Publication: A multigrid preconditioner and automatic differentiation for non-equilibrium radiation diffusion problems
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A multigrid preconditioner and automatic differentiation for non-equilibrium radiation diffusion problems

- Article in a journal -
 

Area
Radiation

Author(s)
Roland Glowinski , Jari Toivanen

Published in
Journal of Computational Physics

Year
2005

Abstract
We study the efficient solution of non-equilibrium radiation diffusion problems. An implicit time discretization leads to the solution of systems of non-linear equations which couple radiation energy and material temperature. We consider the implicit Euler method, the mid-point scheme, the two-step backward differentiation formula, and a two-stage implicit Runge-Kutta method for time discretization. We employ a Newton-Krylov method in the solution of arising non-linear problems. We describe the computation of the Jacobian matrix for Newton's method using automatic differentiation based on the operator overloading in Fortran 90. For GMRES iterations, we propose a simple multigrid preconditioner applied directly to the coupled linearized problems. We demonstrate the efficiency and scalability of the proposed solution procedure by solving one-dimensional and two-dimensional model problems.

BibTeX
@ARTICLE{
         Glowinski2005Amp,
       title = "A multigrid preconditioner and automatic differentiation for non-equilibrium radiation
         diffusion problems",
       journal = "Journal of Computational Physics",
       volume = "207",
       number = "1",
       pages = "354--374",
       year = "2005",
       issn = "0021-9991",
       doi = "DOI: 10.1016/j.jcp.2005.01.032",
       url =
         "http://www.sciencedirect.com/science/article/B6WHY-4FY3P80-1/2/328924fa186d345737bd44585668f6cc",
       author = "Roland Glowinski and Jari Toivanen",
       keywords = "Non-equilibrium radiation diffusion,Multigrid method,Preconditioning,Newton-Krylov
         method",
       abstract = "We study the efficient solution of non-equilibrium radiation diffusion problems. An
         implicit time discretization leads to the solution of systems of non-linear equations which couple
         radiation energy and material temperature. We consider the implicit Euler method, the mid-point
         scheme, the two-step backward differentiation formula, and a two-stage implicit Runge-Kutta method
         for time discretization. We employ a Newton-Krylov method in the solution of arising non-linear
         problems. We describe the computation of the Jacobian matrix for Newton's method using
         automatic differentiation based on the operator overloading in Fortran 90. For GMRES iterations, we
         propose a simple multigrid preconditioner applied directly to the coupled linearized problems. We
         demonstrate the efficiency and scalability of the proposed solution procedure by solving
         one-dimensional and two-dimensional model problems.",
       ad_area = "Radiation"
}


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