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Degenerate kernel for ellipse

Degenerate kernel for ellipse. Reporter: Sheng-Kai Gau (B92520121) Advisor: Jeng-Tzong Chen Date: 2007/01/18 Place: HR2 307. Outline. Motivation Degenerate kernel for ellipse ◎ Conformal mapping technique ◎ Some properties of ellipse ◎ Derivation of degenerate kernel

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Degenerate kernel for ellipse

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  1. Degenerate kernel for ellipse Reporter: Sheng-Kai Gau (B92520121) Advisor: Jeng-Tzong Chen Date: 2007/01/18 Place: HR2 307

  2. Outline • Motivation • Degenerate kernel for ellipse ◎Conformal mapping technique ◎Some properties of ellipse ◎ Derivation of degenerate kernel ◎Convergence of degenerate kernel • A numerical example • Conclusions • Further studies

  3. Outline • Motivation • Degenerate kernel for ellipse ◎Conformal mapping technique ◎Some properties of ellipse ◎ Derivation of degenerate kernel ◎Convergence of degenerate kernel • A numerical example • Conclusions • Further studies

  4. Motivation In the course, the discussion of the degenerate kernel for ellipse excited my interest.

  5. Outline • Motivation • Degenerate kernel for ellipse ◎Conformal mapping technique ◎Some properties of ellipse ◎ Derivation of degenerate kernel ◎Convergence of degenerate kernel • A numerical example • Conclusions • Further studies

  6. Conformal mapping technique z plane w plane

  7. Some properties of ellipse When R>1 z plane w plane

  8. Some properties of ellipse When R<1 z plane w plane

  9. Some properties of ellipse

  10. Derivation of degenerate kernel

  11. Derivation of degenerate kernel

  12. Outline • Motivation • Degenerate kernel for ellipse ◎Conformal mapping technique ◎Some properties of ellipse ◎ Derivation of degenerate kernel ◎Convergence of degenerate kernel • A numerical example • Conclusions • Further studies

  13. w plane z plane Numerical examples

  14. Numerical examples

  15. Numerical examples w plane z plane

  16. Numerical examples

  17. The end Thanks for your kind attention. Your comments will be highly appreciated. Welcome to visit the web site of MSVLAB: http://ind.ntou.edu.tw/~msvlab

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