The Comparison of Finite Difference Methods for Radiation Diffusion Equations
In this paper, the difference between the Alternating
Direction Method (ADM) and the Non-Splitting Method (NSM) is
investigated, while both methods applied to the simulations for 2-D
multimaterial radiation diffusion issues. Although the ADM have the
same accuracy orders with the NSM on the uniform meshes, the
accuracy of ADM will decrease on the distorted meshes or the
boundary of domain. Numerical experiments are carried out to
confirm the theoretical predication.
[1] P.G. Ciarlet and J.L. Lions, Handbook of Numerical Analysis, Volume I,
Finite Difference Methods (Part 1), Splitting and Alternating Direction
Methods, G.I. Marchuk (North-Holland, 1990).
[2] Deyuan Li, Hongshou Shui, Minjun Tang, On the finite difference scheme
of two-dimensional parabolic equation in a non-rectangular mesh, J.
Numer. Methods Comput. Appl. 4 (1980) 217.
[3] Guangwei Yuan, Zhiqiang Sheng, Analysis of accuracy of a finite volume
scheme for diffusion equations on distorted meshes. J. Comput. Phys.
(2007) 224.
[1] P.G. Ciarlet and J.L. Lions, Handbook of Numerical Analysis, Volume I,
Finite Difference Methods (Part 1), Splitting and Alternating Direction
Methods, G.I. Marchuk (North-Holland, 1990).
[2] Deyuan Li, Hongshou Shui, Minjun Tang, On the finite difference scheme
of two-dimensional parabolic equation in a non-rectangular mesh, J.
Numer. Methods Comput. Appl. 4 (1980) 217.
[3] Guangwei Yuan, Zhiqiang Sheng, Analysis of accuracy of a finite volume
scheme for diffusion equations on distorted meshes. J. Comput. Phys.
(2007) 224.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:61404", author = "Ren Jian and Yang Shulin", title = "The Comparison of Finite Difference Methods for Radiation Diffusion Equations", abstract = "In this paper, the difference between the Alternating
Direction Method (ADM) and the Non-Splitting Method (NSM) is
investigated, while both methods applied to the simulations for 2-D
multimaterial radiation diffusion issues. Although the ADM have the
same accuracy orders with the NSM on the uniform meshes, the
accuracy of ADM will decrease on the distorted meshes or the
boundary of domain. Numerical experiments are carried out to
confirm the theoretical predication.", keywords = "Alternating Direction Method, Non-SplittingMethod, Radiation Diffusion.", volume = "2", number = "8", pages = "584-3", }