The closed-form solution of vector finite element integral equations for three dimensional electromagnetic analysis

Abstract

In this paper, a set of closed-form formulas for vector Finite Element Method (FEM) to analyze three dimensional electromagnetic problems is presented on the basis of Gaussian quadrature integration scheme. By analyzing the open region problems, the first-order Absorbing Boundary Condition (ABC) is considered as the truncation boundary condition and the equation is carried out in a closed-form. Based on the formulas, the hybrid Expanded Cholesky Method (ECM) and MultiFrontal algorithm (MF) is applied to solve finite element equations. Using the closed-form solution, the electromagnetic field of three dimensional targets can be studied sententiously and accurately. Simulation results show that the presented formulas are successfully and concise, which can be easily used to analyze three dimensional electromagnetic problems.