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

Xu Yang; François Golse; Zhongyi Huang; Shi Jin

doi:10.3934/nhm.2006.1.143

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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

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: August 31, 2005

Revised: October 31, 2005

Published: February 2006

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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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Mathematics Subject Classification: 35B25, 65M60, 76R50, 82C70.

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