Multi-GPU fast Fourier transforms in MATLAB (for large-scale phase-field crystal simulations)

2026-03-26

AI Summary

This work addresses the challenges of limited single-GPU memory capacity and low computational efficiency of spectral methods in large-scale phase-field crystal simulations. To overcome these limitations, the authors propose a MATLAB-based multi-GPU parallel framework that supports two- and three-dimensional fast Fourier transforms (FFT) for efficiently solving high-order partial differential equations discretized via pseudospectral methods. The framework integrates two complementary multi-GPU strategies to simultaneously alleviate memory bottlenecks and significantly enhance computational performance, while correctly enforcing periodic boundary conditions. Experimental results demonstrate that the proposed approach achieves approximately 6× speedup over a state-of-the-art CPU implementation with hundreds of cores for standard phase-field crystal simulations, with acceleration ratios reaching up to 60× in multiphysics-coupled scenarios.

Abstract

We present a MATLAB-based framework for two- and three-dimensional fast Fourier transforms on multiple GPUs for large-scale numerical simulations using the pseudo-spectral Fourier method. The software implements two complementary multi-GPU strategies that overcome single-GPU memory limitations and accelerate spectral solvers. This approach is motivated by and applied to phase-field crystal (PFC) models, which are governed by tenth-order partial differential equations, require fine spatial resolution, and are typically formulated in periodic domains. Our resulting numerical framework achieves significant speedups, approximately sixfold for standard PFC simulations and up to sixtyfold for multiphysics extensions, compared to a purely CPU-based implementation running on hundreds of cores.

Problem

• phase-field crystal
• multi-GPU
• fast Fourier transform
• large-scale simulation
• spectral solver

Innovation

• multi-GPU FFT
• phase-field crystal
• pseudo-spectral method
• large-scale simulation
• MATLAB framework