Integral Equation Methods And Fast Algorithm For Electromagnetic Radiation And Scattering Of Multiscale Structures

In resent decades,computational electromagnetics has been extensive used in electrocommunication,telemetry and telecontrol and many other research areas.Proved powerful tools of electromagnetic simulation for engineering designs and scientific researches.However,along with the progress of science and technology,especially the development of electronic technology,the request of electromagnetic simulation capability is accumulated.The multi-scale problem in electromagnetic which is the main topic of this paper,is one of the hot issues in computational electromagnetics.Multi-scale problems not only with large amounts of unknown,also contains sophisticated tinny subwavelength structure.Thus will lead to new problems and challenges when solving it.In this paper the multi-scale problems is studied with the view point of integral equations methods.The discussion is arranged base on following three aspect: the hybrid fast algorithm for multi-scale problems,the stable integral equations for mid and lowfrequency multi-scale problems and the multi-scale problems for planar layered structures.To overcome the inefficient defect of multilevel fast multi-pole method when solving multi-scale electromagnetic problems,the hybrid fast algorithm for multi-scale problems is studied.The studied is based on low-frequency stable method the accelerated Cartesian expansion algorithm.By transformation the algorithm is combined with multilevel fast multi-pole method,and is used to make up the defects of multilevel fast multi-pole method in solving multi-scale problems.Several key technical points are involved in the study,including the influence of the differential operator acting on the Cartesian tensor,different ways of construction for the hybrid fast method,the hybrid fast algorithm of the volume surface integral equations and the preconditioning technique of the hybrid fast algorithm.Finally,a hybrid multi-scale fast algorithm solver for solving the electrical,magnetic and metal composite materials is formed based on the surface and volume integral equations.In the case of using the electric field integral equation solving mid and low-frequency problems,the fine grid included in the multi-scale structure will cause the low-frequency breakdown problem of the electric field integral equation.In order to solve this problem,this paper first analyzes the significance of the Helmholtz decomposition for the low frequency breakdown problem of the electric field integral equation.By introducing the constraint condition,improved electric field integral equations which can be used to solve the low-frequency problem is deduced.Furthermore,the method of perturbation is introduced to solve the problem that the improved electric field integral equation is not accurate at extremely low-frequency.By using the series expansion of the impedance matrix elements,the three equations of the electric field integral equation,the augmented electric field integral equation and the perturbation of electric field integral equation are integrated to form a high efficiency impedance matrix filling algorithm covering the mid and low-frequency.An efficient algorithm of method of moments for wideband problems is formed.In addition,a fast solver for mid and low-frequency multi-scale problems is constructed by means of augmented electric field integral equation and a hybrid form multi-scale fast method.From the aspect of solving multi-scale electromagnetic problems for planar layered structures.Aiming at the characteristics of planar layered structure,two kinds of mode matching methods are studied.Respectively,based on the spectral domain mode matching method of using rigorous coupled-wave analysis,and based on two-dimensional finite element method of numerical mode matching method.Finally,the fast calculation method under the condition of continuous change of parameters is studied according to the engineering requirements.The model order reduction method based on the reduced basis method is studied.In this paper,we study the affine decomposition method of the moment method for solving the wide band problem,and apply the reduced basis method to the efficient calculation of the moment method under the wide band.The estimation technique of estimating the vector characteristics by the right-hand term of the matrix equation is studied,and the reduced basis method is applied to the efficient calculation of the moment method of different plane wave incident angle.