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Wave-Scattering by Periodic Media


Fernandez-Lado, Agustin Gabriel (2020) Wave-Scattering by Periodic Media. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/G7XQ-RT85.


This thesis presents a full-spectrum, well-conditioned, Green-function methodology for evaluation of scattering by general periodic structures, which remains applicable on a set of challenging singular configurations, usually called Rayleigh-Wood (RW) anomalies, where most existing methods break down. After reviewing a variety of existing fast-converging numerical procedures commonly used to compute the classical quasi-periodic Green-function, the present work explores the difficulties they present around RW-anomalies and introduces the concept of hybrid "spatial/spectral" representations. Such expressions allow both the modification of existing methods to obtain convergence at RW-anomalies as well as the application of a slight generalization of the Woodbury-Sherman-Morrison formulae together with a limiting procedure to bypass the singularities. Although, for definiteness, the overall approach is applied to the scalar (acoustic) wave-scattering problem in the frequency domain, the approach can be extended in a straightforward manner to the harmonic Maxwell's and elasticity equations. Ultimately, the thorough understanding of RW-anomalies this thesis provides yields fast and highly-accurate solvers, which are demonstrated with a variety of simulations of wave-scattering phenomena by arrays of particles, crossed impenetrable and penetrable diffraction gratings, and other related structures. In particular, the methods developed in this thesis can be used to "upgrade" classical approaches, resulting in algorithms that are applicable throughout the spectrum, and it provides new methods for cases where previous approaches are either costly or fail altogether. In particular, it is suggested that the proposed shifted Green function approach may provide the only viable alternative for treatment of three-dimensional high-frequency configurations. A variety of computational examples are presented which demonstrate the flexibility of the overall approach, including, in particular, a problem of diffraction by a double-helix structure, for which numerical simulations did not previously exist, and for which the scattering pattern presented in this thesis closely resembles those obtained in crystallography experiments for DNA molecules.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Wave scattering Periodic media High-order methods Rayleigh Wood anomalies Numerical methods Simulation Ewald
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied And Computational Mathematics
Awards:The W.P. Carey and Co., Inc., Prize in Applied Mathematics, 2020.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Bruno, Oscar P.
Thesis Committee:
  • Desbrun, Mathieu (chair)
  • Schroeder, Peter
  • Owhadi, Houman
  • Bruno, Oscar P.
Defense Date:23 August 2019
Record Number:CaltechTHESIS:08252019-170117522
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for Chapter 4
Fernandez-Lado, Agustin Gabriel0000-0002-8141-3792
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11764
Deposited By: Agustin Fernandez Lado
Deposited On:04 Sep 2019 23:34
Last Modified:12 Jun 2020 18:45

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