Fast Far-field computations for finite element domain decomposition method

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 domain decomposition finite element method (DD-FEM) 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.