The method of moments solution of electromagnetic surface integral equation formulations for perfect electric conductors or impedance boundary objects is obtained using hierarchical vector basis functions. The singular and hypersingular integrals involved in the near field coupling matrix are computed fully numerically using adaptive singularity cancellation technique. Multilevel fast multipole method with spherical harmonics expansion of the -space representations of the basis vectors and the incoming waves at the finest level is utilized for its memory and computation time efficient implementation. Improved performance of the proposed techniques in terms of accuracy, computational time, and memory requirements is demonstrated by comparing various results with some of the existing implementations available in the literature.Index Terms-Higher order, integral equations, -space integral, method of moments (MoM).

Abstract-An inverse equivalent surface current method working with equivalent electric and/or magnetic surface current densities on appropriately chosen Huygens surfaces is investigated. The considered model with triangular surface meshes is compatible with the models known from method of moments (MoM) solutions of surface integral equations. Divergence conforming current basis functions of order 0.5 and of order 1.5 are considered, where the order 0.5 functions are the well-known Rao-Wilton-Glisson basis functions. Known near-field samples typically obtained from measurements are mapped on the unknown equivalent surface current densities utilizing the radiation integrals of the currents as forward operator, where the measurement probe influence is formulated in a MoM like weighting integral. The evaluation of the forward operator is accelerated by adaptation of the multilevel fast multipole method (MLFMM) to the inverse formulation, where the MLFMM representation is the key to full probe correction by employing only the far-field patterns of the measurement probe antennas. The resulting fully probe corrected algorithm is very flexible and efficient, where it is found that the computation speed is mostly dependent on the MLFMM configuration of the problem and not that much on the particular equivalent current expansion as long as the expansion is able to represent the currents sufficiently well. Inverse current and far-field pattern results are shown for a variety of problems, where near-field samples obtained from simulations as well as from realistic measurements are considered.

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