高階CESE方法模擬

The Simulation of High-Order Conservation Element and Solution Element Method

黃閔琨

指導教授 ： 江進福

國立交通大學/理學院/物理研究所/碩士(2012年)

https://doi.org/10.6842/NCTU.2012.00596

摘要

本論文主要的研究目是利用高階時空守恆法模擬各種已知精確解一維微分 方程式 (例如 :波動方程式，量子力學問題 )最後應用在高次諧波的情況。

關鍵字

時空守恆法

並列摘要

The purpose of this thesis is to calculate the High-Order space-time conservation element and solution element method,and to simulate known exact solutions of one-dimensional differential equations (for example: the wave equation, quantum mechanics problem), the last application in the High-order Harmonic Generation

並列關鍵字

CESE

參考文獻

[1] Sin-Chung Chang, “A New Approach For Constructing Highly Stable High Order CESE Schemes”AIAA-2010-543 48th AIAA Aerospace Science Meeting,Orlando,FL 4-7 Jan 2010

[2] B.H bransden, C.J. Joachain, physics of Atoms and Molecules, second edition , Prentice- Hall,2003,ISBN-9780582356924

[3] Bingbing Wang, Taiwang Cheng, Xiaofeng Li, and Panming Fu “Pulse-duration of high-order harmonic generation with coherent superposition state”physical Rev A72 063412,2005.

[5] S.-C. Chang, A. Himansu, C.-Y. Loh, X.-Y. Wang and S.-T.J. Yu, "Robust and Simple Non-Reflecting Boundary Conditions for the Euler Equations, A New Approach Based on the Space-Time CE/SE Method," NASA/TMX2003-212495/REV1 ,2003.

[7] XAVIER ANTOINE, CHRISTOPHE BESSE, AND VINCENT MOUYSSET “Number Schemes For The Simulation Of The Two-dimensional Schrodonger Equationsing Non-Reflecting Boundary Conditions” MATHEMATICS OF COMPUTATION Volume 73, Number 248, Pages 1779-1799