In this paper we introduce a numerical approach adapted to the minimization of the eigenmodes of a membrane with respect to the domain. This method is based on the combination of the Level Set method of S. Osher and J.A. Sethian with the relaxed approach. This algorithm enables both changing the topology and working on a fixed regular grid.
In this paper we introduce a numerical approach adapted to the minimization of the eigenmodes of a membrane with respect to the domain. This method is based on the combination of the Level Set method of S. Osher and J.A. Sethian with the relaxed approach. This algorithm enables both changing the topology and working on a fixed regular grid.
We study variational problems with volume constraints, , with level sets of prescribed measure. We introduce a numerical method to approximate local minimizers and illustrate it with some two-dimensional examples. We demonstrate numerically nonexistence results which had been obtained analytically in previous work. Moreover, we show the existence of discontinuous dependence of global minimizers from the data by using a -limit argument and illustrate this with numerical computations. Finally we...
Page 1