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Wave enhancement through spectral optimization

Mathematics Colloquium

Wave enhancement through spectral optimization
Series: Mathematics Colloquium
Location: ONLINE
Presenter: Nilima Nigam, Simon Fraser University

We present an efficient approach for optimizing the transmission signal between two points in a cavity at a given frequency, by changing boundary conditions from Dirichlet to Neumann. The optimization 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. Highly accurate calculations of the mixed Dirichlet-Neumann eigenvalues are performed via a layer potential approach. 

This is joint work with Habib Ammari, Oscar Bruno and Kthim Imeri.