Electromagnetic Field Calculation Of Compactly Supported Wavelet Time-domain And Multi-resolution Analysis Method,

FDTD method had been used in electromagnetism computation widely for its simple, agility and efficiency. It has to satisfy two physical intrinsic and limitations: numerical dispersion and stability. In order to reduce the numerical dispersion, it need more fine net grids, usually, smaller than 1/10 wavelengh. But it will cause more computer memory and long time.The Maxwell's equations were extended by the compactly supported wavelets' transformation in this paper .The renewed formats of them are more succinct than conventional MRTD's equations. Meanwhile the certain value of the total field can be got by the shift interpolation not have to carry out the definite integral ?of the sampled fields .The numerical experiment shows that adopting the method can approach the limitation of the Nyquist's sampling theorem and possesses a better numerical dispersion in addition that it can attain the same calculating as the FDTD's provided to use much fewer nets for simulating the electromagnetic structures.FDTD's time step based on distinctness difference format limited by the Courant condition and it should smaller than CFL(Courant-Friedich-Lecy) condition. This will make long time to computer. Recently, ADI-FDTD was used to solve the Maxwell equation. This method base on the ADI and was used in Yee grids. It resulted in a un-condition steady method. When there are fine structures in computation area, its efficiency is better than the conventional FDTD method.The alternating direction implicit technique that is based on the compactly wavelets was used in the method of WGTD, from which the calculating formulas both in air and in Gedney' s UPML medium on the successive approximation were derived. Based on the formula, the simulating calculation of two-dimensional data were carried out and compared with the conventional FDTD and ADI-FDTD. The results show that there are non-conditional time stability and excellent numerical dispersion in the method.