On linearization and preconditioning for radiation diffusion coupled to material thermal conduction equations

Authors:
Tao Feng;Hengbin An;Xijun Yu;Qin Li;Rongpei Zhang
Affiliations:
-;-;-;-;-
Venue:
Journal of Computational Physics
Year:
2013

Citing 13
Cited 0

Hybrid Krylov methods for nonlinear systems of equations

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Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion

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Preconditioning Strategies for Fully Implicit Radiation Diffusion with Material-Energy Transfer

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A choice of forcing terms in inexact Newton method

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On choosing a nonlinear initial iterate for solving the 2-D 3-T heat conduction equations

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A Jacobian-free Newton-Krylov algorithm for compressible turbulent fluid flows

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Improving the numerical convergence of viscous-plastic sea ice models with the Jacobian-free Newton-Krylov method

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On finite difference approximation of a matrix-vector product in the Jacobian-free Newton-Krylov method

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Abstract

Jacobian-free Newton-Krylov (JFNK) method is an effective algorithm for solving large scale nonlinear equations. One of the most important advantages of JFNK method is that there is no necessity to form and store the Jacobian matrix of the nonlinear system when JFNK method is employed. However, an approximation of the Jacobian is needed for the purpose of preconditioning. In this paper, JFNK method is employed to solve a class of non-equilibrium radiation diffusion coupled to material thermal conduction equations, and two preconditioners are designed by linearizing the equations in two methods. Numerical results show that the two preconditioning methods can improve the convergence behavior and efficiency of JFNK method.