Accelerating the Fourier split operator method via graphics processing units

TL;DR

This paper demonstrates that graphics processing units significantly accelerate the Fourier split operator method, enabling efficient solutions to time-dependent PDEs like Schrödinger and Dirac equations with over tenfold performance improvements.

Contribution

The paper introduces GPU-accelerated implementations of the Fourier split operator method, achieving substantial speedups over traditional CPU-based approaches.

Findings

Over tenfold performance improvement in solving PDEs

Efficient GPU-based Fourier transforms

Potential for real-time quantum simulations

Abstract

Current generations of graphics processing units have turned into highly parallel devices with general computing capabilities. Thus, graphics processing units may be utilized, for example, to solve time dependent partial differential equations by the Fourier split operator method. In this contribution, we demonstrate that graphics processing units are capable to calculate fast Fourier transforms much more efficiently than traditional central processing units. Thus, graphics processing units render efficient implementations of the Fourier split operator method possible. Performance gains of more than an order of magnitude as compared to implementations for traditional central processing units are reached in the solution of the time dependent Schr\"odinger equation and the time dependent Dirac equation.