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Numerical calculation of localized eigenfunctions of the Laplacian

IIIUL, Room B2-01
2014-12-10 15:30 .. 16:30
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Pedro Antunes (GFMUL & FCUL, Portugal)

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 Hadamard shape derivatives. Several numerical simulations illustrate the good performance of the method.
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