1 On the nonuniqueness of BIEM/BEM using SVD J T Chen, Life-time Distinguished Prof. Taiwan Ocean University August 26 14:50 Room B August 24-29, Adelaide.

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1 On the nonuniqueness of BIEM/BEM using SVD J T Chen, Life-time Distinguished Prof. Taiwan Ocean University August 26 14:50 Room B August 24-29, Adelaide Adelaide Convention Center Australia (IUTAM2008.ppt) National Taiwan Ocean University MSVLAB ( 海大河工系 ) Department of Harbor and River Engineering Taiwan

2 Nonuniqueness problems in BIEM/BEM BIEM/BEM failure (mathematical degeneracy) Degenerate boundary Degenerate scale True and spurious eigensolution (interior prob.) Fictitious frequency (exterior acoustics) SVD structure for influence matrices in dual BEM Outline

3 SVD structure for influencematrices (U, T, L, M) Degenrate scale 1-D static rod EABE 2008 (degenerate scale) 2-D Laplace, Comp & Structure, 2003 (degenerate scale) Spurious eigenvalue (simply connected domain using real-part BEM) 1-D rod vibration EABE 2008 (real-part BEM) Accepted 2-D interior eigenvalue JCA 2006 (real-part BEM) Spurious eigenvalue (multiply connected domain using Complex-valued BEM) 2-D Helmholtz (eigen problems-spurious eigenvalues) annular and eccentric cases Proc. Royal Soc. Lon. Ser. 2001, D Helmholtz (eigen problems-spurious eigenvalues) concentric sphere Fictitious frequency 2-D Helmholtz (multi-cylinders) CMAME D Helmholtz (multi-spheres) 2-D Degenerate boundary

4 SVD structure for four influence matrices UT LM spurious mode, fictitious mode (mathematics) true mode, rigid body mode (physics) The same

5 SVD updating technique (Extracting true and spurious information) UT LM spurious mode, fictitious mode (mathematics) true mode, rigid body mode (physics) The same [ ] ()

6 Conclusions Review of nonuniqueness problems in BIEM/BEM SVD structures for the nonuniqueness are examined.