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Computational design of acoustic materials using an adaptive optimization algorithm

Journal article
Authors Larisa Beilina
Eugene Smolkin
Published in Applied Mathematics and Information Sciences
Volume 12
Issue 1
Pages 33-43
ISSN 1935-0090
Publication year 2018
Published at Department of Mathematical Sciences
Pages 33-43
Language en
Links dx.doi.org/10.18576/amis/120103
Keywords Acoustic wave equation, Adaptive finite element method, Coefficient inverse problem, Finite difference method, Invisibility acoustic cloaking, Lagrangian approach, Tikhonov functional
Subject categories Signal Processing, Control Engineering, Computational Mathematics

Abstract

© 2018 NSP Natural Sciences Publishing Cor. We consider the problem of design of the acoustic structure of arbitrary geometry with prescribed desired properties. We use optimization approach for the solution of this problem and minimize the Tikhonov functional on adaptively refined meshes. These meshes are refined locally only in places where the acoustic structure should be designed. Our special symmetric mesh refinement strategy together with interpolation procedure allows the construction of the symmetric acoustic material with prescribed properties. Efficiency of the presented adaptive optimization algorithm is illustrated on the construction of the symmetric acoustic material in two dimensions.

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