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

TL;DR

This paper introduces a parallel implementation of the Split-Step Fourier method for solving the Nonlinear Schrödinger equation, achieving significant speedup on high-performance computing systems for wave propagation simulations.

Contribution

The paper develops a parallel version of the SSF method using distributed and shared memory paradigms, optimizing the 1D FFT for improved computational efficiency.

Findings

Achieves near-perfect speedup with small processor counts

Parallel FFT implementation enhances computational performance

Applicable to other FFT-constrained computational problems

Abstract

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.