Diffusion approximations and domain decomposition method of linear transport equations: Asymptotics and numerics
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© 2015 Elsevier Inc.In this paper we construct numerical schemes to approximate linear transport equations with slab geometry by diffusion equations. We treat both the case of pure diffusive scaling and the case where kinetic and diffusive scalings coexist. The diffusion equations and their data are derived from asymptotic and layer analysis which allows general scattering kernels and general data. We apply the half-space solver in  to resolve the boundary layer equation and obtain the boundary data for the diffusion equation. The algorithms are validated by numerical experiments and also by error analysis for the pure diffusive scaling case.
Published Version (Please cite this version)10.1016/j.jcp.2015.03.014
Publication InfoLi, Q; Lu, Jianfeng; & Sun, W (2015). Diffusion approximations and domain decomposition method of linear transport equations: Asymptotics and numerics. Journal of Computational Physics, 292. pp. 141-167. 10.1016/j.jcp.2015.03.014. Retrieved from https://hdl.handle.net/10161/14099.
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Associate Professor of Mathematics
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science and other related fields.More specifically, his current research focuses include:Electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis; rare events and sampling techniques.