Abstract:
This work introduces a fast algorithm for the energy space boson Boltzmann collision operator. Compared to the direct O(N^3) calculation and the previous O(N^2 logN) method, the new algorithm runs in complexity O(N log^2 N), which is optimal up to a logarithmic factor (N is the number of gird points in energy space). The basic idea is to partition the 3-D summation domain recursively into elementary shapes so that the summation within each shape becomes a special double convolution that can be computed efficiently by the fast Fourier transform. Numerical examples are presented to illustrate the efficiency and accuracy of the proposed algorithm. |