Nilima Nigam | Simon Fraser University
Where should we put the Neumann data?
In this talk, we explore an interesting optimization problem: Let's fix a pair of points inside a domain, and specify a target frequency. Let's place an acoustic source at one of the points, and a receiver at the other. For a given configuration of zero Dirichlet and Neumann boundary conditions, we can figure out the acoustic field at the receiver. But is it possible to specify a configuration of the Dirichlet and Neumann boundary conditions to enhance the field at the receiver, at least for frequencies near the target frequency?
We'll see this can be related to a problem in spectral optimization for the Laplacian with mixed data. We'll describe how to solve the eigenvalue problems to very high accuracy. We'll then combine this numerical method with Rouche's theorem to solve the optimization problem. This is joint work with H. Ammari, O. Bruno and K. Imeri