讲座题目：Solvinghighly-oscillatory NLS with SAM: numerical efficiency and geometric properties

主讲人：张勇博士(维也纳大学)

主持人：陈秀卿副教授

时　间：2014年6月5日（周四）下午3:30-4:30

地　点：主楼1214

主要内容：

In this paper, we present the StroboscopicAveraging Method (SAM), which aims at numerically solving highly-oscillatorydifferential equations. More specifically, we first apply SAM to theSchrodinger equation on the 1-dimensional torus and on the real line with harmonicpotential, with the aim of assessing its efficiency: as compared to thewell-established standard splitting schemes, the stiffer the problem is, thelarger the speed-up grows (up to a factor 100 in our tests). The geometricproperties of SAM are also explored: on very long time intervals, symmetricimplementations of the method show a very good preservation of the massinvariant and of the energy. In a second series of experiments on 2-dimensionalequations, we demonstrate the ability of SAM to capture qualitatively thelong-time evolution of the solution (without spurring high oscillations).

报告人简介：

Yong ZHANG，Wolfgang Pauli Institute。

Research Interests：

• Fast algorithms and their applications

• Computational electromagnetic

• Numerical methods and analysis of differential equations

• Highly oscillatory system

• Bose-Einstein Condensate