A stochastic asymptotic-preserving scheme for the bipolar semiconductor Boltzmann-Poisson system with random inputs and diffusive scalings
For researchers in computational physics and uncertainty quantification, this work provides a rigorous framework for handling random inputs in multiscale kinetic models, though it is an incremental extension of existing gPC-SG methods.
This paper develops a stochastic asymptotic-preserving scheme for the bipolar semiconductor Boltzmann-Poisson system with random inputs, achieving uniform spectral convergence in the random space and exponential decay in time. Numerical experiments validate the method's accuracy and efficiency.
In this paper, we study the bipolar Boltzmann-Poisson model, both for the deterministic system and the system with uncertainties, with asymptotic behavior leading to the drift diffusion-Poisson system as the Knudsen number goes to zero. The random inputs can arise from collision kernels, doping profile and initial data. We adopt a generalized polynomial chaos approach based stochastic Galerkin (gPC-SG) method. Sensitivity analysis is conducted using hypocoercivity theory for both the analytical solution and the gPC solution for a simpler model that ignores the electric field, and it gives their convergence toward the global Maxwellian exponentially in time. A formal proof of the stochastic asymptotic-preserving (s-AP) property and a uniform spectral convergence with error exponentially decaying in time in the random space of the scheme is given. Numerical experiments are conducted to validate the accuracy, efficiency and asymptotic properties of the proposed method.