Computational Physics and Methods A fast spectral method for the Boltzmann collision operator with general collision kernels

We propose a simple fast spectral method for the Boltzmann collision operator with general collision kernels. Compared with the direct spectral method [8] which requires O(N6) memory to store precomputed weights and has O(N6) numerical complexity, the new method has complexity O(MN4 logN), where N is the number of discretization points in each velocity dimension, M is the total number discretization points on a sphere and M N2. Furthermore, it requires only O(MN4) memory to store precomputed functions for more general collision kernels. Unlike previous methods, our new method can apply to arbitrary collision kernels including angularly dependent models. A series of numerical tests is performed to illustrate the efficiency and accuracy of the proposed method.