On monotone iteration and Schwarz methods for nonlinear parabolic PDEs
Journal of Computational and Applied Mathematics
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Journal of Computational Physics
A choice of forcing terms in inexact Newton method
Journal of Computational and Applied Mathematics
Journal of Computational Physics
On choosing a nonlinear initial iterate for solving the 2-D 3-T heat conduction equations
Journal of Computational Physics
ICCS '09 Proceedings of the 9th International Conference on Computational Science: Part I
Partial Differential Equation-Based Applications and Solvers At Extreme Scale
International Journal of High Performance Computing Applications
Accelerating an inexact Newton/GMRES scheme by subspace decomposition
Applied Numerical Mathematics
SIAM Journal on Scientific Computing
Anderson Acceleration for Fixed-Point Iterations
SIAM Journal on Numerical Analysis
Parallel Algorithms for Fluid-Structure Interaction Problems in Haemodynamics
SIAM Journal on Scientific Computing
Domain decomposition methods for PDE constrained optimization problems
VECPAR'04 Proceedings of the 6th international conference on High Performance Computing for Computational Science
A combined linear and nonlinear preconditioning technique for incompressible navier-stokes equations
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Domain decomposition strategies for nonlinear flow problems in porous media
Journal of Computational Physics
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
Advances in Engineering Software
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Inexact Newton algorithms are commonly used for solving large sparse nonlinear system of equations $F(u^{\ast})=0$ arising, for example, from the discretization of partial differential equations. Even with global strategies such as linesearch or trust region, the methods often stagnate at local minima of $\|F\|$, especially for problems with unbalanced nonlinearities, because the methods do not have built-in machinery to deal with the unbalanced nonlinearities. To find the same solution $u^{\ast}$, one may want to solve instead an equivalent nonlinearly preconditioned system ${\cal F}(u^{\ast})=0$ whose nonlinearities are more balanced. In this paper, we propose and study a nonlinear additive Schwarz-based parallel nonlinear preconditioner and show numerically that the new method converges well even for some difficult problems, such as high Reynolds number flows, where a traditional inexact Newton method fails.