Scientific Computing Group Seminars - Detail View

Speaker: N. Ben Abdallah

Affiliation: University of Toulouse

Talk Title: Multiscale schemes for the Schrodinger equation

Invited by: Chi-Wang Shu

Time: Nov. 21 2008 11 a.m.

Location: 182 George Street, Room 110

Abstract:

The simulation of open quantum devices relies on the resolution of a large number of Schrodinger equations coupled to the Poisson equation which model, in the mean field approximation, the coulomb interaction between the electron themselves. The wavelengths corresponding to the Schrodinger equations are reasonably large for low energies but might be rather small for large energies which have to be resolved in order to compute the current densities. The charge density which is computed as the sum of contributions of the various states is however quite slowly variying. Therefore one might want to use a coarse position mesh for solving the Schrodinger equations. we present here a multiscale finite element or finite volume method based on the WKB expansion for high energies. We show how the method is derived in the one dimensional case. The generalization to the fully two-d case is still an open problem because of discontinuity issues but the method can be generalized to the case of two dimensional waveguides. Convergence results are shown in the 1D case and simulations illustrating the computational time gain are shown. In the one dimensional case of the resonant tunneling diode. the discretization of the energy variable is also discussed. Using the notion of resonant states, we derive an efficient numerical scheme which considerably reduces the numerical cost. Work in collaboration with Olivier Pinaud (Lyon) and Claudia Negulescu (Marseille)