Research On Fast Algorithm Of Transient Electromagnetic Fields In Complex Medium

Sponsored by the National Natural Science Foundation of China under grant 50577019 and Nutural Science Foundation of Hebei Province under grant E2006000678, the fast multipole method for calculating the transient electromagnetic field of substation grounding grid, the parallel fast multipole method for calculating the transient electromagnetic field of substation grounding grid and the time-domain integral equation method of thin conductor in lossy half-space are researched. The methods presented in this thesis are verified by comparing the results with those published references and other famous software. Main achievements are presented as follows:1. The basic principles of the modified image method and establishment of frequency-domain integral equation in lossy half-space are researched. This method avoids Sommerfeld integral arising from the frequency-domain integral equation in lossy half-space; establishs a theoretical foundation for the fast multipole method and time-domain integral equation method.2. The fast multipole algorithm to calculate lightning electromagnetic field of the thin wire structure in lossy half-space is presented. This algorithm is used to rapidly calculate the electromagnetic field of buried thin wire conductors and provides an efficient computational tool for large grounding analysis.3. An algorithm for using the translation in variance to calculate the elements in nearby group of fast multipole method is presented. This algorithm can reduce the excess calculation for transfer impedance matrix elements, and improve the speed for calculating the elements in nearby group.4. The parallel fast multipole algorithm to calculate lightning electromagnetic field of the thin wire structure in lossy half-space is presented. This algorithm is based on the serial fast multipole algorithm in lossy half-space. This algorithm can improve the efficicncy of a serial algorithm and distribute computing tasks on the processors. This algorithm is more suitable for fast calculating the transient electromagnetic field of electrically large, complex conductors.5. A novel time-domain integral equation of the lossy half-pace is presented. This algorithm can be used to calculate the case that the wire is close to the ground. and it contains the impact of soil conductivity. The limit of the traditional time-domain integral equation is made up by this algorithm.6. An algorithm to construct the temporal basis functions for time-domain integral equation method generated by current excitation source is presented. This method can avoid the late instabilitv during the solution of the time-domain integral equation. Meanwhile. the unknown quantity involved in this algorithm is very small.The calculation speed for transient electromagnetic field can be significantly improved by this algorithm.