An Isaac Newton Institute Workshop

Effective Computational Methods for Highly Oscillatory Problems: The Interplay between Mathematical Theory and Applications

Level Set methods for capturing semiclassical dynamics of Schroedinger equations with different potentials

Author: Hailiang Liu (Iowa State University)

Abstract

In this talk we present newly developed level methods for capturing semiclassical dynamics of Schr\"{o}dinger equations with different potentials. We discuss the essential ideas behind the techniques, the coupling of these techniques to handle several canonical potentials, including the phase space based level set method for given smooth potentials; the field space based level set method for self-consistent potentials governed by the Poisson equation; as well as the Bloch-band based level set method for periodic potentials. The relations between computed multi-valued solutions and desirable physical observables are established. Numerical examples are presented to validate the numerical methods.