Year: 2012
Numerical Mathematics: Theory, Methods and Applications, Vol. 5 (2012), Iss. 1 : pp. 62–84
Abstract
An algebraic Newton-multigrid method is proposed in order to efficiently solve systems of nonlinear reaction-diffusion problems with stochastic coefficients. These problems model the conversion of starch into sugars in growing apples. The stochastic system is first converted into a large coupled system of deterministic equations by applying a stochastic Galerkin finite element discretization. This method leads to high-order accurate stochastic solutions. A stable and high-order time discretization is obtained by applying a fully implicit Runge-Kutta method. After Newton linearization, a point-based algebraic multigrid solution method is applied. In order to decrease the computational cost, alternative multigrid preconditioners are presented. Numerical results demonstrate the convergence properties, robustness and efficiency of the proposed multigrid methods.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2011.m12si04
Numerical Mathematics: Theory, Methods and Applications, Vol. 5 (2012), Iss. 1 : pp. 62–84
Published online: 2012-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Multigrid stochastic Galerkin finite element method reaction-diffusion problems implicit Runge-Kutta method and PDEs with random coefficients.
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A two-level stochastic collocation method for semilinear elliptic equations with random coefficients
Chen, Luoping
Zheng, Bin
Lin, Guang
Voulgarakis, Nikolaos
Journal of Computational and Applied Mathematics, Vol. 315 (2017), Iss. P.195
https://doi.org/10.1016/j.cam.2016.10.030 [Citations: 8]