Fast full-wave scattering at extremely large and complex multiscale objects

In recent years, the computational electromagnetics community has witnessed a rapid increase in the electrical size of scattering problems that can be solved. This increase can be mainly attributed to the use of boundary integral equations and the development of the multilevel fast multipole algorithm (MLFMA) and its parallelized analogues. However, many challenges remain, especially when it comes to broadband behavior and large and complex multiscale geometries. The geometrical problem, on the one hand, is adequately solved by means of a very accurate calculation of the moment integrals. This is accomplished by using the singularity extraction method not only for the selfpatch but also for the neighbor contribution. On the other hand, the problem with the LF-breakdown of the MLFMA is solved by switching to the so-called normalized plane wave method (NPWM) for the lowest levels. This method is error-controllable at LF but still uses plane waves and thus leads to diagonal translations, unlike multipole based methods. Additionally, these techniques were incorporated in the parallel framework open FMM, such that the large number of unknowns necessary for the discretization of the geometry can be handled.