# Numerical methods for solving wave scattering problems

## K-REx Repository

 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  and . en_US 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. dc.description.sponsorship The work in this thesis used the Extreme Science and Engineering Discovery Environment en_US (XSEDE), which is supported by National Science Foundation grant number OCI-1053575. 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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