Newton-Multigrid for Biological Reaction-Diffusion Problems with Random Coefficients
| Autor: | Nico Scheerlinck, Stefan Vandewalle, Eveline Rosseel |
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| Rok vydání: | 2012 |
| Předmět: |
Control and Optimization
Discretization Applied Mathematics Mathematical analysis MathematicsofComputing_NUMERICALANALYSIS Computer Science::Numerical Analysis Finite element method Mathematics::Numerical Analysis Computational Mathematics Nonlinear system stochastic finite element method Multigrid method Linearization Modeling and Simulation Convergence (routing) Stochastic optimization Algebraic number stochastic PDEs multigrid Mathematics |
| Zdroj: | Numerical Mathematics: Theory, Methods and Applications. 5:62-84 |
| ISSN: | 2079-7338 1004-8979 |
| Popis: | 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. ispartof: Numerical Mathematics vol:5 issue:1 pages:62-84 status: published |
| Databáze: | OpenAIRE |
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