Broadband Multilevel Fast Multipole Methods

Numerical simulations of electromagnetic fields are very important for a plethora of modern applications like antenna design, wireless communication systems, optical systems, high-frequency circuits and so on. As a consequence, there is much interest in finding algorithms that make these simulations as computationally efficient as possible. One of the leading classes of algorithms consists of the so-called Fast Multipole Methods. These methods use a subdivision of the geometry into boxes on multiple levels, in combination with a decomposition of the Green function. For high frequency simulations, where the wavelength is smaller then the smallest features of the geometry, a propagating plane wave decomposition leads to a very efficient algorithm. Unfortunately, this decomposition fails when the geometry contains features smaller than the wavelength, which is the case for broadband simulations. Broadband simulations are becoming increasingly important, for example in the simulation of high frequency printed circuit boards and microwave circuits, metamaterials or the scattering of radar waves off complex shapes. Because of the failure of the propagating plane wave decomposition, performing broadband simulations requires the construction of a hybrid algorithm which uses the propagating plane wave decomposition when the boxes are large enough and some low frequency decomposition when they are not. However, the known low frequency decompositions are usually suboptimal compared to the theoretical performance of the propagating plane wave decomposition. In this work, the focus will be on these low frequency decompositions. First, an improvement over a known low frequency decomposition (the spectral decomposition) is presented. Among other techniques, the well-known Beltrami decomposition of electromagnetic fields is shown to significantly reduce the computational burden in this scheme. Secondly, entirely novel ways of decomposing the Green function are developed in both two and three dimensions. These decompositions use evanescent plane waves, so they can handle small boxes. Nevertheless, they have the same convergence characteristics as the propagating plane wave decomposition. Therefore, these decompositions are also very efficient. Finally, the novel techniques are applied in the full-wave homogenization of various metamaterials.

Author dc:creator

• Bogaert, Ignace

Contributors dc:contributor

• Olyslager, F

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

und

Identifier

https://biblio.ugent.be/publication/472031
http://doi.org/1854/11741
https://biblio.ugent.be/publication/472031/file/4334752

OAI identifier oai:identifier

oai:archive.ugent.be:472031