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Report: C.E. Lin Number: M98520025 Adviser: J.T. Chen Date: Jan.07.2010

DUAL BOUNDARY INTEGRAL EQUATIONS FOR HELMHOLTZ EQUATION AT A CORNER USING CONTOUR APPROACH AROUND SINGULARITY. Report: C.E. Lin Number: M98520025 Adviser: J.T. Chen Date: Jan.07.2010. NTOU HRE. Outlines. NTOU HRE. Dual Integral formulation of BEM for Helmholtz equation with a corner

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Report: C.E. Lin Number: M98520025 Adviser: J.T. Chen Date: Jan.07.2010

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  1. DUAL BOUNDARY INTEGRAL EQUATIONS FOR HELMHOLTZ EQUATION AT A CORNER USING CONTOUR APPROACH AROUND SINGULARITY Report: C.E. Lin Number: M98520025 Adviser: J.T. Chen Date: Jan.07.2010 NTOU HRE

  2. Outlines NTOU HRE • Dual Integral formulation of BEM for Helmholtz equation with a corner • Discussions on the Laplace and He-lmholtz equations at a corner • Conclusions

  3. Dual Integral formulation of BEM for Helmholtz equation with a corner NTOU HRE

  4. NTOU HRE

  5. Single layer potential: Double layer potential: Normal derivative of single layer potential: Normal derivative of double layer potential: Tangent derivative of single layer potential: Tangent derivative of double layer potential:

  6. NTOU HRE

  7. Discussions on the Laplace and Helmholtz equations at a corner ⋯Wave equation ⋯Helmholtz equation “k” is very small and can be negligible ⋯ Laplace equation NTOU HRE

  8. Conclusions NTOU HRE The free terms of the six kernel functions in the dual integral equation for the Helmholtz equation at a corner have been examined It is discovered that employing the contour appr-oach the jump term comes half and half from the free terms in the L and M kernel integrations, re-spectively, which differs from the limiting process from an interior point to a boundary point where the jump term is descended from the L kernel only.

  9. NTOU HRE • Laplace equation is a special case of the Helmholtz equation when the value of w-ave number approaches zero.

  10. NTOU HRE THANKS FOR YOUR KIND OF ATTENTION

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