| This paper study the basic theory and practical application of the connected local field(CLF) method in the one-dimensional, two-dimensional, three-dimensional and the reconstruction of two-dimensional local field situation systematically, and then give the detailed derivation process of the formulas by the CLF method in the above cases. Finally, we verify the superiorities of the CLF method in calculation accuracy, sampling density and other aspects by calculating the actual electromagnetic radiation and scattering numerical examples.For the simple case of one-dimensional homogeneous Helmholtz equation, we present a derivation of the formula for solving the one-dimensional homogeneous with high precision numerical solution and a brief review of the one-dimensional finite-difference frequency-domain(FDFD) equation. Then, these two algorithms are used to calculate the changes of the amplitude and phase of TEM waves when propagate in free space and along the z axis. By comparison with the analytical results and numerical dispersion error analysis, verify the advantages compared to the traditional one-dimensional FDFD method of the one-dimensional CLF method on mesh generation density and the calculate accuracy of the amplitude and phase.Study and implement the two-dimensional CLF method that based on Fourier-Bessel series expansion. Five-point two-dimensional local field formula based on Fourier-Bessel series expansion is derived, and the formula is used for practical frequency domain finite difference(FDFD) calculation. The numerical results show that the method in this paper are better than existing five-point FDFD method both in the density of mesh generation and the calculation accuracy of phase obviously. At the same time, the practical results show that general FDFD calculation cannot achieve the case said in the literature that the spatial sampling density nearly to two points per wavelength for the complexity of the field distribution.Specific to the reconstruction problem for the two-dimensional local field, we present a concise deduction process of nine-point two-dimensional field reconstruction formula based on the Fourier-Bessel series expansion, greatly simplifies the derivation of the reconstruction formula in the reference, and then the errors of the reconstruction formula in the reference are corrected. On this basis, the examples of reconstructing the field of single line source and two line sources are given. The numerical results show that the literature method is unable to get the right field reconstruction results, but the algorithm in this paper is still able to get accurate results in the case that the reconstruction region is as large as 50 square wavelengths.Three-dimensional method of connected local field is more complicated. We finally give the detailed derivation steps of the CLF equation(namely LFE3D-27) in three-dimensional, and describe the added form of electric dipole source and electric dipole radiation in the traditional three-dimensional FDTD method briefly. Then, both algorithms are used to calculate the electric dipole far-field radiation pattern. By comparing the numerical results of the two algorithms with the analytical solution, verify the calculation accuracy and computational performance of the three-dimensional CLF method in the actual calculation. |
