A FAST ALGORITHM FOR THE ENERGY SPACE BOSON BOLTZMANN COLLISION OPERATOR

作者：Hu Jingwei^*; Ying Lexing

来源：Mathematics of Computation, 2015, 84(291): 271-288.

• Quantum Boltzmann equation
• energy space boson Boltzmann equation
• recursive domain decomposition
• double convolution
• fast Fourier transform

This paper introduces a fast algorithm for the energy space boson Boltzmann collision operator. Compared to the direct O(N-3) calculation and the previous O(Nlog(2)N) method [Markowich and Pareschi, 2005], the new algorithm runs in complexity O(N log(2)N), which is optimal up to a logarithmic factor (N is the number of grid 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.

• 出版日期2015-1