A Matrix Compression Scheme for Spherical Harmonics Expansions of the Boltzmann Transport Equation

We investigate the numerics behind the numerical solution of the Boltzmann transport equation using an expansion of the distribution function in spherical harmonics for the purpose of electronic device simulation. Traditional implementations of higher order spherical harmonics expansions suffer from huge memory requirements especially for two and three dimensional devices. To overcome these complexity limitations, a compressed matrix storage scheme based on Kronecker products is proposed, which reduces the memory requirements for the storage of the system matrix such that the total memory requirements are asymptotically dominated by the memory required for the unknowns.