Department of Electrical Engineering, The Pennsylvania State University, University Park, PA, 16802, USA.
Sci Rep. 2017 May 18;7(1):2126. doi: 10.1038/s41598-017-02194-1.
A highly efficient numerical approach for simulating the wideband optical response of nano-architectures comprised of Drude-Critical Points (DCP) media (e.g., gold and silver) is proposed and validated through comparing with commercial computational software. The kernel of this algorithm is the subdomain level discontinuous Galerkin time domain (DGTD) method, which can be viewed as a hybrid of the spectral-element time-domain method (SETD) and the finite-element time-domain (FETD) method. An hp-refinement technique is applied to decrease the Degrees-of-Freedom (DoFs) and computational requirements. The collocated E-J scheme facilitates solving the auxiliary equations by converting the inversions of matrices to simpler vector manipulations. A new hybrid time stepping approach, which couples the Runge-Kutta and Newmark methods, is proposed to solve the temporal auxiliary differential equations (ADEs) with a high degree of efficiency. The advantages of this new approach, in terms of computational resource overhead and accuracy, are validated through comparison with well-known commercial software for three diverse cases, which cover both near-field and far-field properties with plane wave and lumped port sources. The presented work provides the missing link between DCP dispersive models and FETD and/or SETD based algorithms. It is a competitive candidate for numerically studying the wideband plasmonic properties of DCP media.
提出并验证了一种高效数值方法，用于模拟由德拜临界点（DCP）介质（如金和银）构成的纳米结构的宽带光响应。该算法的核心是子域水平不连续伽辽金时域（DGTD）方法，它可以看作是谱元时域方法（SETD）和有限元时域（FETD）方法的混合。hp 细化技术可用于减少自由度（DoFs）和计算要求。共节点 E-J 方案通过将矩阵的求逆转换为更简单的向量操作，有助于求解辅助方程。提出了一种新的混合时间步长方法，它结合了龙格-库塔和纽曼方法，以高效的方式求解时间辅助微分方程（ADE）。通过与三种不同情况下的知名商业软件进行比较，验证了这种新方法在计算资源开销和准确性方面的优势，这些情况涵盖了平面波和集中端口源的近场和远场特性。所提出的工作在 DCP 色散模型和基于 FETD 和/或 SETD 的算法之间提供了缺失的联系。它是数值研究 DCP 介质宽带等离子体特性的有竞争力的候选者。
