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The numerical solution of frequency-domain acoustic and electromagnetic periodic scattering problems / by Yuxiang Liu

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Author	Liu, Yuxiang
Title	The numerical solution of frequency-domain acoustic and electromagnetic periodic scattering problems / by Yuxiang Liu
Date	2016
Abstract	'The control of waves using periodic structures is crucial for modern optical, electromagnetic and acoustic devices such as diffraction gratings, filters, photonic crystals, solar cells, sensors, and absorbers. We present a high-order accurate boundarybased numerical solver for three-dimensional (3D) frequency-domain scattering from a doubly-periodic grating of obstacles. We focus on the case of axisymmetric objects, and handle both acoustic and electromagnetic cases. We combine the method of fundamental solutions (MFS) with a new periodizing scheme, using various fast algorithms such as the fast multiple method and the so-called "skeletonization". Our scheme has exponential convergence for analytic shapes and avoids singular quadratures, periodic Green''s functions, and lattice sums. Furthermore, the convergence rate of our scheme is unaffected by resonances within obstacles. The periodizing scheme is also independent of the complexity of the objects and the frequency can reach 13ƛ x 13ƛ x 13ƛ in each periodic unit, which covers the vast majority of scattering problems in practice; meanwhile, the solver can achieve 10 digits of accuracy, takes less than 1 hour of computational time, and requires less than 6GB of RAM space. We also propose a way to efficiently solve scattering problems on boundaries with corners using the MFS to achieve 10 digits of accuracy for a range of corner angles. Also, we can observe exponential convergence as the number of unknowns increases for corner problems. Lastly, we develop and test the use of a recently-developed fast direct solver for least squares problems to solve high frequency scattering problems on general (non-axisymmetric) smooth objects using the MFS.'
Description	1 online resource (xxix, 171 leaves) : color illustrations
Format	application/pdf
College	Dartmouth College -- Department of Physics and Astronomy.
Issuing Body	Dartmouth Dissertations are made available through the Dartmouth Digital Library.
Degree	Thesis (Ph.D)--Dartmouth College.
Copyright	Made available by the author under a Creative Commons Attribution-NonCommercial License.; Made available by the Trustees of Dartmouth College under a Creative Commons Attribution-NonCommercial License. https://creativecommons.org/licenses/by-nc/4.0/
DOI	https://doi.org/10.1349/ddlp.2447

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The numerical solution of frequency-domain acoustic and electromagnetic periodic scattering problems / by Yuxiang Liu

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