An OpenCL implementation for the solution of TDSE on GPU and CPU architectures

TL;DR

This paper presents an OpenCL-based GPU implementation for solving the Time-Dependent Schrödinger Equation, demonstrating significant speedups over CPU implementations on NVIDIA and AMD GPUs.

Contribution

It introduces a generic parallel OpenCL code for solving first-order ODEs, specifically applied to the TDSE for atomic hydrogen in strong laser fields.

Findings

GPU implementation achieved up to 40x speedup over CPU.

Excellent scalability observed on different GPU architectures.

Significant performance improvements over serial CPU computations.

Abstract

Open Computing Language (OpenCL) is a parallel processing language that is ideally suited for running parallel algorithms on Graphical Processing Units (GPUs). In the present work we report on the development of a generic parallel single-GPU code for the numerical solution of a system of first-order ordinary differential equations (ODEs) based on the OpenCL model. We have applied the code in the case of the Time-Dependent Schr\"odinger Equation of atomic hydrogen in a strong laser field and studied its performance on NVIDIA and AMD GPUs against the serial performance on a CPU. We found excellent scalability and a significant speed-up of the GPU over the CPU device which tended towards a value of about 40 with significant speedups expected against multi-core CPUs.