**数学与系统科学研究院**

**计算数学所学术报告**

**报告人**：
Hailiang Liu

Iowa State University, USA

**报告题目**
Computing High-Frequency Waves By the Level Set Method

**Abstract:**
We introduce a new level set method for
computational high frequency wave propagation in dispersive media,
with an application to linear Schrodinger equations with
efficiently highly oscillating initial data. The high-frequency
asymptotics of dispersive equations often lead to the well known
WKB system, where the phase evolves according to a nonlinear
Hamilton-Jacobi equation and the intensity of the plane wave is
governed by a linear conservation law. Based on the
Hamilton-Jacobi equation wave fronts with multi-phases are
constructed and captured by solving a linear Liouville equation in
the phase space, and the multi-valued phase is resolved via the
intersection of several zero level sets in an augmented phase
space. In this context we also discuss the new development on
computing multi-valued energy density and other physical
observables.

**报告时间**：2004年7月13日 下午3：00

**报告地点**：科技综合楼三层报告厅