Higher Order Frequency-Domain Computational Electromagnetics

A review of the higher order computational electromagnetics (CEM) for antenna, wireless, and microwave engineering applications is presented. Higher order CEM techniques use current/field basis functions of higher orders defined on large (e.g., on the order of a wavelength in each dimension) curvilinear geometrical elements, which greatly reduces the number of unknowns for a given problem. The paper reviews all major surface/volume integral- and differential-equation electromagnetic formulations within a higher order computational framework, focusing on frequency-domain solutions. With a systematic and unified review of generalized curved parametric quadrilateral, triangular, hexahedral, and tetrahedral elements and various types of higher order hierarchical and interpolatory vector basis functions, in both divergence- and curl-conforming arrangements, a large number of actual higher order techniques, representing various combinations of formulations, elements, bases, and solution procedures, are identified and discussed. The examples demonstrate the accuracy, efficiency, and versatility of higher order techniques, and their advantages over low-order discretizations, the most important one being a much faster (higher order) convergence of the solution. It is demonstrated that both components of the higher order modeling, namely, higher order geometrical modeling and higher order current/field modeling, are essential for accurate and efficient CEM analysis of general antenna, scattering, and microwave structures.