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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2023

On global and monotone convergence of the preconditioned Newton's method for some mildly nonlinear systems

Résumé

For mildly nonlinear systems involving only diagonal nonlinearities, the global, and essentially monotone, convergence of Newton's method can be established based on concavity/convexity arguments and provided that the Jacobian of the system has a nonnegative inverse. We show that the nonlinear preconditioning resulting from the multi-splitting of the system can preserve those attractive theoretical properties. Our convergence analysis applies in particular to block Jacobi-Newton, RASPEN and the two-step RAS/Newton method. The numerical experiment, based on a discrete porous media equation, shows that the performance of those methods is essentially independent of the mesh size.
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Dates et versions

hal-03876457 , version 1 (28-11-2022)
hal-03876457 , version 2 (14-04-2023)

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  • HAL Id : hal-03876457 , version 2

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Konstantin Brenner. On global and monotone convergence of the preconditioned Newton's method for some mildly nonlinear systems. 2023. ⟨hal-03876457v2⟩
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