Fast finite element far-field computations for electromagnetics

Summary form only given. Often the end product of an electromagnetic simulation is a far-field quantity such as antenna gain, radiated power or radar cross section (RCS). When the underlying CEM solver is a frequency domain finite element method which solves for the near-field electric fields, an extra near-to-far-field transformation step must be invoked for each frequency and excitation. Traditionally this step involves the integration of equivalent electric and magnetic currents over a surface enclosing the object under investigation. However, the challenge of evaluating such radiation integrals is two-fold: (1) The presence of the curl operator in the evaluation of the equivalent electric currents reduces its effective approximation order leading to inaccuracies; (2) The numerical integration of the radiation integrals could be time consuming since the integration work for a single observation direction scales quadratically with electric size, i.e. O(kd)² and the angular sampling of the Ewald sphere increases linearly O(kd), leading to a total of O(N²) operations (where N is the number of equivalent surface current samples). These effects are further exacerbated over wide bandwidths, and multi-port excitations, severely slowing down computations.To combat this unfavorable complexity, Stephenson in (M. Stephenson, OSU, Thesis, 2007) used a divide-and-conquer algorithm along with fast interpolations, similar in spirit to the fast multipole method, to compute the radiation integrals over the Ewald sphere at O(N1.5) cost. Following a completely different vision, Monk in (P. Monk et al., Journal of Computational Physics, pp.614-641, 2001) proposed a variational computation of the near-to-far-field transform for TVFEM that improves accuracy. Following Monk´s approach, we propose a variational near-to-far-field transform that leverages the benefits of model order reduction (MOR) in both frequency and observation angle parameters. The method is b- sed on a simple and elegant matrix representation of the near-to-far-field transform that requires only sparse matrix vector multiplications instead of integral evaluations. The paper, first outlines previous research on this topic, and then proceed by formulating the fast near-to-far-field transformation in the context of second-order tangential vector finite elements. Results from phased arrays and scattering problems will be used to showcase the accuracy and efficiency of the proposed methodology.