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

Xu Yang; François Golse; Zhongyi Huang; Shi Jin; Xu Yang; François Golse; Zhongyi Huang; Shi Jin

doi:10.3934/nhm.2006.1.143

Networks and Heterogeneous Media

2006, Volume 1, Issue 1: 143-166. doi: 10.3934/nhm.2006.1.143

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

Xu Yang ^{1
,},
François Golse ^{2
,},
Zhongyi Huang ^{3
,},
Shi Jin ^{1
,}

1.
Department of Mathematics, University of Wisconsin, Madison, WI 53706
2.
Institut Universitaire de France & Département de Mathématiques et Applications, Ecole Normale Supérieure Paris, 45 rue d'Ulm, 75230 Paris cedex 05
3.
Dept. of Mathematical Sciences, Tsinghua University, Beijing 100084

Received: 01 September 2005 Revised: 01 November 2005
35B25, 65M60, 76R50, 82C70.

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].
- Linear transport equation,
- diffusion approximation,
- domain decomposition,
- numerical approximation
Citation: Xu Yang, François Golse, Zhongyi Huang, Shi Jin. Numerical study of a domain decomposition method for a two-scale linear transport equation[J]. Networks and Heterogeneous Media, 2006, 1(1): 143-166. doi: 10.3934/nhm.2006.1.143

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Abstract

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].
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