Now showing items 1-6 of 6
Diffusion approximations and domain decomposition method of linear transport equations: Asymptotics and numerics
(Journal of Computational Physics, 2015-07-01)
© 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 ...
Validity and Regularization of Classical Half-Space Equations
(Journal of Statistical Physics, 2017-01-01)
© 2016, Springer Science+Business Media New York.Recent result (Wu and Guo in Commun Math Phys 336(3):1473–1553, 2015) has shown that over the 2D unit disk, the classical half-space equation (CHS) for the neutron transport ...
A convergent method for linear half-space kinetic equations
We give a unified proof for the well-posedness of a class of linear half-space equations with general incoming data and construct a Galerkin method to numerically resolve this type of equations in a systematic way. Our main ...
Randomized sampling for basis functions construction in generalized finite element methods
In the context of generalized finite element methods for elliptic equations with rough coefficients $a(x)$, efficiency and accuracy of the numerical method depend critically on the use of appropriate basis functions. This ...
Half-space kinetic equations with general boundary conditions
(Mathematics of Computation, 2017-01-01)
© 2016 American Mathematical Society.We study half-space linear kinetic equations with general boundary conditions that consist of both given incoming data and various types of reflections, extending our previous work on ...
An asymptotic preserving method for transport equations with oscillatory scattering coefficients
We design a numerical scheme for transport equations with oscillatory periodic scattering coefficients. The scheme is asymptotic preserving in the diffusion limit as Knudsen number goes to zero. It also captures ...