Numerical Methods For Cavity Scattering Problems

Maxwell equation describes the phenomenon of electromagnetic wave propagation,which has important applications in engineering practice and science and technology.Electromagnetic scattering is a special form of electromagnetic wave propagation.Because of its important applications in military and industry,it has been widely paid attention to in engineering and applied mathematics.For example,the radar scattering cross section(RCS)can measure the target by radar system can detect,in practice according to different purpose of increase or decrease the target of the RCS is very important,and to realize the control of the RCS,you need to understand the electromagnetic scattering characteristics of targets,cavity scattering problem is one of the important research content in this field.Cavity scattering is mathematically related to the solution of Maxwell equation,which can be simplified to the solution of Helmholtz equation in two-dimensional case.In this paper,we take single cavity as the research object,and consider two physical models of electromagnetic scattering of open cavity,namely rectangular cavity and irregular cavity.Since the open cavity problem is defined in an infinite region,in order to truncate the unbounded physical region in a bounded region for numerical calculation,we need to introduce artificial boundary conditions.In this paper,two kinds of boundary conditions are introduced to truncate the scattering field,namely the PML boundary condition and the transparent boundary condition.The truncated region is the calculated region.In numerical simulation,it is often necessary to design different numerical algorithms for different geometric structures and material properties.For the scattering of irregular cavity,the finite element method can be used effectively,because the finite element method has strong adaptability and can deal with the irregular boundary well.As for the rectangular cavity,due to the particularity of its structure,it can be simulated by more efficient numerical methods.In this paper,the vertical mode expansion method is developed to deal with this kind of problems.Because this method only needs to discrete the region in the vertical direction,the calculation amount is greatly reduced and the efficiency of calculation is improved.The main structure of this paper is as follows: in the first chapter,the research background and research status at home and abroad are briefly introduced.In chapter 2,the Helmholtz equation is derived from Maxwell equation and the PML boundary conditions are introduced.In chapter 3,the scattering problem of rectangular open cavity is studied,and the finite element method with PML boundary and the vertical module expansion method are established respectively.In chapter 4,the scattering of irregular cavity is studied.First,by solving the external problem,the Dt N mapping is constructed and the transparent boundary condition is introduced.Then,a finite element method is established to solve the scattering field in the truncated region.In chapter 5,a numerical example is given to verify the effectiveness of the proposed algorithm.The computational methods presented in this paper provide a powerful tool for the simulation of cavity scattering,and the development of these computational methods to optimize the radar scattering cross section is also of great significance.