Studies On Fast Algorithms Of Time-Domain Integral Equation

The thesis chooses time-domain integral equation (TDIE) theory as the theoretical foundation, marching-on-in-time (MOT) method as numerical process and a variety of fast algorithms to accelerate the solving process and analyze some complicated electromagnetic problems. The content of this thesis can be divided into three parts, the first part expounds the TDIE basic theory and its solution techniques based on MOT algorithm, the second part investigates three fast algorithms'theoretical basis and their implements method, the third part describes the method of matrix compression storage and the rapid solution technology of the large sparse matrix linear equations.The first part of this thesis is the theoretical foundation of the thesis. First of all, the time-domain electric field, magnetic field and combined field integral equations for metallic structures are elaborated based on the surface equivalence principle and boundary conditions, and their applications and numerical performance are analyzed briefly. Then MOT algorithm for the solution of arbitrary conductor TDIE is elaborated, and the stability and precision of three TDIEs are studied. Subsequently, the method of modeling complex objects built of arbitrary line, surface and volume structures is developed. The setting method of basis functions of the multi-surface connection problem is solved. And the methods of adding excitations and setting electromagnetic parameters are introduced.As the core of the full text, the second part of this thesis focuses on three fast algorithms for solving TDIE. Firstly, the multi-region method based on MOT is proposed by the frequency-domain multi-region model. In this algorithm, the target under consideration is divided by multiple regions. And this method improves the computational efficiency of TDIE through the approximate calculation of the current approximation region, and employs the accuracy of TDIE and the efficiency of the multi-region model completely. Then time domain adaptive integral method (TD-AIM) is studied to accelerate traditional MOT. The theoretical basis and key techniques are expounded, and the blocking framework of space-time FFT is improved. The detailed implement of the algorithm is designed. As a fast TDIE solver with high accuracy and efficiency, plane wave time domain (PWTD) algorithm is studied deeply in this part. The implementation of two-level PWTD-enhanced MOT schemes is described and the numerical efficiency is presented. Finally, the combination of the two-region model and PWTD has been proposed. And this algorithm can further improve the computational efficiency of the two-region method based on MOT. In the third part of this thesis,compressed storage technique for matrixes together with iteration algorithm of large sparse matrix linear equations are investigated. The focus is the efficiency and precision of different iteration algorithms and precondition techniques. Rules of iteration algorithms with precondition techniques in the solving process of TDIE are summarized according to numerical computation examples.