BibTeX
@ARTICLE{
Glowinski2005Amp,
title = "A multigrid preconditioner and automatic differentiation for nonequilibrium radiation
diffusion problems",
journal = "Journal of Computational Physics",
volume = "207",
number = "1",
pages = "354374",
year = "2005",
issn = "00219991",
doi = "DOI: 10.1016/j.jcp.2005.01.032",
url =
"http://www.sciencedirect.com/science/article/B6WHY4FY3P801/2/328924fa186d345737bd44585668f6cc",
author = "Roland Glowinski and Jari Toivanen",
keywords = "Nonequilibrium radiation diffusion,Multigrid method,Preconditioning,NewtonKrylov
method",
abstract = "We study the efficient solution of nonequilibrium radiation diffusion problems. An
implicit time discretization leads to the solution of systems of nonlinear equations which couple
radiation energy and material temperature. We consider the implicit Euler method, the midpoint
scheme, the twostep backward differentiation formula, and a twostage implicit RungeKutta method
for time discretization. We employ a NewtonKrylov method in the solution of arising nonlinear
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
onedimensional and twodimensional model problems.",
ad_area = "Radiation"
}
