ECCENTRIC PROBLEM OF LAPLACE EQUATION VIA BEM AND BIEM

1 / 31

# ECCENTRIC PROBLEM OF LAPLACE EQUATION VIA BEM AND BIEM - PowerPoint PPT Presentation

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'ECCENTRIC PROBLEM OF LAPLACE EQUATION VIA BEM AND BIEM' - verlee

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

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

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 )

Introduction of BEPO2D problem

2. 程式流程示意圖：

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

F16.DAT

F77.DAT

F78.DAT

BEPO2D 程式

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

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

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)

(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

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:

3 1

8 -1

(2)輸入Neumann邊界條件(t)於f 02.dat, 格式如下:

1 0

2 0

4 0

5 0

6 0

7 0

Introduction of BEPO2D problem

(3)輸入邊界條件(t,u)於 f 03.dat,其格式如下:

0

0

0

0

0

0

1

-1

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

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

Introduction of BEPO2D problem

(5) 建立內點座標於 f 80.dat

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

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

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

u=x

u=y

u=0

u=0

Numerical examples 1

：node

NELM 80

NINTER 81

Exact sloution u=xy

Numerical examples 1

Exact sloution

NELM 20

NINTER 81

NELM 40

NINTER 81

NELM 80

NINTER 81

Numerical examples 2

u=1

R=2.5

r=1.0

NELM=21+21

NINTER=504

u=0

R

r

Exact solution

Numerical examples 2

Exact sloution

NELM=5+5

NINTER=504

NELM=21+21

NINTER=504

NELM=11+11

NINTER=504

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

Introduction of present method

The idea of the present formulation

collocation point

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

Numerical examples

u=1

R=2.5

r=1.0

NELM=42

NINTER=504

u=0

R

r

Exact solution

Numerical examples

Exact sloution

M=10

BIEM

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

Comparison of two method

Comparison of two method

Error %

Comparison of two method

number

number

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

The end