We present a surface integral equation (SIE) to model the electromagnetic behavior of metallic objects at optical frequencies. The electric and magnetic current combined field integral equation considering both tangential and normal equations is applied. The SIE is solved by using a method-of-moments (MoM) formulation. The SIE-MoM approach is applied only on the material boundary surfaces and interfaces, avoiding the cumbersome volumetric discretization of the objects and the surrounding space required in differential-equation formulations. Some canonical examples have been analyzed, and the results have been compared with analytical reference solutions in order to prove the accuracy of the proposed method. Finally, two plasmonic Yagi–Uda nanoantennas have been analyzed, illustrating the applicability of the method to the solution of real plasmonic problems.

The performance of most widespread surface integral equation (SIE) formulations with the method of moments (MoM) are studied in the context of plasmonic materials. Although not yet widespread in optics, SIE-MoM approaches bring important advantages for the rigorous analysis of penetrable plasmonic bodies. Criteria such as accuracy in near and far field calculations, iterative convergence and reliability are addressed to assess the suitability of these formulations in the field of plasmonics.

An efficient parallel implementation of the multilevel fast multipole algorithm-fast Fourier transform (MLFMA-FFT) has been successfully used to solve an electromagnetic problem involving one billion of unknowns, which indeed becomes the largest problem solved with the surface integral-equation approach up to now. In this paper, we present a deep review of this challenging execution, focusing on the details of the parallel implementation step by step, with the aim of describing the different stages of the parallel algorithm and analyzing its overall parallel performance.

An efficient parallel implementation of the Fast Multipole Method (FMM) combined with the fast Fourier transform (FFT) is presented in this paper. The good scaling properties of the FMM-FFT, combined with a smart parallelization strategy, has been shown to be very effective when using large parallel supercomputers. A challenging problem with more than 150 million unknowns has been solved, demonstrating that the proposed implementation of the FMM-FFT constitutes a real alternative to the more frequently used multilevel approaches, such as the Multilevel FMM (MLFMA). Even more importantly, we have achieved a high efficiency with 1,024 parallel processors, which indeed constitutes one of the better scalability results ever reached for a rigorous integral-equation electromagnetic solver.

A surface integral equation together with the multilevel fast multipole algorithm is successfully applied to fast and accurate resolution of plasmonic problems involving a large number of unknowns. The absorption, scattering, and extinction efficiencies of several plasmonic gold spheres of increasing size are efficiently obtained solving the electric and magnetic current combined-field integral equation. The numerical predictions are compared with reference analytic results to demonstrate the accuracy, suitability, and capabilities of this approach when dealing with large-scale plasmonic problems.