Equivalence Principle Algorithm And Its Applications In Complex Vector Electromagnetic Problems

The equivalence principle algorithm(EPA) is studied systematically to deal with multi-scale property of real electromagnetic(EM) scattering and radiation problems in this dissertation. Athorough research has been accomplished to cover the EPA for perfect electric conductors(PEC), homogeneous dielectric cases and conductor-dielectric composers. For the PEC case, EPA is studied to solve not only mid frequency EM problems but also low frequency problems. The main research content includes five parts.First, the basic theorem of EPA and the main process of numerical solving EPA by method of moments(MoM) are introduced. In the EPA, the coupling from inside complicated objects to ouside objects can be expressed by equivalence currents and translation operator. The interacton between equivalence currents and induced currents on the inside objects can be expressed by equivalence principle operator. Due to the EM coupling between objects has been transformed to the coupling between equivalence currents on the equivalence surfaces, the number of unknowns on equivalence surfaces is much less than that on objects. Therefore the EPA is suitable for the solution of complicated multi-scale EM problems. The electric field integral equation(EFIE) and combined field integral equation(CFIE) are used to solve PEC object in the equivalence surface. For the conductor-dielectric composers, both the VSIE and EFIE-PMCHWT methods are derived and verified in details. Finally, the calculation of coupling between equivalence currents on equivalence surfaces is accelerated by multilevel fast multipole algorithm(MLFMA) further.The choice of equivalence surface form and the field projection error on equivalence surface have been studied. The smooth and uniform surface should be chosen as equivalence surface in order to guarantee accuracy. The field projection error on equivalence surface mainly includes the high frequency noise and the numerical discretization error of identity operator. The accuracy of EPA is improved from two different aspects, which are using tangential EPA(T-EPA) to change the way of field projection and using grid-robust higher order vector basis(GRHOVB) to reduce high frequency noise. Numerical examples show that these two methods can improve the accuracy of EPA efficently.For the EM simulation of large array structures, the EPA accelerated by fast algorithm still needs huge computation time and memory storage. In order to improve the efficience of EPA, a great improvement on the traditional EPA is made from two aspects. On one hand the entire domain basis function-CBF is constructed on the equivalence surfaces to reduce the number of unknowns, on the other hand the ?-LUD is used as a fast direct inverse solver which is basd on ?-Matrix scheme to reduce the computational complexity of object impedance matrix in EPA. The capability of EPA for solving large array has been enhanced efficiently due to the improvement of above two aspects.The objects often connect with each other in the real engineering problems. When using the equivalence surfaces to divided the objects into subdomains, the objects will be cut off by the equivalence surfaces, which lead to singular currents at the place of cut off. The singularity matching approach is introducted first, and then the physical process of singular currents generate singular fields is derived. However, singularity matching approach is difficult to implement using numerical method. In this dissertation we utilize the tap basis to model the continuous currents and avoid the generation of singular currents. The GRHOVB is used on the equivalence surfaces to improve the accuracy of EPA. The iteration process is accelerated by right hand precondioner further. The computation of coupling between different domains is also accelerated by MLFMA. Numerical results show that this method is suitable for the multi-scale cases.At last, the single-source equivalence principle algorithm(SS-EPA) at mid and low frequency is proposed. According to extinction theorem, equivalence magnetic current can be expressed by electric current on the equivalence surface and vice versa. Then the equivalence principle operator and translation operator of SS-EPA are derived. Therefore, only electric current or magnetic current is the unknown in the final formulation. The relationship between scattering matrix and generalized impedance matrix is studied further. In order to overcome the low-frequency breakdown problem of EPA, both the EPA based on AEFIE method and EPA based on loop-tree basis decomposition method are constructed. Then the SS-EPA based on loop-tree basis decomposition is proposed to reduce number of unknown further. Finally, the relationship between EPA and GIBC at low frequency is derived to improve the theory of EPA further.The research presented in this dissertation covers the major topics of the EPA for multi-scale objects. Using fast algorithms to reduce computational complexity and memory consuming, it provides us with a new fast and accurate solution tool for the simulation of complicated multi-scale EM problems.