Ultra broadband fast frequency sweep for polynomial finite element matrix equations using single point model order reduction without linearization

CAD tools that can achieve rapid, accurate simulations of electromagnetic phenomena are in demand. One possible methodology for broadband frequency simulations is model order reduction (MORe). Several MORe techniques have been used for various simulations and they generally fit into one of two categories. In the first category are methods that are very broadband, but they require the matrix equation to be linear in the MORe parameter. The second category includes methods such as asymptotic waveform evaluation. Although these methods admit nonlinear matrix equation variations in the MORe parameter, they are not as broadband as category one methods. Until now, when polynomial matrix equations (such as the quadratic equations commonly encountered in the finite element method) were solved, researchers would either introduce extra degrees of freedom (unknowns) to linearize their equations and use category one methods, or they would use category two methods with multiple, piecewise, small-band, local approximations. We introduce a method which has both the broadband characteristics of category one methods and the nonlinear flexibility of category two methods. We give examples of a bowtie antenna placed on a half-sphere absorber and uniform plane wave scattering from a material cylinder.