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課程名稱 |
數值偏微分方程式二
NUMERICAL PARTIAL DIFFERENTIAL EQUATIONS(Ⅱ) |
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開課學期 |
97-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
薛克民 |
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課號 |
MATH7413 |
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課程識別碼 |
221 U3950 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期二6,7,8(13:20~16:20) |
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上課地點 |
舊數103 |
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備註 |
研究所，大學部高階選修課程。
總人數上限：30人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/972npde2 |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
This course will start from the very elementary level of the mathematical theory for the solutions of hyperbolic partial differential equations. With the basic solution structures of some simple model problems
in mind, we then discuss various approaches to construct approximate solutions for problems that can be described by hyperbolic PDEs. The tentative plan for the course follows essentially the book of LeVeque, and is outlined as follows:
(1) Conservation laws and differential equations
(2) Characteristics and Riemann problems foe linear hyperbolic equations
(3) Finite volume methods
(4) Introduction to CLAWPACK software
(5) High-resolution methods
(6) Boundary conditions
(7) Convergence, accuracy, and stability
(8) Variable-coefficient linear equations
(9) Other approaches to high resolution
(10) Extensions to nonlinear equations |
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課程目標 |
The goal of this course is to discuss the state-of-the-art numerical methods for solving partial differential equations of hyperbolic type. Typical mathematical models of this kind are the Maxwell equations for electromagnetism, elastic-plastic equations for solid materials, LWR (Lighthill, Whitham, Richards) equation for traffic flow, Savage-Hutter model for granular flow, Euler equations for gas dynamics, and so on.
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課程要求 |
(1) Basic knowledge of the solution for linear hyperbolic PDEs
(2) Basic knowledge on how to write a computer program with a chosen computer language
(3) Students who take this course are required to select a computational project and work on that throughout the semester |
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預期每週課後學習時數 |
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Office Hours |
每週三 11:00~12:00 |
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指定閱讀 |
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參考書目 |
1. Randall J. LeVeque, Finite Volume methods for Hyperbolic Problems,
Cambridge, 2002
2. E. F. Toro, Numerical Solvers and Numerical Methods for Fluid Dynamics,
Springer, 1999
3. Recent journal papers |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
專題報告 |
30% |
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2. |
專題計畫 |
70% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/17 |
Overview of conservation laws, computation of high frequency solutions for wave eqations |
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第2週 |
2/24 |
Derivation of conservation laws, linear acoustics, shallow water equations |
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第3週 |
3/03 |
Riemann problem for hyperbolic system of conservation laws:
weak solutions, rarefaction waves, & shocks |
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第4週 |
3/10 |
Godunov's method |
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第5週 |
3/17 |
計中110 |
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第6週 |
3/24 |
計中110 |
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第7週 |
3/31 |
計中110 |
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第8週 |
4/07 |
Conservative methods, high resolution schemes |
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第9週 |
4/14 |
Student term-project proposal presentation & ENO-type schemes |
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第10週 |
4/21 |
WENO & TVDRK |
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第11週 |
4/28 |
Entropy inequality & its applications |
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第12週 |
5/05 |
Well-balanced scheme |
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第13週 |
5/12 |
Hyperbolic problems in multi-D |
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第14週 |
5/19 |
Student term project: progress report |
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第15週 |
5/26 |
Wave equation with discontinuous coefficients & related problems |
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第16週 |
6/02 |
No class |
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第17週 |
6/09 |
Dispersion-relation-preserving scheme |
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第18週 |
6/16 |
Student term project presentation II |
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第18週 |
6/19 |
Student term project presentation: 10:00am+ |
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