The Finite Element Analysis Of BOR's Electromagnetic Scattering Problem

The Finite Element Method (FEM) is one of the major numericalmethods in computational electromagnetic. Due to its versatility andflexibility, the FEM is capable of modeling complicated structures aswell as inhomogeneous materials. The soul of FEM is the transition fromthe boundary problem to variational function.The history and actuality of FEM are analyzed at first, based onwhich the special character of the Body of Revolution (BOR) is given.Then, the progress of FEM is presented, such as the discrete methodof 2nd order isoparametric element and the disperse program using scalarand vector quantity.When solving electromagnetic (EM) scattering problem with FEM,the infinite region exterior to the scatter must be truncated by afictitious boundary. In this paper, based on the Perfectly MatchedLayer (PML), the character of conformal PML (CPML) is discussed, suchas the attenuation parameter, continuity between elements. Then thecomplementary CPML (Com-CPML) is given, which will minish thenon-physical reflection with a little increase of computing.Due to the revolutionary symmetry of BOR, the 3D problem can besolved by 2D methods. The previouse MOM and CAP method can not satisfythe requirement of study. Hence, the paper is started with the analysisof the scatter of the common body. The 3D FEM algorithm is discussedin detail, at the same time, the 2D simplified method is given. Thelast chapter of this paper provides the study of BOR using FEM- modeexpansion.The principal contributions of this paper are as follows:1. In the analysis of conformal PML, a new concept—the geometriccontinuity is introduced. The patches in the CPML region arerequired to meet with G~2 (geometric C~2-condition) continuity. 2. The 3D conformal PML is realized. To avoid the difficultiesassociated with G~2 continuous mesh generation and instabilities inprincipal curvature evaluation, a normal curvature-basedapproximation is proposed.3. The 3D Complementary Conformal PML is realized, which will decreasethe non-physics reflection of the mesh dispersing and thenincreasing the precision of solutions.4. The numerical investigation reveals that for cylindrical PML ofgiven thickness, the optimal value of the loss parameter willincrease with the electrical size of the scatter.5. The FEM method of BOR scattering is realized6. The proper boundary conditions on z axis are discussed.