快速傅里叶变换（FFT）算法广泛应用于科学计算等领域。为了充分挖掘图形处理器（GPU）的计算能力并进一步提高FFT的计算效率，该文针对矩阵形式的Stockham FFT，提出了一种基于Matrix Core的高性能多维FFT计算方案。在计算优化方面，该方案利用Matrix Core加速FFT计算中的矩阵乘运算，同时通过编译器内部指令完成小粒度的矩阵乘加，使得Matrix Core支持更多尺寸的FFT计算。在内存优化方面，该方案使用2层迭代策略，以充分利用共享内存，减少与全局内存的数据交换；根据Matrix Core的矩阵数据在各个线程寄存器中的分布规律，直接在寄存器上完成FFT计算中大量存在的矩阵逐元素乘操作；通过对共享内存中的数据进行重排来缓解存储体冲突，并采用双缓冲策略缓解访存瓶颈。该文还提出了高效的矩阵转置策略，以加速多维FFT计算。在AMD MI250 GPU平台上将该方案与GPU上主流的高性能FFT计算库rocFFT和VkFFT进行了比较实验，结果表明：该方案在AMD MI250上的1维、2维和3维FFT平均计算效率均优于rocFFT和VkFFT，3维FFT的平均计算效率为rocFFT的1.5倍，为VkFFT的2.0倍，具有较好的性能提升；mcFFT的计算精度与rocFFT和VkFFT保持在相同水平。

Fast Fourier transform (FFT) algorithm finds widespread application in scientific computing and related fields. To fully leverage the computational power of the GPU and further enhance the performance of FFT calculations, this paper proposed a high-performance multi-dimensional FFT computation scheme based on the Matrix Core for the matrix form of Stockham FFT. In terms of computational optimization, this scheme utilizes Matrix Core to accelerate matrix multiplications in FFT computation while leveraging compiler intrinsic instructions to perform small-grained matrix multiply-accumulate operations, enabling Matrix Core to support FFT computations of more sizes. To minimize memory access, the proposed scheme directly performs matrix element-wise multiplication operations in the registers according to the distribution pattern of Matrix Core’s data across thread registers. It also mitigates bank conflicts by reordering data in shared memory, adopts a double-buffering strategy to alleviate access bottlenecks, and proposes an efficient matrix transposition strategy to accelerate multidimensional FFT computations. In this paper, the proposed scheme was compared to the well-known high-performance FFT computation libraries rocFFT and VkFFT on the AMD MI250 GPU platform. The results demonstrate that the proposed scheme outperforms rocFFT and VkFFT in terms of average computational performance for 1-dimensional, 2-dimensional, and 3-dimensional FFTs on the AMD MI250 GPU platform. For 3D FFT calculation, this method has an average performance that is 1.5 times faster than rocFFT and 2.0 times faster than VkFFT, demonstrating significant performance improvements.