Parallel Implementations of the Split-Step Fourier Method for Solving Nonlinear Schr\"odinger Systems

We present a parallel version of the well-known Split-Step Fourier method (SSF) for solving the Nonlinear Schr\"odinger equation, a mathematical model describing wave packet propagation in fiber optic lines. The algorithm is implemented under both distributed and shared memory programming paradigms on the Silicon Graphics/Cray Research Origin 200. The 1D Fast-Fourier Transform (FFT) is parallelized by writing the 1D FFT as a 2D matrix and performing independent 1D sequential FFTs on the rows and columns of this matrix. We can attain almost perfect speedup in SSF for small numbers of processors depending on both problem size and communication contention. The parallel algorithm is applicable to other computational problems constrained by the speed of the 1D FFT.