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Numerical Algorithms
Erschienen in: Numerical Algorithms 1/2024

18.08.2023 | Original Paper

Local and parallel multigrid method for semilinear Neumann problem with nonlinear boundary condition

verfasst von: Fei Xu, Bingyi Wang, Manting Xie

Erschienen in: Numerical Algorithms | Ausgabe 1/2024

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Abstract

A novel local and parallel multigrid method is proposed in this study for solving the semilinear Neumann problem with nonlinear boundary condition. Instead of solving the semilinear Neumann problem directly in the fine finite element space, we transform it into a linear boundary value problem defined in each level of a multigrid sequence and a small-scale semilinear Neumann problem defined in a low-dimensional correction subspace. Furthermore, the linear boundary value problem can be efficiently solved using local and parallel methods. The proposed process derives an optimal error estimate with linear computational complexity. Additionally, compared with existing multigrid methods for semilinear Neumann problems that require bounded second order derivatives of nonlinear terms, ours only needs bounded first order derivatives. A rigorous theoretical analysis is proposed in this paper, which differs from the maturely developed theories for equations with Dirichlet boundary conditions.
Vorheriger Artikel High order hybrid asymptotic augmented finite volume methods for nonlinear degenerate wave equations
Nächster Artikel On the viscosity approximation type iterative method and its non-linear behaviour in the generation of Mandelbrot and Julia sets

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Metadaten
Titel
Local and parallel multigrid method for semilinear Neumann problem with nonlinear boundary condition
verfasst von
Fei Xu
Bingyi Wang
Manting Xie
Publikationsdatum
18.08.2023
Verlag
Springer US
Erschienen in
Numerical Algorithms / Ausgabe 1/2024
Print ISSN: 1017-1398
Elektronische ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-023-01643-5

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