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Published July 1, 2015 | public
Journal Article Open

Diffusion approximations and domain decomposition method of linear transport equations: Asymptotics and numerics


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.

Additional Information

© 2015 Elsevier Inc. Received 29 August 2014; Received in revised form 5 February 2015; Accepted 9 March 2015; Available online 24 March 2015. The research of Q.L. was supported in part by the AFOSR MURI grant FA9550-09-1-0613 and the National Science Foundation under award DMS-1318377. The research of J.L. was supported in part by the Alfred P. Sloan Foundation and the National Science Foundation under award DMS-1312659. The research of W.S. was supported in part by the Simon Fraser University President's Research Start-up Grant PRSG-877723 and NSERC Discovery Individual Grant #611626.

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August 22, 2023
August 22, 2023