involving concave diagonal nonlinearities, semi-global monotone convergence of Newton’s method is guarantied provided that the Jacobian of the system is an M-matrix. However, regardless this convergence result, the efficiency of Newton’s method becomes poor for stiff nonlinearities. We propose a nonlinear preconditioning procedure inspired by the Jacobi method and resulting in a new system of equations, which can be solved by Newton’s method much more efficiently. The obtained preconditioned method is shown to exhibit semi-global convergence.