Section: New Results

Frequency domain methods for the analysis and control of systems governed by PDE's

In [20] , we use microlocal analysis techniques to build artificial boundary conditions for reltivistic quantum dynamics.

In [11] , we give a complete analysis of some new domain decomposition techniques and investigate their approximations for application in quantum physics.

In the chapter [28] , we give an introduction to the modeling and the simulation of equilibrium states of Gross-Pitaevskii equations modeling Bose-Einstein condensates.

In [17] , we give the basic methodology to use the software 3D GPELab for the simulation of Bose-Einstein condensates.

In [10] , we develop a pseudo-spectral iterative method to compute equilibrium state of fast rotating Gross-Pitaevskii equations.

In [18] , we develop a new approximation and implementation of a Magnetic-to-Electric operator for 3D-Maxwell equations.

In [13] , we consider the inverse problem of determining the potential in the dynamical Schrödinger equation on the interval by the measurement on the boundary. Using the Boundary Control Method we first recover the spectrum of the problem from the observation at either left or right end points. Taking advantage of the one-dimensional configuration, we recover then the spectral function, reducing the problem to the classical one of determining the potential from the spectral function. This can be done by known methods. In order to handle more realistic situations, we also consider the case where only a finite number of eigenvalues are available and we prove the convergence of the reconstruction method as this number tends to infinity.