Computational & Applied Mathematics (CAM) Seminar

Time: 3:15pm, Apr. 5 (周三下午 3:15)

Location: Conference Room 4, Jin Chun Yuan West Bldg. (近春园西楼二楼第四会议室)

Title: Optimal error estimate for the first-order Gaussian beam approach to the Schrodinger equation

Speaker: Chunxiong Zheng, Tsinghua

Abstract：Gaussian beams are generally local asymptotic solutions to the linear wave equations in the high-frequency regime. Each Gaussian beam is concentrated around a specific ray path determined by the underlying Hamiltonian system. Expressed as some superposition of Gaussian beams, Gaussian beam approximation is expected to be a high-frequency asymptotic solution which remains globally valid even around caustics.

We derive optimal first-order error estimates for first- order Gaussian beam approximations, in both continuous and discrete levels, to the Schro ̈dinger equation equipped with a WKB initial data. Our error estimates are valid for any spatial dimension and unaffected by the presence of caustics.

For details, please see http://ymsc.tsinghua.edu.cn/CAM