适用于周期性问题的Poisson模块库求解器的开发及验证OA

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.