Parallel preconditioning for spherical harmonics expansions of the Boltzmann transport equation

While the Monte Carlo method for the Boltzmann transport equation for semiconductors has already been parallelized, this is much more difficult to accomplish for the deterministic spherical harmonics expansion method which requires the solution of a linear system of equations. For the typically employed iterative solvers, preconditioners are required to obtain good convergence rates. These preconditioners are serial in nature and cannot be applied efficiently in a black-box manner to arbitrary systems. Motivated by the underlying physical processes, we present a parallel block-preconditioning scheme that allows us to use existing serial preconditioners in a parallel setting. A reduction of execution times by up to one order of magnitude on current multi-core processors as well as graphics processing units is observed.