Deterministic Numerical Solution of the Boltzmann Transport Equation

Abstract

Due to its deterministic nature, the spherical harmonics expansion method is an attractive alternative to the Monte Carlo method for the solution of the Boltzmann Transport Equation for the purpose of electronic device simulation. However, since the problem is posed in a six-dimensional problem space emerging from the three-dimensional space variable and the three-dimensional momentum variable, deterministic approaches typically suffer from huge memory requirements, which have prohibited their application to two and three-dimensional simulations. To reduce these high memory requirements, we first show that the coupling of the resulting system of partial differential equations is only weak and then propose a new scheme for the lossless compression of the resulting system of linear equations after discretization. This reduces the overall memory requirements significantly and paves the way for deterministic three-dimensional device simulations. Numerical experiments demonstrate the applicability of our method and confirm our theoretical results.