Optimization of dispersive coefficients in the homogenization of the wave equation in periodic structures

We study dispersive effects of wave propagation in periodic media, which can be modelled by adding a fourth-order term in the homogenized equation. The corresponding fourth-order dispersive tensor is called Burnett tensor and we numerically optimize its values in order to minimize or maximize disper...

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Bibliographic Details
Published in:Numerische Mathematik Vol. 140; no. 2; pp. 265 - 326
Main Authors: Allaire, Grégoire, Yamada, T
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Science and Business Media LLC 01.10.2018
Springer Berlin Heidelberg
Springer Nature B.V
Springer Verlag
Subjects:
49K20
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Bloch waves
dispersion
homogenization
Lower bounds
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical models
Mathematics
Mathematics and Statistics
MSC 35B27
MSC 35B27, 49K20
Numerical Analysis
Numerical and Computational Physics
Optimization
Optimization and Control
periodic structure
Periodic structures
Periodic variations
shape optimization
Simulation
Theoretical
Wave dispersion
Wave equations
Wave propagation
35B27
49K20
homogenization
periodic structure
shape optimization
Bloch waves
dispersion
ISSN:0029-599X, 0945-3245
Online Access:Get full text
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Summary:We study dispersive effects of wave propagation in periodic media, which can be modelled by adding a fourth-order term in the homogenized equation. The corresponding fourth-order dispersive tensor is called Burnett tensor and we numerically optimize its values in order to minimize or maximize dispersion. More precisely, we consider the case of a two-phase composite medium with an eightfold symmetry assumption of the periodicity cell in two space dimensions. We obtain upper and lower bound for the dispersive properties, along with optimal microgeometries.
Bibliography:ObjectType-Article-1
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ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-018-0972-4