Development of level set methods for computing the semiclassical limit of Schrödinger equations with potentials

Abstract

<p>In this thesis, several level set methods are developed and analyzed for computing multi-valued solutions to the semiclassical limits of Schroedinger equations. Both formulation and numerical results are obtained for level set method. Superposition is also proved via let set method setting. Meanwhile, multi-valued solutions of the Euler-Poisson equations are also analyzed and computed using level set formulation via field space. Multi-scale computation and homogenization are studied for a class of Schroedinger equations. A Bloch band based level set method is developed with a series of numerical examples.</p>