Diffusion approximations and domain decomposition method of linear transport equations: Asymptotics and numerics
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2015-07-01
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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 [20] 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.
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Li, Q, J Lu and W Sun (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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Jianfeng Lu
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science, machine learning, and other related fields.
More specifically, his current research focuses include:
High dimensional PDEs; generative models and sampling methods; control and reinforcement learning; electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis.
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