Abstract-An efficient hybrid MPI/OpenMP parallel implementation of an innovative approach that combines the Fast Fourier Transform (FFT) and Multilevel Fast Multipole Algorithm (MLFMA) has been successfully used to solve an electromagnetic problem involving 620 millions of unknowns. The MLFMA-FFT method can deal with extremely large problems due to its high scalability and its reduced computational complexity. The former is provided by the use of the FFT in distributed calculations and the latter by the application of the MLFMA in shared computation.

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.

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