Abstract
In 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
