Volume 6, pp. 271-290, 1997.

Krylov subspace acceleration for nonlinear multigrid schemes

T. Washio and C. W. Oosterlee


In this paper we present a Krylov acceleration technique for nonlinear PDEs. As a ‘preconditioner’ we use nonlinear multigrid schemes such as the Full Approximation Scheme (FAS) [1]. The benefits of nonlinear multigrid used in combination with the new accelerator are illustrated by difficult nonlinear elliptic scalar problems, such as the Bratu problem, and for systems of nonlinear equations, such as the Navier-Stokes equations.

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Key words

nonlinear Krylov acceleration, nonlinear multigrid, robustness, restarting conditions.

AMS subject classifications

65N55, 65H10, 65Bxx.

ETNA articles which cite this article

Vol. 10 (2000), pp. 1-20 Achi Brandt: General highly accurate algebraic coarsening
Vol. 15 (2003), pp. 165-185 C. W. Oosterlee: On multigrid for linear complementarity problems with application to American-style options
Vol. 55 (2022), pp. 285-309 Fei Xue: One-step convergence of inexact Anderson acceleration for contractive and non-contractive mappings

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