High Accuracy Finite Difference Time Domain Method And Its Application

The finite-difference time-domain has been widely used in solving electromagnetic problems because of its good performance of instantaneity and adaptability. When it comes to the traditional finite-difference time-domain method, second-order central difference scheme, which arises low accuracy and great dispersion error, is involved in both the space domain and the time domain. For the late-time analysis of electrically large domains, the waveform is often distorted seriously because of the accumulation of numerical errors. This is the inherent drawbacks of finite-difference time-domain method.To improve the accuracy performance of FDTD method, many high-order finite difference time domain methods has been presented during these decades. Among these high order schemes, the time domain scheme based on symplectic method has excellent performance of accuracy. In this work, the discrete singular convolution method is involved in approximating the spatial derivatives where 2Mth order accuracy can be acquired. Meanwhile, the symplectic integrator propagator method is applied in time domain where the accuracy in time domain is improved to 4th order. To the issue of the accuracy and effectiveness of FDTD, innovative and exploratory work are listed as follow.1. High order FDTD method based on wave equations is derived, where discrete singular convolution method with 2M-th order accuracy is involved in approximating the 2nd order partial derivatives. And the symplectic integrator propagator method is applied in time domain where 4th order accuracy is achieved. Numerical examples show the accuracy performance of the presented high order scheme, and the flexibility is also proved in analysis of complex boundary conditions. Referring to the exact solutions of regular waveguides, the errors of high order schemes is about 200dB less than the traditional FDTD method. Meanwhile, the first 4 cutoff wave numbers of ridged waveguides are acquired by our high order schemes, which coincide well with the results already been published. 2. The application of perfectly matched layer to (2M, 4) scheme FDTD is derived, where 2M-th order discrete singular convolution in space domain and 4th order symplectic integrator propagator method in time domain is applied. Meanwhile, the connecting boundary condition of total-field and scattered field based on high order scheme is also presented. Based on the conclusion above, the bistatic RCS of both single conducting cylinder and double conducting cylinders are computed. The results show the good performance of (2M, 4) scheme FDTD. Applying the periodic boundary conditions, both the monostatic and bistatic RCS of one-dimensional metallic wire array are computed, and its performance of absorbing EM waves is proved. Meanwhile, the scattering properties of metallic cylinder coated by metallic wire array are analyzed. Results show that the forward scattering is strengthened while the backward scattering is decreased to some level.