Numerical calculation of localized eigenfunctions of the Laplacian
07/05/2015 Thursday 7th May 2015, 15:00 (Room P3.10, Mathematics Building)
Pedro Antunes, GFM-ULisboa
It is well known that for some planar domains, the Laplacian eigenfunctions are localized in a small region of the domain and decay rapidly outside this region. We address a shape optimization problem of minimizing or maximizing the $L^2$ norm of the eigenfunctions in some sub-domains. This problem is solved by a numerical method involving the Method of Fundamental Solutions and the adjoint method for a fast calculation of the shape gradient.
Several numerical simulations illustrate the good performance of the method.