Numerical study of a domain decomposition method for a two-scale linear transport equation
Xu Yang - 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  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 . We also provide an improved second order method that provides a more accurate numerical solution than that proposed in .
Keywords: Linear transport equation, diffusion approximation, domain decomposition, numerical approximation.
Received: September 2005; Revised: November 2005; Published: January 2006.
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