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

Pages: 143 - 166, Volume 1, Issue 1, March 2006

doi:10.3934/nhm.2006.1.143       Abstract        Full Text (495.5K)       Related Articles

Xu Yang - Department of Mathematics, University of Wisconsin, Madison, WI 53706, United States (email)
François Golse - Institut Universitaire de France & Département de Mathématiques et Applications, Ecole Normale Supérieure Paris, 45 rue d'Ulm, 75230 Paris cedex 05, France (email)
Zhongyi Huang - Dept. of Mathematical Sciences, Tsinghua University, Beijing 100084, China (email)
Shi Jin - Department of Mathematics, University of Wisconsin, Madison, WI 53706, United States (email)

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].

Keywords:  Linear transport equation, diffusion approximation, domain decomposition, numerical approximation.
Mathematics Subject Classification:  35B25, 65M60, 76R50, 82C70.

Received: September 2005;      Revised: November 2005;      Published: January 2006.