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Quadrature by Parity Asymptotic eXpansions (QPAX) for Scattering by High Aspect Ratio Particles

Carvalho, Camille; Kim, Arnold; Lewis, Lori; Moitier, Zoïs

Abstract:

We study scattering by a high aspect ratio particle using boundary integral equation methods. This problem has important applications in nanophotonics problems, including sensing and plasmonic imaging. To illustrate the effect of parity and the need for adapted methods in the presence of high aspect ratio particles, we consider the scattering in two dimensions by a sound-hard, high aspect ratio ellipse. This fundamental problem highlights the main challenge and provides valuable insights to tackle plasmonic problems and general high aspect ratio particles. For this problem, we find that the boundary integral operator is nearly singular due to the collapsing geometry from an ellipse to a line segment. We show that this nearly singular behavior leads to qualitatively different asymptotic behaviors for solutions with different parities. Without explicitly taking this nearly singular behavior and this parity into account, computed solutions incur a large error. To address these challenges, we introduce a new method called quadrature by parity asymptotic expansions (QPAX) that effectively and efficiently addresses these issues. We first develop QPAX to solve the Dirichlet problem for Laplace's equation in a high aspect ratio ellipse. ... mehr


Verlagsausgabe §
DOI: 10.5445/IR/1000143151
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Publikationstyp Zeitschriftenaufsatz
Publikationsmonat/-jahr 01.2021
Sprache Englisch
Identifikator ISSN: 1540-3459, 1540-3467
KITopen-ID: 1000143151
Erschienen in Multiscale modeling & simulation
Verlag Society for Industrial and Applied Mathematics (SIAM)
Band 19
Heft 4
Seiten 1857–1884
Schlagwörter boundary integral methodsasymptotic analysisnumerical quadraturescattering
Nachgewiesen in Dimensions
Scopus
Web of Science
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