Fast and Accurate Electromagnetic Analysis of Metamaterials With Parallel Multilevel Fast Multipole Algorithm

点击翻译按钮获取中文摘要

Metamaterials are artificial structures having a vast variety of potential applications, such as sub-wavelength focusing, invisibility cloaking, and miniaturization of the antennas, due to their unusual electromagnetic properties. Solutions of electromagnetics problems involving metamaterials are extremely important to analyze these structures and their interactions with the environment. For example, accurate solutions of metamaterial problems can provide essential information on novel designs even before their actual realizations, preventing the waste of sources and time during the manufacturing of the prototypes. Unfortunately accurate simulations of metamaterials are extremely difficult since they are composite multi-scale structures, i.e., they consist of thousands of unit cells with small details whereas their overall dimensions can be very large with respect to the wavelength. Hence, accurate numerical analysis of metamaterials using full-wave solvers may require the solution of huge matrix equations involving millions of unknowns. In addition, metamaterials are usually functional at some resonance frequencies, where the numerical solutions may become unstable. Due to the limitations in their computational solutions, metamaterials could not be investigated in sufficient depth, and most of the studies in the literature are based on approximate homogenization techniques that are unable to provide rigorous and accurate analysis of realistic structures. The purpose of this study is to develop a fast and accurate solver based on a parallel implementation of a powerful algorithm, namely, the multilevel fast multipole algorithm (MLFMA), for the analysis of metamaterials. By developing a sophisticated simulation environment consisting of diverse components from different areas, such as numerical techniques, iterative method, fast algorithms, parallelization, and parallel computers, real-life problems involving complex metamaterials will be solved with unprecedented levels of accuracy and detail. In addition to academic impacts in computer science and high performance computing, the results are expected have high impacts in science and technology in a broad sense by showing the feasibility of new metamaterial designs for constructing the devices of the future's world.