We perform a numerical optimization of the first ten nontrivial eigenvalues of the Neumann Laplacian for planar Euclidean domains. The optimization procedure is done via a gradient method, while the… (More)

We present a numerical study for the first Dirichlet eigenvalue of certain classes of planar regions. Based on this, we propose new types of bounds and establish several conjectures regarding the… (More)

We develop the first numerical study in four dimensions of optimal eigenmodes associated with the Dirichlet Laplacian. We describe an extension of the method of fundamental solutions adapted to the… (More)

In this work we study the application of the Method of Fundamental Solutions (MFS) to the numerical calculation of the eigenvalues and eigenfunctions for the 2D Bilaplacian in simply connected… (More)

We consider the numerical solution of an inverse problem of finding the shape and location of holes in an elastic body. The problem is solved by minimizing a functional depending on the eigenvalues… (More)

It is well known that the sound produced by string instruments has a well defined pitch. Essentially, this is due to the fact that all the resonancefrequencies of the string have integer ratio with… (More)

We study some shape optimization problems related to sums and quotients of Dirichlet Laplacian eigenvalues kn for planar domains. We show how to minimize a sum ðkk þ kkþ1ÞjXj; k 1⁄4 1;2; . . . when… (More)

Some meshless methods have been applied to the numerical solution of boundary value problems involving the Helmholtz equation. In this work, we focus on the method of fundamental solutions and the… (More)