Randomized trial demonstrates spectral accuracy in a stochastic Galerkin method for diffusive scaling in semiconductor modeling, indicating improved computational efficiency.
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.
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Jin et al. (2017) studied this question.
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