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High-Order Integral Equation Methods for Diffraction Problems Involving Screens and Apertures


Lintner, Stéphane Karl (2012) High-Order Integral Equation Methods for Diffraction Problems Involving Screens and Apertures. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/VP8P-DP74.


This thesis presents a novel approach for the numerical solution of problems of diffraction by infinitely thin screens and apertures. The new methodology relies on combination of weighted versions of the classical operators associated with the Dirichlet and Neumann open-surface problems. In the two-dimensional case, a rigorous proof is presented, establishing that the new weighted formulations give rise to second-kind Fredholm integral equations, thus providing a generalization to open surfaces of the classical closed-surface Calderon formulae. High-order quadrature rules are introduced for the new weighted operators, both in the two-dimensional case as well as the scalar three-dimensional case. Used in conjunction with Krylov subspace iterative methods, these rules give rise to efficient and accurate numerical solvers which produce highly accurate solutions in small numbers of iterations, and whose performance is comparable to that arising from efficient high-order integral solvers recently introduced for closed-surface problems. Numerical results are presented for a wide range of frequencies and a variety of geometries in two- and three-dimensional space, including complex resonating structures as well as, for the first time, accurate numerical solutions of classical diffraction problems considered by the 19th-century pioneers: diffraction of high-frequency waves by the infinitely thin disc, the circular aperture, and the two-hole geometry inherent in Young's experiment.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Integral Equations, Open Surface, Screen, Diffraction, Aperture, High-Order
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied And Computational Mathematics
Awards:W.P. Carey & Co., Inc., Prize in Applied Mathematics, 2012
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Bruno, Oscar P.
Thesis Committee:
  • Bruno, Oscar P. (chair)
  • Meiron, Daniel I.
  • Owhadi, Houman
  • Yang, Changhuei
Defense Date:1 June 2012
Record Number:CaltechTHESIS:06072012-004925615
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7143
Deposited By: Stephane Lintner
Deposited On:07 Jun 2012 22:00
Last Modified:03 Oct 2019 23:56

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