Optimal design of acoustic metamaterial cloaks under uncertainty

Chen, Peng; Haberman, Michael R.; Ghattas, Omar

doi:10.1016/j.jcp.2021.110114

Optimal design of acoustic metamaterial cloaks under uncertainty

Journal Article · Mon Jan 11 00:00:00 EST 2021 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2021.110114· OSTI ID:1853042

Chen, Peng ^[1]; Haberman, Michael R. ^[2]; Ghattas, Omar ^[3]

Univ. of Texas, Austin, TX (United States). Oden Inst. for Computational Engineering & Sciences; Univ. of Texas, Austin, TX (United States)
Univ. of Texas, Austin, TX (United States). Walker Dept. of Mechanical Engineering
Univ. of Texas, Austin, TX (United States). Oden Inst. for Computational Engineering & Sciences; Univ. of Texas, Austin, TX (United States). Walker Dept. of Mechanical Engineering; Univ. of Texas, Austin, TX (United States). Dept. of Geological Sciences

In this work, we consider the problem of optimal design of an acoustic cloak under uncertainty and develop scalable approximation and optimization methods to solve this problem. The design variable is taken as an infinite-dimensional spatially-varying field that represents the material property, while an additive infinite-dimensional random field represents the variability of the material property or the manufacturing error. Discretization of this optimal design problem results in high-dimensional design variables and uncertain parameters. To solve this problem, we develop a computational approach based on a Taylor approximation and an approximate Newton method for optimization, which is based on a Hessian derived at the mean of the random field. We show our approach is scalable with respect to the dimension of both the design variables and uncertain parameters, in the sense that the necessary number of acoustic wave propagations is essentially independent of these dimensions, for numerical experiments with up to one million design variables and half a million uncertain parameters. Additionally, we demonstrate that, using our computational approach, an optimal design of the acoustic cloak that is robust to material uncertainty is achieved in a tractable manner. The optimal design under uncertainty problem is posed and solved for the classical circular obstacle surrounded by a ring-shaped cloaking region, subjected to both a single-direction single-frequency incident wave and multiple-direction multiple-frequency incident waves. Finally, we apply the method to a deterministic large-scale optimal cloaking problem with complex geometry, to demonstrate that the approximate Newton method’s Hessian computation is viable for large, complex problems.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: SC0019303

OSTI ID:: 1853042

Alternate ID(s):: OSTI ID: 1775930
OSTI ID: 23203395

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 431; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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71 CLASSICAL AND QUANTUM MECHANICS
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97 MATHEMATICS AND COMPUTING
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Optimal design of acoustic metamaterial cloaks under uncertainty

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