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

被引：15
|
作者：
Allaire, G. [1 ]
Yamada, T. [2 ]
机构：
[1] Ecole Polytech, CMAP, Palaiseau, France
[2] Kyoto Univ, Dept Mech Engn & Sci, Kyoto, Japan
来源：
NUMERISCHE MATHEMATIK | 2018年 / 140卷 / 02期
关键词：
HETEROGENEOUS MULTISCALE METHOD; LEVEL SET METHOD; SHAPE OPTIMIZATION; TOPOLOGY OPTIMIZATION; SENSITIVITY; PROPAGATION; EVOLUTION;
D O I：
10.1007/s00211-018-0972-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：265 / 326
页数：62
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