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High-Order Perturbation of Surfaces Algorithms for the Simulation of Localized Surface Plasmon Resonances in Two Dimensions

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Abstract

The capability of simulating scattering returns of electromagnetic radiation from bounded obstacles is of overwhelming importance to scientists and engineers. Furthermore, such simulations must be of both surpassing accuracy and high fidelity for many applications of interest. High-Order Spectral methods deliver highly accurate simulations with a relatively small number of degrees of freedom, while interfacial formulations which utilize these discretizations have orders of magnitude smaller execution times and memory requirements. Among these, the High-Order Perturbation of Surfaces algorithms have proved to be a method of choice in layered media applications, and we display here how two of these-the Methods of Field Expansions and Transformed Field Expansions-extend to obstacles of bounded cross-section. In this contribution we provide not only a detailed prescription of the algorithms, but also validate the schemes and point out their benefits and shortcomings. With numerical experiments we show the remarkable efficiency, fidelity, and high-order accuracy one can achieve with implementations of these algorithms.

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Acknowledgements

D.P.N. gratefully acknowledges support from the National Science Foundation through Grant No. DMS-1522548.

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  1. Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL, 60607, USA

    David P. Nicholls & Xin Tong

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  1. David P. Nicholls
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Correspondence to David P. Nicholls.

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Nicholls, D.P., Tong, X. High-Order Perturbation of Surfaces Algorithms for the Simulation of Localized Surface Plasmon Resonances in Two Dimensions. J Sci Comput 76, 1370–1395 (2018). https://doi.org/10.1007/s10915-018-0665-2

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