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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. 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

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  1. 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

  2. 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

  3. 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

  4. 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

  5. Introduction of BEPO2D problem 2. 程式流程示意圖： 否 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

  6. 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

  7. 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

  8. (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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

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

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

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

  27. Comparison of two method Error % 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  28. 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

  29. 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

  30. 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

  31. 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

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