American Institute of Mathematical Sciences

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March  2006, 1(1): 143-166. doi: 10.3934/nhm.2006.1.143

Numerical study of a domain decomposition method for a two-scale linear transport equation

Xu Yang 1, , François Golse 2, , Zhongyi Huang 3, and  Shi Jin 1,

1. 

Department of Mathematics, University of Wisconsin, Madison, WI 53706, United States, United States
2. 

Institut Universitaire de France & Département de Mathématiques et Applications, Ecole Normale Supérieure Paris, 45 rue d'Ulm, 75230 Paris cedex 05, France
3. 

Dept. of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received  September 2005 Revised  November 2005 Published  January 2006

We perform a numerical study on a domain decomposition method proposed in [13] for the linear transport equation between a diffusive and a non-diffusive region. This method avoids iterating the diffusion and transport solutions as in a typical domain decomposition method. Our numerical results, in both one and two space dimensions, confirm the theoretical analysis of [13]. We also provide an improved second order method that provides a more accurate numerical solution than that proposed in [13].
Keywords: domain decomposition, Linear transport equation, numerical approximation., diffusion approximation.
Mathematics Subject Classification: 35B25, 65M60, 76R50, 82C7.
Citation: Xu Yang, François Golse, Zhongyi Huang, Shi Jin. Numerical study of a domain decomposition method for a two-scale linear transport equation. Networks and Heterogeneous Media, 2006, 1 (1) : 143-166. doi: 10.3934/nhm.2006.1.143
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