A Bi-fidelity Method For The Semiconductor Boltzmann Equation With Random Parameters

In this thesis,we use the bi-fidelity method to solve the semiconductor Boltzmann equation with a large number of random variables.Due to the complexity of the numerical solution of the semiconductor Boltzmann equation,the classical Monte Carlo method will be impossible to implement when the number of sampling points of random variables is huge.Jin Shi and Liu Liu successfully applied the stochastic Galerkin method to the semiconductor Boltzmann equation,but solving the semiconductor Boltzmann equation by the bi-fidelity method is still unfinished.The main work of this thesis is to solve the semiconductor Boltzmann equation with random inputs.