Application Of MRTD And Its Improved Algorithms To Electromagnetic Scattering

This paper focused on the improved algorithm of finite difference time domain(FDTD) method, which is named multi-resolution time domain (MRTD). The history,actuality and disadvantages of the FDTD scheme are introduced. It is found that thetraditional FDTD algorithm has been limited by two physical limitations: numericaldispersion and stability. In order to reduce the numerical dispersion, more fine gridsare required. In other words, each grid size must be smaller than one tenth wavelength,which causes more computer memory and long CPU time required.It is the grids constraint conditions that influence the efficiency of conventionalFDTD. To solve the problem, we study the MRTD scheme in detail, and derive thebasis equations from the original Maxwell's equations. The numerical experimentsshow that the method can approach the limitation of the Nyquist's sampling theoremand possesses a better numerical dispersion. In addition, it can obtain the sameaccuracy as that of the FDTD method with much fewer grids for simulating theelectromagnetic structures. Compared with the FDTD scheme, the connectionboundary and incident plane wave are difficult for MRTD, since the number of thecoefficients used in MRTD are much more than FDTD. In order to overcome thedifficulties that arise because of the non-localized characteristics of the scaling andwavelet basis functions that employed in the MRTD scheme, the pure scattered fieldformulation is adopted. Radar cross section (RCS) of the two-dimensional (2-D) andthree-dimensional (3-D) objects are computed, and the numerical results arecompared with the traditional FDTD method. It is shown that the computationalresource is reduced drastically without sacrificing much accuracy.The traditional MRTD scheme still used second order centered difference in thetime. In order to get higher precision, the Runge-Kutta scheme is applied to theMRTD method. The basal RK-MRTD equations are derived and the stability,dispersion and convergence are discussed, which verifies that the method has betterprecision. Based on explicit difference, the time step of MRTD is limited by the Courantcondition, when there are fine structures in computation area, the smaller steps areneeded, which will make long time to computer. Recently, ADI-FDTD is used to solvethe Maxwell's equations. The other method ADI-MRTD was advanced. We derivedthe general ADI-MRTD equations and discuss the key techniques such as theabsorbing and boundary condition. Finally the numerical dispersion was analyzed andcompared with the conventional FDTD and MRTD. The results show that thealgorithm provided is non-conditional stable and presents desirable numericaldispersion.