Fast computation of electromagnetic near-fields with the multilevel fast multipole method combining near-field and far-field translations

In Electromagnetic Compatibility (EMC) problems, computation of electromagnetic near-fields in the vicinity of complex radiation and scattering systems is often required. Numerical solution of such problems is achieved using Boundary Integral (BI) based approaches, where the involved Integral Equations (IE's) are solved with the Method of Moments (MoM). The MoM solution process is speeded up by fast IE solvers such as the Multilevel Fast Multipole Method (MLFMM). In the end the desired amplitudes of the expansion of the equivalent current densities on the discrete elements all over the Huygens' surfaces are known. Computation of the electromagnetic fields produced by the equivalent currents at observation points being in the near-field regions requires integration of the current densities over the Huygens' surfaces. Numerical evaluation of the near-field integrals using conventional integration rules can become extremely time consuming for large objects and large number of observation points. In this contribution, acceleration of the near-field integration of the equivalent current densities is provided using a postprocessing MLFMM, where near-field and far-field translations are combined in order to achieve optimum performance. The proposed approach was applied in the postprocessing stage of a power-ful Finite Element Boundary Element (FEEI) method, resulting in significant decrease of the postprocessing computation time. The formulation of the proposed acceleration is presented and numerical results are shown.