# Wave Enhancement through Optimization of Boundary Conditions

## TL;DR

This paper introduces an efficient method to optimize wave transmission in cavities by adjusting boundary conditions, utilizing recent theoretical insights and metasurface technology to enhance wave control at specific frequencies.

## Contribution

It presents a novel approach combining boundary condition optimization with metasurface design, enabling precise control of wave transmission in cavities.

## Key findings

- Effective boundary condition switching improves transmission signals.
- Numerical experiments validate the accuracy of the proposed method.
- The approach leverages eigenvalue monotonicity and Green's function sensitivity.

## Abstract

It is well known that changing boundary conditions for the Laplacian from Dirichlet to Neumann can result in significant changes to the associated eigenmodes, while keeping the eigenvalues close. 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 the 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.