Higher Order Absorbing Boundary Conditions And Finite Element Method Solution Of Electromagnetic Boundary Value Problem

Nowadays the electromagnetic field engineering has a quite widespread application, along with the development of computer technology, in computational electromagnetism seeking a kind of high-efficient precise electromagnetic numerical computational method became the various countries' research hotspot. For example: aircraft and missiles such as a two-dimensional and three-dimensional structures of scattering problems, antenna radiation and communication problem, phased array antenna, non-uniform and frequency related materials, etc.This paper mainly derive a high order absorbing boundary conditions (ABC)and the influence for computational accuracy, and use finite element method (FEM) to solved the electromagnetic boundary value problems of one-dimensional second-order interpolation function and electromagnetic boundary value problem of two-dimensional linear interpolation function. The boundary conditions of electromagnetic problems can affect the accuracy and efficiency in solving the field. Application of absorbing boundary conditions for finite element matrix equation is sparse. If the absorbing boundary conditions position selected appropriate, we can get the high accuracy solution. First, this paper constructed an exact expression which is to be called the transparent condition (TC) and absorbing boundary conditions ; The TC will be derived directly from Maxwell's equations without making any approximations. In addition, the ABCs will be derived by approximating the term then the difference accuracy degree of absorbing boundary conditions will be obtained. Then the accuracy of absorbing boundary conditions is analyzed and programming and simulates a rectangular waveguide model, calculated reflection coefficient of the 1st, 2nd and 3rd order absorbing boundary conditions and the relation with absorbing angle. Then studied the application of second-order interpolation function of finite element and focused on two-dimension electromagnetic boundary value problem solved by finite element method, from the principle of derivation, including regional discrete, the interpolation function establishment and selection, galerkin weighted residual method of approximate, to derived the general unit vector matrix and vector expression, matrix vector combination process. Finally,based on finite element method computes the classical model of perfectly conducting circular cylinder scatter two-dimension electromagnetic field distribution. Derived the expression of absorbing boundary conditions, and focus on how to solve the equation through imposed the absorbing boundary conditions and finally programming implementation; gives the classic cylindrical scatter's list function analytical solution of Bessel function and Hankel functions, make a contrastive analysis with the result of finite element method computational and list function analytical solutions that the related parameter is programming computational. thus puts forward the related parameters optimization indexes, and achieve a more accurate result.This paper make a basic research for high order absorbing boundary conditions and use the finite element method to solution electromagnetic boundary value problem, and combining the waveguide one-dimensional higher-order interpolation function and two-dimensional electromagnetic boundary value problem of application that display the advantages and potential of use absorbing boundary conditions of finite element method to solution electromagnetic boundary value problem.