AN ASYMPTOTIC-PRESERVING STOCHASTIC GALERKIN METHOD FOR THE SEMICONDUCTOR BOLTZMANN EQUATION WITH RANDOM INPUTS AND DIFFUSIVE SCALINGS

被引：28

作者：

Jin, Shi ^{[1
,2
,3
]}

Liu, Liu ^{[3
]}

机构：

[1] Shanghai Jiao Tong Univ, Inst Nat Sci, Dept Math, MOE LSEC, Shanghai 200240, Peoples R China

[2] Shanghai Jiao Tong Univ, SHL MAC, Shanghai 200240, Peoples R China

[3] Univ Wisconsin Madison, Dept Math, Madison, WI 53706 USA

来源：

MULTISCALE MODELING & SIMULATION | 2017年 / 15卷 / 01期

基金：

美国国家科学基金会;

关键词：

semiconductor Boltzmann equation; uncertainty quantification; diffusion limit; asymptotic preserving; random inputs; generalized polynomial chaos; spectral accuracy; DIFFERENTIAL-EQUATIONS; RELAXATION SCHEMES; AP SCHEMES;

D O I：

10.1137/15M1053463

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

dIn this paper, we develop a generalized polynomial chaos approach based stochastic Galerkin (gPC-SG) method for the linear semiconductor Boltzmann equation with random inputs and diffusive scalings. The random inputs are due to uncertainties in the collision kernel or initial data. We study the regularity (uniform in the Knudsen number) of the solution in the random space and prove the spectral accuracy of the gPC-SG method. We then use the asymptotic-preserving framework for the deterministic counterpart developed in [S. Jin and L. Pareschi, J. Comput. Phys., 161 (2000), pp. 312-330] to come up with the stochastic asymptotic-preserving gPC-SG method for the problem under study which is efficient in the diffusive regime. Numerical experiments are conducted to validate the accuracy and asymptotic properties of the method.

引用

页码：157 / 183

页数：27

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