For Poisson problems with periodic boundary conditions, the use of the traditional SOR solution algorithm does not permit the rapid convergence of the Poisson solver. To address this limitation, a novel multigrid iterative Poisson solver (Poisson-SOR-MG) based on finite difference methods was developed, leveraging multigrid acceleration techniques to overcome the drawbacks of SOR. Additionally, a 3D Fourier spectral transform algorithm was designed by coupling 1D Fast Fourier Transform (FFT) with 3D parallel communication algorithms, eliminating cumbersome transpose techniques. Building on this, a standard 2π-periodic Poisson-Fourier solver was developed and validated, achieving spectral accuracy. However, the standard 2π-periodic Poisson-Fourier solver cannot be directly applied to general engineering problems. To resolve this, theoretical analysis based on coordinate stretching transformations was conducted, leading to the further development and validation of a generalized arbitrary-periodic Poisson-Fourier solver.

 multigrid methods, 3D Fourier spectral transformation, Poisson solvers, SOR iterative methods; coordinate mapping transformation