Parallel 3-dim fast Fourier transforms with load balancing of the plane waves

Abstract: The plane wave method is most widely used for solving the Kohn-Sham equations in first-principles materials science computations. In this procedure, the three-dimensional (3-dim) trial wave functions' fast Fourier transform (FFT) is a regular operation and one of the most demanding algorithms in terms of the scalability on a parallel machine. We propose a new partitioning algorithm for the 3-dim FFT grid to accomplish the trade-off between the communication overhead and load balancing of the plane waves. It is shown by qualitative analysis and numerical results that our approach could scale the plane wave first-principles calculations up to more nodes.