Volume 14, Issue 5
Weighted Interior Penalty Method with Semi-Implicit Integration Factor Method for Non-Equilibrium Radiation Diffusion Equation

Rongpei Zhang, Xijun Yu, Jiang Zhu, Abimael F. D. Loula & Xia Cui

Commun. Comput. Phys., 14 (2013), pp. 1287-1303.

Published online: 2013-11

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  • Abstract

Weighted interior penalty discontinuous Galerkin method is developed to solve the two-dimensional non-equilibrium radiation diffusion equation on unstructured mesh. There are three weights including the arithmetic, the harmonic, and the geometric weight in the weighted discontinuous Galerkin scheme. For the time discretization, we treat the nonlinear diffusion coefficients explicitly, and apply the semiimplicit integration factor method to the nonlinear ordinary differentialequations arising from discontinuous Galerkin spatial discretization. The semi-implicit integration factor method can not only avoid severe timestep limits, but also takes advantage of the local property of DG methods by which small sized nonlinear algebraic systems are solved element by element with the exact Newton iteration method. Numerical results are presented to demonstrate the validity of discontinuous Galerkin method for high nonlinear and tightly coupled radiation diffusion equation.


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@Article{CiCP-14-1287, author = {}, title = {Weighted Interior Penalty Method with Semi-Implicit Integration Factor Method for Non-Equilibrium Radiation Diffusion Equation}, journal = {Communications in Computational Physics}, year = {2013}, volume = {14}, number = {5}, pages = {1287--1303}, abstract = {

Weighted interior penalty discontinuous Galerkin method is developed to solve the two-dimensional non-equilibrium radiation diffusion equation on unstructured mesh. There are three weights including the arithmetic, the harmonic, and the geometric weight in the weighted discontinuous Galerkin scheme. For the time discretization, we treat the nonlinear diffusion coefficients explicitly, and apply the semiimplicit integration factor method to the nonlinear ordinary differentialequations arising from discontinuous Galerkin spatial discretization. The semi-implicit integration factor method can not only avoid severe timestep limits, but also takes advantage of the local property of DG methods by which small sized nonlinear algebraic systems are solved element by element with the exact Newton iteration method. Numerical results are presented to demonstrate the validity of discontinuous Galerkin method for high nonlinear and tightly coupled radiation diffusion equation.


}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.190612.010313a}, url = {http://global-sci.org/intro/article_detail/cicp/7202.html} }
TY - JOUR T1 - Weighted Interior Penalty Method with Semi-Implicit Integration Factor Method for Non-Equilibrium Radiation Diffusion Equation JO - Communications in Computational Physics VL - 5 SP - 1287 EP - 1303 PY - 2013 DA - 2013/11 SN - 14 DO - http://dor.org/10.4208/cicp.190612.010313a UR - https://global-sci.org/intro/article_detail/cicp/7202.html KW - AB -

Weighted interior penalty discontinuous Galerkin method is developed to solve the two-dimensional non-equilibrium radiation diffusion equation on unstructured mesh. There are three weights including the arithmetic, the harmonic, and the geometric weight in the weighted discontinuous Galerkin scheme. For the time discretization, we treat the nonlinear diffusion coefficients explicitly, and apply the semiimplicit integration factor method to the nonlinear ordinary differentialequations arising from discontinuous Galerkin spatial discretization. The semi-implicit integration factor method can not only avoid severe timestep limits, but also takes advantage of the local property of DG methods by which small sized nonlinear algebraic systems are solved element by element with the exact Newton iteration method. Numerical results are presented to demonstrate the validity of discontinuous Galerkin method for high nonlinear and tightly coupled radiation diffusion equation.


Rongpei Zhang, Xijun Yu, Jiang Zhu, Abimael F. D. Loula & Xia Cui. (2020). Weighted Interior Penalty Method with Semi-Implicit Integration Factor Method for Non-Equilibrium Radiation Diffusion Equation. Communications in Computational Physics. 14 (5). 1287-1303. doi:10.4208/cicp.190612.010313a
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