  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.
