A Batch-Processing FFT-based Method for Efficient Homogenisation of Periodic Media Using GPU

This paper presents an efficient GPU-based batch computing algorithm for solving homogenisation problems in periodic media using the Fast Fourier Transform (FFT)-based method. Building upon the basic scheme, the proposed algorithm utilises the parallel computing capabilities of modern GPUs to significantly accelerate the computation of effective material properties. Two homogenisation problems—thermal conductivity and linear elasticity—are studied to demonstrate the algorithm’s effectiveness. Random composite microstructures are generated with various image resolutions and batch sizes tested to assess computational accuracy and efficiency. Results show that the GPU-based algorithm dramatically reduces computation time compared to traditional CPU methods, with the performance advantage becoming more pronounced at higher resolutions. Notably, the NVIDIA A100 GPU can process 100 homogenisation tasks of 256*256 resolution in approximately 0.5 seconds for thermal conductivity and 0.7 seconds for linear elasticity. These findings highlight the potential of the proposed batch computing approach for fast, large-scale homogenisation, particularly in applications requiring extensive data generation, such as design optimisation and deep learning model training.