Maximal and minimal norm of Laplacian eigenfunctions in a given subdomain *PA was partially supported by FCT, Portugal, through the program 'Investigador FCT' with reference IF/00177/2013 and the scientific project PTDC/MAT-CAL/4334/2014. (20th September 2016) - Antunes, Pedro R S
Abstract: It is well known that for some planar domains, some of 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 subdomains. This problem is solved by a numerical method involving the method of fundamental solutions and Hadamard shape derivatives. We use the adjoint method for a fast calculation of the shape gradient. Several numerical simulations illustrate the good performance of the method.