Boundary composed of small Helmholtz resonators: asymptotic approach
https://doi.org/10.17586/2220-8054-2024-15-6-736-741
Abstract
We consider the solution of the two-dimensional Neumann problem for the Helmholtz equation in a complex region composed of a square resonator with large number of smaller square resonators connected to it through small apertures along one side. The sizes of the apertures and distances between the neighbour apertures tend to zero. We use the method of matching of asymptotic expansions of solutions. By directing the number of attached small resonators to infinity, we obtain a problem for the Laplacian in the main square with energy-dependent boundary condition.
Supporting agencies: This work was partially financially supported by Russian Science Foundation (grant 24-21-00107, https://rscf.ru/en/project/24-21-00107/).
About the Authors
I. Y. Popov
ITMO University
Russian Federation
Russian Federation
Igor Y. Popov – Center of Mathematics
Kroverkskiy, 49, St. Petersburg, 197101
E. S. Trifanova
ITMO University
Russian Federation
Russian Federation
Ekaterina S. Trifanova – Center of Mathematics
Kroverkskiy, 49, St. Petersburg, 197101
A. S. Bagmutov
ITMO University
Russian Federation
Russian Federation
Alexander S. Bagmutov – Center of Mathematics
Kroverkskiy, 49, St. Petersburg, 197101
A. A. Lytaev
ITMO University; Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences
Russian Federation
Russian Federation
Alexander A. Lytaev – Center of Mathematics
Kroverkskiy, 49, St. Petersburg, 197101
Vasilievskiy island, Bolshoi av., 61, St. Petersburg, 199178
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Review
For citations:
Popov I.Y., Trifanova E.S., Bagmutov A.S., Lytaev A.A. Boundary composed of small Helmholtz resonators: asymptotic approach. Nanosystems: Physics, Chemistry, Mathematics. 2024;15(6):736-741. https://doi.org/10.17586/2220-8054-2024-15-6-736-741
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