1. SVD application in non-uniqueness problem of BEM/BIEM Reporter : Kao S. K. Advisor : Chen J. T. Date: 2009/03/17 National Taiwan Ocean University MSVLAB Department of Harbor and River Engineering

2. M M S S V V MSVLAB, HRE, NTOU 2 Outline Eigenproblem for concentric sphere Eigenproblem for eccentric sphere Linton and Evans’ method Conclusions

3. M M S S V V MSVLAB, HRE, NTOU 3 Outline Eigenproblem for concentric sphere Eigenproblem for eccentric sphere Linton and Evans’ method Conclusions

4. M M S S V V MSVLAB, HRE, NTOU 4 Concentric sphere

5. M M S S V V MSVLAB, HRE, NTOU 5 Null-field Integral equation - UT

6. M M S S V V MSVLAB, HRE, NTOU 6 Dirichlet B.C. (fixed-fixed)-True U L SVD updating terms

7. M M S S V V MSVLAB, HRE, NTOU 7 Hypersingular formulation-Spurious SVD updating document L M

8. M M S S V V MSVLAB, HRE, NTOU 8 Outline Eigenproblem for concentric sphere Eigenproblem for eccentric sphere Linton and Evans’ method Conclusions

9. M M S S V V MSVLAB, HRE, NTOU 9 Eccentric sphere

10. M M S S V V MSVLAB, HRE, NTOU 10 Singular formulation-Spurious Concentric sphereeccentric sphere

11. M M S S V V MSVLAB, HRE, NTOU 11 Hypersingular formulation-Spurious eccentric sphere concentric sphere

12. M M S S V V MSVLAB, HRE, NTOU 12 Outline Eigenproblem for concentric sphere Eigenproblem for eccentric sphere Linton and Evans’ method Conclusions

13. M M S S V V MSVLAB, HRE, NTOU 13 Linton and Evans ’ method (Multi-pole method) Interior problemExterior problem radiation scattering concentric sphere eccentric sphere

14. M M S S V V MSVLAB, HRE, NTOU 14 Comparison between the present method and LE method [] MethodPresent method Linton and Evans ’ method CoordinateAdaptive observer systemMulti-pole Formulation

15. M M S S V V MSVLAB, HRE, NTOU 15 Problem statement

16. M M S S V V MSVLAB, HRE, NTOU 16

17. M M S S V V MSVLAB, HRE, NTOU 17 The end Thanks for your kind attention. Welcome to visit the web site of MSVLAB: http://ind.ntou.edu.tw/~msvlab