Numerical methods for solving wave scattering problems

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dc.contributor.author Tran, Nhan Thanh
dc.date.accessioned 2016-04-18T16:46:50Z
dc.date.available 2016-04-18T16:46:50Z
dc.date.issued 2016-05-01 en_US
dc.identifier.uri http://hdl.handle.net/2097/32508
dc.description.abstract In this thesis, the author presents several numerical methods for solving scalar and electromagnetic wave scattering problems. These methods are taken from the papers of Professor Alexander Ramm and the author, see [1] and [2]. In Chapter 1, scalar wave scattering by many small particles of arbitrary shapes with impedance boundary condition is studied. The problem is solved asymptotically and numerically under the assumptions a << d << λ, where k = 2π/λ is the wave number, λ is the wave length, a is the characteristic size of the particles, and d is the smallest distance between neighboring particles. A fast algorithm for solving this wave scattering problem by billions of particles is presented. The algorithm comprises the derivation of the (ORI) linear system and makes use of Conjugate Orthogonal Conjugate Gradient method and Fast Fourier Transform. Numerical solutions of the scalar wave scattering problem with 1, 4, 7, and 10 billions of small impedance particles are achieved for the first time. In these numerical examples, the problem of creating a material with negative refraction coefficient is also described and a recipe for creating materials with a desired refraction coefficient is tested. In Chapter 2, electromagnetic (EM) wave scattering problem by one and many small perfectly conducting bodies is studied. A numerical method for solving this problem is presented. For the case of one body, the problem is solved for a body of arbitrary shape, using the corresponding boundary integral equation. For the case of many bodies, the problem is solved asymptotically under the physical assumptions a << d << λ, where a is the characteristic size of the bodies, d is the minimal distance between neighboring bodies, λ = 2π/k is the wave length and k is the wave number. Numerical results for the cases of one and many small bodies are presented. Error analysis for the numerical method are also provided. en_US
dc.description.sponsorship The work in this thesis used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number OCI-1053575. en_US
dc.language.iso en_US en_US
dc.publisher Kansas State University en
dc.subject Wave scattering en_US
dc.subject numerical method
dc.subject fast algorithm
dc.subject many bodies
dc.subject many particles
dc.subject electromagnetic
dc.title Numerical methods for solving wave scattering problems en_US
dc.type Dissertation en_US
dc.description.degree Doctor of Philosophy en_US
dc.description.level Doctoral en_US
dc.description.department Department of Mathematics en_US
dc.description.advisor Alexander G. Ramm en_US
dc.date.published 2016 en_US
dc.date.graduationmonth May en_US


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