Research On The High-Order Runge-Kutta Multiresolution Time Domain Method And Its Application

The finite difference time domain (FDTD) method, which is the most commonly use time-domain method, has been widely used in the computational electromagnetics. Because of the constraints of the numerical dispersion and the numerical stability, the method is needed to consume much memory and computing time in the calculation of electrically large size of the electromagnetic problems, so the FDTD method is restricted the computation of the electrically large problems. The multiresolution time-domain (MRTD) method, proposed in 1996, was to improve significantly the dispersion error. The high-order Runge-Kutta multiresolution time-domain (RK-MRTD) scheme, which was the way of improving the efficiency of the MRTD method, was presented in 2006. The main task in this master thesis is that we study carefully and analysis the properties of the RK-MRTD method and some numerical behaviors, and we apply the method to some examples from one-dimensional case to three-dimensional case.In the thesis, first of all, we have analyzed and discussed systematically the basic theory of the MRTD and the RK-MRTD methods and the key skills used in the non-continuous interfaces. At same time, we have analyzed the variety of features of the RK-MRTD method and have obtained the related basic conclusions.Secondly, the RK-MRTD method has been applied to the related simulation experiments involved in one-dimensional (1D) to three-dimensional (3D) cases, which are included the two-dimensional (2D) rectangular cavity resonator, the reflection experiments of the 1D plan wave, the study of the radar cross section (RCS) for the 2D square columns, the 3D uniform rectangular cavity resonator and 3D half-filled rectangular dielectric resonator.Then, we have approached the RK-MRTD method, which is expanded by the scaling function, based on the Coifman wavelet function. Because of the unique characteristics about the vanishing moments of the Coifman wavelet function, the sampled valued have been replaced by those of the electromagnetic fields directly in the updated processing, which simplify the computational processing.Finally, we have proposed a new MRTD method based on locally one-dimensional (LOD) technology, namely LOD-MRTD method, which has been improved the computational efficiency of the MRTD method used by the unconditionally stable methods. Compared with the unconditionally stable ADI-MRTD method, our method has consumed the same computational memory and has had same dispersion error as the ADI-MRTD method, but it has been had simpler formats, fewer updated equations, and have saved computational CPU time. Key Words: high-order runge-kutta multiresolution time-domain scheme (RK-MRTD), wavelet analysis, multiresolution analysis (MRA), dispersion relation, dissipative error, locally one-dimensional (LOD)...