Year: 2024
Author: Youjun Deng, Lingzheng Kong, Hongyu Liu, Liyan Zhu
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 5 : pp. 1252–1276
Abstract
Strong field concentration may occur between two nearly-touching high-contrast material inclusions due to an incident field. The degree of concentration is characterised by the blowup rate of the underlying gradient field. This phenomenon has received considerable attention in the literature due to its practical implications in the theory of composite materials. However, most of the existing studies are concerned with the static cases. In this paper, we present a comprehensive numerical investigation of this intriguing phenomenon associated to the Helmholtz system in the quasi-static frequency regime. On the one hand, we present extensive numerical results to corroborate the theoretical findings in [16], and on the other hand, we derive new findings that cannot be handled by the theoretical analysis yet. Our focus is on the static effect, frequency effect, the geometric (curvature) effect to the gradient estimates.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2023-0104
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 5 : pp. 1252–1276
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Field concentration gradient estimates Helmholtz system high-contrast inclusions blow up quasi-static multi-scale curvature.