Use of the vector finite element method for the solution of electromagnetic problems

The vector finite element method (VFEM) is formulated for the time-harmonic Maxwell's equations to model microwave integrated circuits and electronic packages at high frequencies. A number of computational challenges often appear during the formulation of these problems ranging from proper excitation of the input ports and reflection-free truncation of the unbounded infinite domain to accurate modeling of material interfaces and anisotropies. To deal with the challenge of proper excitation/termination of the ports, a generalized eigenvalue problem is formulated at each of the ports in order to obtain the dispersive propagation characteristics and governing modes of the 2-D structure; these modal characteristics are subsequently used to properly excite and terminate the input and output ports of the 3-D structure under investigation. In the case where scattering is involved, the unbounded infinite domain is properly truncated using first-, second-, or even higher-order absorbing boundary conditions (ABCs), a perfectly matched layer (PML), or an exact radiation condition based on a boundary-integral (BI) method. Numerical results on a number of practical engineering applications illustrate the power and effectiveness of the VFEM in solving complex electromagnetic problems.