An Efficient Goal-Oriented Adaptive Finite Element Method for Accurate Simulation of Complex Electromagnetic Radiation Problems

A goal-oriented adaptive frequency-domain finite element method (FEM) for solving electromagnetic radiation problems including complex structures is presented in this article. Compared with the traditional adaptive FEM, the goal-oriented method can flexibly control the refined regions according to the parameters of interest; therefore, it has better convergence and has made significant progress in scattering problems and eigenvalue problems. To simulate complex antennas, this article proposes an error indicator with high accuracy and low computational cost, and it uses the adjoint problem to weight element residuals without additional degrees of freedom (DoF). Moreover, high-quality mesh refinement algorithms adapted to this indicator are developed using a suitable point insertion strategy for multiscale structures. By simulating two practical antennas, comparisons with the traditional goal-oriented FEM and the well-developed
$h$
-adaptive FEM in commercial software demonstrate the accuracy and efficiency of the proposed method.