FFT-Based Method With Near-Matrix Compression

In this paper, a novel grouping scheme of the basis functions within the framework of the fast Fourier transform (FFT)-based method is proposed for creating a block-sparse structure for the near-matrix, and then FFT-based method with near-matrix compression is established for the efficient analysis of multiscale problems. For a multiscale problem, if an FFT-based method is required to maintain both higher efficiency and higher accuracy at calculating the far interactions, then the near-matrix will be inevitably very large. Compared with the traditional FFT-based method, the proposed method can significantly reduce the near-matrix memory requirement without increasing the time spent. Several numerical examples are provided to demonstrate the correctness and the efficiency of the proposed method.