光電物理中之數值方法導論

Introduction to Numerical Methods in Optical Physics

學期

113-2

學分

3 學分

當期課號

535421

永久課號

EEEO30026

開課單位

光電工程學系

授課教師

賴英杰

校區

光復

類別

選修

上課時間表

節	週二
5 13:20–14:10	光電物理中之數值方法導論 EO105 3 節連堂
6 14:20–15:10
7 15:30–16:20

* 根據陽明交大上課時間表所列

概述

以光電物理中的實際問題作為例子,教授學生如何用數值方法來解決問題。課程的內容將集中在教授如何以有限差分、有限元素、及其他常用數值方法來解常微分、偏微分方程之邊界值、起始值、固有值、或最佳化之問題。

先修科目

大學部工程數學(或物理數學)及電磁學,能夠用任何一種計算機語言(Mathematica, Python, Matlab, Julia, C/C++/D, Fortran等)來寫作程式。

教學方式

課程網頁: NYCU e3 教學平台 https://e3p.nycu.edu.tw/

評分方式

三個程式習題: 90% 上課表現: 10%

週次計畫

週次	主題
第 1 週	Introduction
第 2 週	Finite difference methods (I) : ODE boundary value problems
第 3 週	Finite difference methods (II): ODE initial value problems
第 4 週	Finite difference methods (III): PDE initial value problems
第 5 週	Finite difference methods (IV): PDE split-step FFT methods
第 6 週	Finite difference methods (V): finite different time domain methods
第 7 週	Finite difference methods (VI): eigenvalue problems
第 8 週	Finite element methods (I): general scheme
第 9 週	Finite element methods (II): 1D & 2D elements
第 10 週	Finite element methods (III): mesh generation and 2D examples
第 11 週	Plane wave expansion methods: RCWA and photonic crystals
第 12 週	Iterative methods of numerical Linear algebra (I)
第 13 週	Iterative methods of numerical Linear algebra (II)
第 14 週	Optimization problems (I) https://nycu.webex.com/nycu/e.php?MTID=m363d28a44d8bc6c522ea55ba6fe8d757 參與者亦需知道會議密碼:nm2025
第 15 週	Optimization problems (II)
第 16 週	More numerical problems in optical physics
第 17 週
第 18 週

教科書

There is no particular textbook for the course. The following are some reference sources that may be useful. Additional references will be given during the lectures if needed. Main References: 1. M. T. Heath, "Scientific Computing: An Introductory Survey", (McGraw-Hill 2002) (For a good survey and clearer comparison on different numerical methods) (Book website on http://heath.cs.illinois.edu/scicomp/ . In particular, you can find excellent lecture notes and library/software information on the website.) 2. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, "Numerical Recipes 3rd Edition: The Art of Scientific Computing in C++", (https://numerical.recipes/) (For general reference and code examples on numerical methods) 3. L.N. Trefethen and D. Bau, III, "Numerical Linear Algebra," Philadelphia, PA: Society for Industrial and Applied Mathematics, 1997. (http://people.sc.fsu.edu/~jburkardt/classes/nla_2015/numerical_linear_algebra.pdf ) 4. R. L. Burden and J. D. Faires, "Numerical Analysis", 9th ed. Belmont, CA: Brooks Cole, 2011. (Textbook for Numerical Analysis.) (https://faculty.ksu.edu.sa/sites/default/files/numerical_analysis_9th.pdf) 5. G. Dahlquist and Å. Björck, "Numerical Methods in Scientific Computing", Vol. I and II, SIAM 2008. (For more details on Numerical analysis) ( Two volumes: https://cristiancastrop.wordpress.com/wp-content/uploads/2010/09/dahlquist-bjorck-vol-1.pdf https://cristiancastrop.wordpress.com/wp-content/uploads/2010/09/dahlquist-bjorck-vol2.pdf ) 6. Barrett, et al., "Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods," Philadelphia, PA: Society for Industrial and Applied Mathematics, 1993. (on-line book: https://www.netlib.org/templates/templates.pdf ) 7. Bai, et al., "Templates for the Solution of Algebraic Eigenvalue Problems: a Practical Guide," Philadelphia, PA: Society for Industrial and Applied Mathematics, 2000. ISBN: 9780898714715. (on-line book: https://epubs.siam.org/doi/book/10.1137/1.9780898719581) 8. M. P. Deisenroth, A. Aldo Faisal, and Cheng Soon Ong., "Mathematics for Machine Learning" (For a good introduction on mathematics for machine learning) (on-line book: https://mml-book.github.io/ )

Office Hours

地點: 田家炳光電大樓215B室
時間: Wednesday 2:00PM-4:00PM (Make an appointment with me first)
聯絡方式: yclai@nycu.edu.tw (03)5731746