A nonlinear elimination preconditioned inexact Newton (NEPIN) algorithm is proposed for problems with localized strong nonlinearities. Due to unbalanced nonlinearities ("nonlinear stiffness''), the traditional inexact Newton method often exhibits a long plateau in the norm of the nonlinear residual or even fails to converge. NEPIN implicitly removes the components causing trouble for the global convergence through a correction based on nonlinear elimination within a subspace that provides a modified direction for the global Newton iteration. Numerical experiments show that NEPIN can be more robust than global inexact Newton algorithms and maintain fast convergence even for challenging problems, such as full potential transonic flows. NEPIN complements several previously studied nonlinear preconditioners with which it compares favorably experimentally on a classic shocked duct flow problem considered herein. NEPIN is shown to be fairly insensitive to mesh resolution and “bad” subproblem identification based on the local Mach number or the local nonlinear residual for transonic flow over a wing.
|Original language||English (US)|
|Number of pages||1|
|Journal||SIAM Journal on Scientific Computing|
|State||Published - Jun 21 2022|
Bibliographical noteKAUST Repository Item: Exported on 2022-06-24
Acknowledgements: The work of the first author was supported by the National Natural Science Foundation of China (11901296) and by the Natural Science Foundation of Jiangsu (BK20180450). The work of the third author was supported by the National Natural Science Foundation of China (11701547). The authors are grateful for the use of a Cray XC40 (Shaheen II) operated by the Supercomputing Laboratory of the King Abdullah University of Science and Technology.
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics