Domain Decomposition Method For Stepwise Integral Equation Of Time Domain Order In Electromagnetic Scattering Analysis

The electromagnetic scattering analysis plays an important role in computational electromagnetics (CEM). More and more attentions are paid to analyze the electromagnetic scattering from electrically large targets with high efficiency. The domain decomposition method (DDM) is introduced to the integral equations for solving this problem. In this thesis, a hybrid time-domain domain decomposition method (TD-DDM) is proposed to efficiently analyze the transient EM scattering by using the equivalence principle algorithm (EPA). Limited memory requirement and CPU time are needed by taking advantage of the rotationally symmetrical property of BORs.This thesis focuses on the time domain integral equation combined with the domain decomposition method which is based on the equivalence principle algorithm. The main works of this thesis are listed as follows:Firstly, the EPA-based domain decomposition method is introduced. Then both the temporal and spatial basis functions are given. The weighted Laguerre Polynomials are chosen as the temporal basis functions. For BORs, the spatial basis functions are piecewise linear in the longitudinal direction and they are composed of a finite Fourier series in the azimuthal direction because of the rotationally symmetrical property. On the other hand, for non-BORs, the RWG basis functions are served as the spatial basis functions. Moreover, the definition of the radar scattering cross section (RCS) is given.Secondly, an efficient time domain equivalence principle algorithm (TD-EPA) based on the marching-on-in-degree scheme is proposed for the analysis of the transient electromagnetic scattering from multiple conducting bodies of revolution (MBORs) with arbitrary axis. The self-acting of each BOR can be calculated by use of the rotationally symmetrical property in its local BOR coordinate system. The interaction between any two BORs can be replaced by the one between two equivalence spheres which enclose corresponding BOR with EPA. In this way, the number of unknowns can be reduced greatly by using spatial basis functions of BOR and thus the impedance matrix can be solved independently for each Fourier mode in corresponding coordinate system. The adaptive cross approximation algorithm (ACA) is introduced to reduce the memory requirement.At last, a MOD-based TD-DDM is proposed to efficiently analyze the transient EM scattering from electrically large multiscale targets by using the EPA. The algorithm begins with an octree which divide the whole scattering target into several subdomains. Then each subdomain is enclosed with an equivalence sphere where both the RWG and BOR spatial basis functions are used to discretize it. The near-field interactions are calculated by the method of moments (MOM) while the far-field interactions can be replaced by the ones between their corresponding equivalence spheres with EPA. By taking advantage of the rotationally symmetrical property of the equivalence spheres, the computational resources are reduced significantly when compared with the traditional MOD method. Moreover, the MPI scheme is used to accelerate the calculation. Some numerical results are presented to illuminate the accuracy and efficiency of proposed algorithm.