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Electromagnetic scattering from three dimensional periodic structures

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Electromagnetic scattering from three dimensional periodic structures
作者:	Barnes, Andrew L.
面頁冊數:	163 p.
附註:	Source: Dissertation Abstracts International, Volume: 65-01, Section: B, page: 0245.
附註:	Supervisor: Stephanos Venakides.
Contained By:	Dissertation Abstracts International65-01B.
標題:	Mathematics.
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3120174
ISBN:	049667546X

Electromagnetic scattering from three dimensional periodic structures
Barnes, Andrew L.

Electromagnetic scattering from three dimensional periodic structures [electronic resource] - 163 p.

Source: Dissertation Abstracts International, Volume: 65-01, Section: B, page: 0245.

Thesis (Ph.D.)--Duke University, 2003.

The original Muller formulation was for compact scatterers and it used a free space Green's function for the Helmholtz equation. We solve a periodic problem with a periodic Helmholtz Green's function. This Green's function has the same degree of singularity as the free space Helmholtz Green's function, but it is an infinite sum that converges very slowly. We use a resummation technique (due to P. P. Ewald) to perform an efficient calculation of the periodic Green's function. We solve the integral equation by a Galerkin method and use RWG vector basis functions to discretize surface currents on the scatterer. We perform a careful extraction of all singularities from the integrals that we compute. We use a triangular Gaussian quadrature method for calculation of the non-singular parts of the integrals. We analytically compute the remaining singular and nearly singular integrals. We also perform an acceleration technique that treats several frequencies simultaneously and leads to decreased computational times. In addition to the numerical code, we present an alternative way of looking at electromagnetic scattering in terms of Calderon projection operators.

ISBN: 049667546XSubjects--Topical Terms:

184409
Mathematics.

Electromagnetic scattering from three dimensional periodic structures
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500 $a Source: Dissertation Abstracts International, Volume: 65-01, Section: B, page: 0245.
500 $a Supervisor: Stephanos Venakides.
502 $a Thesis (Ph.D.)--Duke University, 2003.
520 # $a The original Muller formulation was for compact scatterers and it used a free space Green's function for the Helmholtz equation. We solve a periodic problem with a periodic Helmholtz Green's function. This Green's function has the same degree of singularity as the free space Helmholtz Green's function, but it is an infinite sum that converges very slowly. We use a resummation technique (due to P. P. Ewald) to perform an efficient calculation of the periodic Green's function. We solve the integral equation by a Galerkin method and use RWG vector basis functions to discretize surface currents on the scatterer. We perform a careful extraction of all singularities from the integrals that we compute. We use a triangular Gaussian quadrature method for calculation of the non-singular parts of the integrals. We analytically compute the remaining singular and nearly singular integrals. We also perform an acceleration technique that treats several frequencies simultaneously and leads to decreased computational times. In addition to the numerical code, we present an alternative way of looking at electromagnetic scattering in terms of Calderon projection operators.
520 # $a We have developed a numerical method for solving electromagnetic scattering problems from arbitrary, smooth, three dimensional structures that are periodic in two directions and of finite thickness in the third direction. We solve Maxwell's equations via an integral equation that was first formulated by Claus Muller. The Muller integral equation is Fredholm of the second kind, so it is a well-posed problem.
520 # $a We have validated our computer code by comparing the numerical results with results from two separate cases. The first case is that of a flat dielectric slab of finite thickness, for which exact formulae are available. The second case is a periodic array of a row of infinite cylinders. In this case, we compare our results with those obtainedv from a two dimensional code developed by S. P. Shipman, S. Venakides and M. A. Haider (SIAM J. Appl. Math., 62, No. 6 (2002), 2129--2148). We have used our code to obtain transmission profiles for scattering from dielectric slabs with dimples.
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