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課程名稱 |
邊界元素法
BOUNDARY ELEMENT METHOD |
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開課學期 |
96-2 |
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授課對象 |
工學院 工程科學及海洋工程學研究所 |
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授課教師 |
王昭男 |
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課號 |
ESOE5009 |
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課程識別碼 |
525 U0120 |
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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 |
星期五2,3,4(9:10~12:10) |
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上課地點 |
工科202 |
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備註 |
總人數上限：56人 |
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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 |
1. Introduction
2. Mathematical preliminary
2.1 vectors
2.2 integral equations
2.3 Green’s second identity
2.4 Fundamental solution
2.5 Gauss guadrature
3. Indirect method (potential problem)
3.1 Elements of potential theory
3.2 Indirection formulation
3.3 Constant element
4. Direct method (Laplace equation)
4.1 Derivation of the singular boundary integral equation
4.2 BEM- constant element
4.3 Linear element (2D)
4.4 Quadratic element (2D)
4.5 Mixed type boundary condition
4.6 Boundary elements for 3D problems
4.7 Sub-regions
4.8 Infinite region---exterior problem
4.9 Special fundamental solution ( Semi-infinite region)
4.10 Poisson equation
5. Helmholtz equation
5.1 Preliminary consideration
5.2 Boundary integral equation
5.3 Dual reciprocity method
5.4 The non-unique problem
5.5 Frequency interpolation
5.6 Multiple reciprocity method
5.7 Arbitrary-order boundary element method
6. Elasticstatic problem
6.1 Stress and tractions
6.2 Reciprocal work theorem
6.3 Boundary integral equation
7. Introduction to the hypersingular integral equation)
7.1 Response-gradient boundary integral equations
7.2 Hypersingular boundary integral equations
7.3 Regularization of Hypersingular boundary integral equations
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課程目標 |
介紹邊界元素法之基本概念及其初步應用
1. 簡介(Introduction)
2. 數學基礎(Mathematics Preliminary)
3. 勢流問題(Potential Problems)(間接法)
4. 拉普拉斯方程式(Laplace equation)(直接法)
5. 聲學問題(Acoustic Problems)
6. 彈性力學問題(Elastostatic Problems)
7. 超奇異積分介紹(Introduction to hypersingular integral)
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課程要求 |
先修課程:工程數學、數值分析 |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
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參考書目 |
1. C. A. Brebbia, J. C. F. Telles and L. C. Wrobel `Boundary Element Techniques Theory and application in Engineering`
2. A. A. Becker, `The Boundary Element Method in Engineering`, McMraw-Hill Book Company.
3. P. K. Kytbe, “An introduction to Boundary Element methods” CRC Press. |
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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. |
期末考 |
25% |
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2. |
程式作業 |
75% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/22 |
Introduction(1) |
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第2週 |
2/29 |
Introduction(2) |
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第3週 |
3/07 |
Mathematical preliminary(1) |
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第4週 |
3/14 |
Mathematical preliminary(2) |
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第5週 |
3/21 |
Mathematical preliminary(3) |
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第6週 |
3/28 |
Indirect method(1) |
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第7週 |
4/04 |
Indirect method(2) |
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第8週 |
4/11 |
Indirect method(3) |
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第9週 |
4/18 |
Direct method(1) |
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第10週 |
4/25 |
Direct method(2) |
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第11週 |
5/02 |
Direct method(3) |
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第12週 |
5/09 |
Helmholtz equation(1) |
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第13週 |
5/16 |
Helmholtz equation(2) |
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第14週 |
5/23 |
Helmholtz equation(3) |
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第15週 |
5/30 |
Introduction to the hypersingular integral equation(1) |
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第16週 |
6/06 |
Introduction to the hypersingular integral equation(2) |
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第17週 |
6/13 |
Introduction to the hypersingular integral equation(3) |
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