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Ammari, Habib; Bruno, Oscar; Imeri, Kthim; Nigam, Nilima

Wave enhancement through optimization of boundary conditions. (English) Zbl 1430.35171

SIAM J. Sci. Comput. 42, No. 1, B207-B224 (2020).
Summary: In this paper, we present a new and efficient approach for optimizing the transmission signal between two points in a cavity at a given frequency, by changing boundary conditions. The proposed approach makes use of recent results on the monotonicity of the eigenvalues of the mixed boundary value problem and on the sensitivity of Green’s function to small changes in the boundary conditions. The switching of the boundary condition from Dirichlet to Neumann can be performed through the use of the recently modeled concept of metasurfaces which are comprised of coupled pairs of Helmholtz resonators. A variety of numerical experiments are presented to show the applicability and the accuracy of the proposed new methodology.

Cited in 3 Documents

MSC:

35P15 Estimates of eigenvalues in context of PDEs
35R30 Inverse problems for PDEs
35C20 Asymptotic expansions of solutions to PDEs

Keywords:

Zaremba eigenvalue problem; boundary integral operators; mixed boundary conditions; metasurfaces
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\textit{H. Ammari} et al., SIAM J. Sci. Comput. 42, No. 1, B207--B224 (2020; Zbl 1430.35171)
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References:

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