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ECCENTRIC PROBLEM OF LAPLACE EQUATION VIA BEM AND BIEM. FINAL REPORT OF BOUNDARY ELEMENT METHOD Z. H. Kao 1, 24, 2005. Outlines. Introduction of BEPO2D problem Numerical examples Introduction of present method Numerical examples Comparison of two method Conclusions. Outlines.

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eccentric problem of laplace equation via bem and biem

ECCENTRIC PROBLEM OF LAPLACE EQUATION VIA BEM AND BIEM

FINAL REPORT OF BOUNDARY ELEMENT METHOD

Z. H. Kao

1, 24, 2005

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

outlines
Outlines
  • Introduction of BEPO2D problem
  • Numerical examples
  • Introduction of present method
  • Numerical examples
  • Comparison of two method
  • Conclusions

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

outlines1
Outlines
  • Introduction of BEPO2D problem
  • Numerical examples
  • Introduction of present method
  • Numerical examples
  • Comparison of two method
  • Conclusions

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

introduction of bepo2d problem
Introduction of BEPO2D problem

BEPO2D 程式使用說明

1. 適用範圍 :

Laplace場 ( 含退化邊界問題 )

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

introduction of bepo2d problem1
Introduction of BEPO2D problem

2. 程式流程示意圖:

經核函數影響係數

矩陣求未知邊界量

結 束

輸入與讀取

背景資料的

開 始

求內點否?

經積分方程

反求內點值

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

introduction of bepo2d problem2
Introduction of BEPO2D problem

3.輸入輸出介紹:

NELM

NINTER

NU

NT

NELM,NNODE

F01.DAT

F02.DAT

F03.DAT

F15.DAT

F80.DAT

輸入

F16.DAT

F77.DAT

F78.DAT

輸出

BEPO2D 程式

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

introduction of bepo2d problem3
Introduction of BEPO2D problem

NELM ---元素數目

NINTER ---內點數

NU ---已知 u 邊界條件數目

NT ---已知 t 邊界條件數目

NELM,NNODE ---元素數目,結點數目

程式執行時自動要求輸入

F01.DAT ---已知 u 邊界條件

F02.DAT ---已知 t 邊界條件

F03.DAT ---先 t 後u 排成一行

F15.DAT ---結點座標與元素編號

F80.DAT ---內點的編號與座標

程式所要讀取對問題之背景資料

須於程式執行前事先KEY-IN好

F16.DAT ---邊界物理量 u , t 值

F77.DAT ---域內物理量 u 值

F78.DAT ---域內物理量t 值(以 表示)

程式輸出的結果

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

introduction of bepo2d problem4

(1,0.5)

(-1,0.5)

4

7

6

5

8

3

1

2

(-1,-0.5)

(1,-0.5)

Introduction of BEPO2D problem

4. 輸入實例介紹:

5

4

7

6

3

1

2

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

introduction of bepo2d problem5
Introduction of BEPO2D problem

5.使用步驟:

(1)輸入Dirichlet邊界條件(u)於 f 01.dat,其格式如下:

元素編號已知邊界 u 值

3 1

8 -1

(2)輸入Neumann邊界條件(t)於f 02.dat, 格式如下:

元素編號已知邊界 t 值

1 0

2 0

4 0

5 0

6 0

7 0

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

introduction of bepo2d problem6
Introduction of BEPO2D problem

(3)輸入邊界條件(t,u)於 f 03.dat,其格式如下:

已知邊界條件(先 t 後 u 排成一行)

0

0

0

0

0

0

1

-1

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

introduction of bepo2d problem7
Introduction of BEPO2D problem

(4)建立節點坐標與元素編號於 f 15.dat,格式如下:

-1

15

1 0 0 11 -.10000D+01 -0.50000D+00 0.00000E+00

2 0 0 11 0.00000D+00 -0.50000D+00 0.00000E+00

3 0 0 11 1.00000D+00 -0.50000D+00 0.00000E+00

4 0 0 11 1.00000D+00 0.50000D+00 0.00000E+00

5 0 0 11 0.00000D+00 0.50000D+00 0.00000E+00

6 0 0 11 0.00000D+00 0.00000D+00 0.00000E+00

7 0 0 11 -.10000D+01 0.50000D+00 0.00000E+00

-1

節點編號 x y z

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

introduction of bepo2d problem8
Introduction of BEPO2D problem

-1

71

1 1 21 1 1 7 2

1 2

2 1 21 1 1 7 2

2 3

3 1 21 1 1 7 2

3 4

4 1 21 1 1 7 2

4 5

5 1 21 1 1 7 2

5 6

6 1 21 1 1 7 2

6 5

7 1 21 1 1 7 2

6 7

8 1 21 1 1 7 2

7 1

-1

元素編號

節點連結

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

introduction of bepo2d problem9
Introduction of BEPO2D problem

(5) 建立內點座標於 f 80.dat

內點編號 x y z

111 0 0 11 0.02000E+00 .02000E+00 .00000E+00

112 0 0 11 0.02000E+00 .04000E+00 .00000E+00

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

outlines2
Outlines
  • Introduction of BEPO2D problem
  • Numerical examples
  • Introduction of present method
  • Numerical examples
  • Comparison of two method
  • Conclusions

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

numerical examples 1

u=x

u=y

u=0

u=0

Numerical examples 1

:node

NELM 80

NINTER 81

Exact sloution u=xy

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

numerical examples 11
Numerical examples 1

Exact sloution

NELM 20

NINTER 81

NELM 40

NINTER 81

NELM 80

NINTER 81

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

numerical examples 2
Numerical examples 2

u=1

R=2.5

r=1.0

NELM=21+21

NINTER=504

u=0

R

r

Exact solution

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

numerical examples 21
Numerical examples 2

Exact sloution

NELM=5+5

NINTER=504

NELM=21+21

NINTER=504

NELM=11+11

NINTER=504

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

outlines3
Outlines
  • Introduction of BEPO2D problem
  • Numerical examples
  • Introduction of present method
  • Numerical examples
  • Comparison of two method
  • Conclusions

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

introduction of present method
Introduction of present method

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

the idea of the present formulation
The idea of the present formulation

collocation point

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

outlines4
Outlines
  • Introduction of BEPO2D problem
  • Numerical examples
  • Introduction of present method
  • Numerical examples
  • Comparison of two method
  • Conclusions

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

numerical examples
Numerical examples

u=1

R=2.5

r=1.0

NELM=42

NINTER=504

u=0

R

r

Exact solution

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

numerical examples1
Numerical examples

Exact sloution

M=10

BIEM

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

outlines5
Outlines
  • Introduction of BEPO2D problem
  • Numerical examples
  • Introduction of present method
  • Numerical examples
  • Comparison of two method
  • Conclusions

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

comparison of two method
Comparison of two method

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

comparison of two method1
Comparison of two method

Error %

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

comparison of two method2
Comparison of two method

number

number

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

outlines6
Outlines
  • Introduction of BEPO2D problem
  • Numerical examples
  • Introduction of present method
  • Numerical examples
  • Comparison of two method
  • Conclusions

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

conclusions
Conclusions
  • Cause comparison of two method we know, the present method can be achieve need so fast.
  • BEM an error precise of a superior grade in boundary and boundary to approach.

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

the end
The end

Thanks for your attentions.

Your comment is much appreciated.

You can get more information on our website.

http://msvlab.hre.ntou.edu.tw

海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw