On a faster parallel implementation of the split-step Fourier method

A new parallel implementation of the split-step Fourier method is presented. The computational core of our scheme focuses on the parallelization of the whole linear step using a combination of fast cyclic convolutions and fast Fourier transforms. For all problems and cluster sizes tested, our method exhibits better performance than conventional parallel implementations of the split-step Fourier method using state-of-the art parallel fast Fourier transforms.