Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
519414 | Journal of Computational Physics | 2010 | 15 Pages |
Abstract
The linear Schrödinger equation with periodic potentials is an important model in solid state physics. The most efficient direct simulation using a Bloch decomposition-based time-splitting spectral method [18] requires the mesh size to be O(ϵ)O(ϵ) where ϵϵ is the scaled semiclassical parameter. In this paper, we generalize the Gaussian beam method introduced in Jin et al. [23] to solve this problem asymptotically. We combine the technique of Bloch decomposition and the Eulerian Gaussian beam method to arrive at an Eulerian computational method that requires mesh size of O(ϵ). The accuracy of this method is demonstrated via several numerical examples.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Shi Jin, Hao Wu, Xu Yang, Zhongyi Huang,