System matrix compression for spherical harmonics expansions of the Boltzmann transport equation

Due to its deterministic nature, the spherical harmonics expansion of the Boltzmann transport equation is an attractive alternative to the Monte Carlo method for the purpose of electronic device simulation. The major drawback when using higher order expansions is the huge memory requirement, especially for two- and three-dimensional simulations. We propose a method to compress the resulting system of linear equations, such that memory requirements are reduced by up to two orders of magnitude. In that context we discuss criteria for the selection of an appropriate linear equation solver and show that execution times for matrix-vector multiplications using the compressed matrix scheme on a single CPU core are comparable to that of an uncompressed system matrix. Numerical results demonstrate the applicability of our method and confirm our theoretical results.