Electromagnetic Modeling By Combining Integral Equation Method And Finite Element Method

This thesis introduces a hybrid algorithm to model electromagnetic field in inhomogeneous medium, which combines integral equation method and finite element method (FEM). Both integral equation method and FEM are important numerical modeling algorithms. In integral equation method, only the inhomogeneous body needs to be discredited, but the coefficient matrix is full; FEM is of capability to model inhomogeneous materials as well as complicated structures, and its coefficient matrix is sparse, however it requires an artificial boundary condition to truncate the computational grid. In the hybrid algorithm, we use FEM to model the EM field in the interior domain, and then use the integral equation to compute the field on the boundary (to provide an artificial boundary condition for FEM system), and the finite element approximation is also convenient for deriving discrete equations of the integral equation. At last, we develop the programs for the hybrid algorithm, and test them using numerical experiments.The main work and achievements of the thesis are follows:(1) Deduce the electric dyadic green' s functions and magnetic dyadic green' s functions of free space and half-space based on the Maxwell' s equations.(2) Aim at the false-solutions(the meaning is the solutions do not satisfy the divergence theorem) of FEM, impose the magnetic divergence conditions ((?·H) on the magnetic coefficient matrix from FEM.(3)The outmost units of the discrete region are in background, thus avoids the problem of singular integration.(4)Test the programs of the hybrid algorithm with Rayleigh scattering in free space, then extend the program to half-space for the 3D EM fields excited by electric dipole source.