An Accurate Conformal Fourier Transform Method for 3D Discontinuous Functions

作者：Zhu Chunhui; Liu Qing Huo; Liu Lijun^*; Liu Yanhui

来源：IEEE Transactions on Antennas and Propagation, 2015, 63(2): 804-809.

DOI：10.1109/TAP.2014.2378315

• 3D
• conformal Fourier transform
• discontinuous functions
• nonuniform fast Fourier transform

Fourier transform of discontinuous functions are often encountered in computational electromagnetics and other areas. In this work, a highly accurate, fast conformal Fourier transform (CFT) algorithm is proposed to evaluate the finite Fourier transform of 3D discontinuous functions. A curved tetrahedron mesh combined with curvilinear coordinate transform, instead of the Cartesian grid, is adopted to flexibly model an arbitrary shape of the discontinuity boundary. This enables us to take full advantages of high order interpolation and Gaussian quadrature methods to achieve highly accurate Fourier integration results with a low sampling density. The 3D nonuniform fast Fourier transform (NUFFT) helps to keep the complexity of the proposed algorithm to that similar to the traditional 3D FFT algorithm. Therefore, the proposed CFT algorithm can achieve order of magnitude higher accuracy than 3D FFT with lower sampling density and similar computation time. The convergence is proved and verified.

• 出版日期2015-2
• 单位厦门大学