Water wave problems using null-field boundary integral equations: ill-posedness and remedies

References

• Schenck , HA . 1968 . Improved integral formulation for acoustic radiation problem . J. Acoust. Soc. Am. , 44 : 41 – 58 .
   Web of Science ®Google Scholar
• Burton , AJ and Miller , GF . 1971 . The application of integral equation methods to numerical solution of some exterior boundary value problems . Proc. R. Soc. London, Ser. A , 323 : 201 – 210 .
   Web of Science ®Google Scholar
• Chen , JT . 1998 . On fictitious frequencies using dual series representation . Mech. Res. Commun. , 25 ( 5 ) : 529 – 534 .
   Web of Science ®Google Scholar
• Chen , JT and Kuo , SR . 2000 . On fictitious frequencies using circulants for radiation problems of a cylinder . Mech. Res. Commun. , 27 ( 1 ) : 49 – 58 .
   Web of Science ®Google Scholar
• Chen , JT , Chen , CT , Chen , HK and Chen , IL . 2000 . On fictitious frequencies using dual BEM for non-uniform radiation problems of a cylinder . Mech. Res. Commun. , 27 ( 6 ) : 685 – 690 .
   Web of Science ®Google Scholar
• Chen , JT , Hong , H-K and Yeh , CS . 1995 . Modal reaction method for modal participation factors in support motion problems . Commun. Numer. Methods Eng. , 9 : 479 – 490 .
   Web of Science ®Google Scholar
• Chen , JT , Hong , H-K , Yeh , CS and Chyuan , SW . 1996 . Integral representations and regularizations for a divergent series solution of a beam subjected to support motions . Earthquake Eng. Struct. Dyn. , 25 : 909 – 925 .
   Web of Science ®Google Scholar
• Chen , JT , Chyuan , SW , You , DW and Wong , FC . 1997 . Normalized quasi-static mass – A new definition for multi-support motion problems . Finite Elem. Anal. Des. , 26 : 129 – 142 .
   Web of Science ®Google Scholar
• Chen , JT , Chen , KH , Chen , IL and Liu , LW . 2003 . A new concept of modal participation factor for numerical instability in the dual BEM for exterior acoustics . Mech. Res. Commun. , 26 ( 2 ) : 161 – 174 .
   Web of Science ®Google Scholar
• Dokumaci , E . 1990 . A study of the failure of numerical solutions in boundary element analysis of acoustic radiation problems . J. Sound Vib. , 139 ( 1 ) : 83 – 97 .
   Web of Science ®Google Scholar
• Juhl , P . 1994 . A numerical study of the coefficient matrix of the boundary element method near characteristic frequencies . J. Sound Vib. , 175 ( 1 ) : 39 – 50 .
   Web of Science ®Google Scholar
• Chien , CC , Rajiyah , H and Atluri , SN . 1990 . An effective method for solving the hypersingular integral equations in 3-D acoustics . J. Acoust. Soc. Am. , 88 ( 2 ) : 918 – 937 .
   Web of Science ®Google Scholar
• Cunefare , KA , Koopmann , G and Brod , K . 1989 . A boundary element method for acoustic radiation valid for all wavenumbers . J. Acoust. Soc. Am. , 85 ( 1 ) : 39 – 48 .
   Web of Science ®Google Scholar
• Chandrasekhar , B and Rao , SM . 2004 . Elimination of internal resonance problem associated with acoustic scattering by three-dimensional rigid body . J. Acoust. Soc. Am. , 115 ( 6 ) : 2731 – 2737 .
   Web of Science ®Google Scholar
• Yang , SA . 2002 . A boundary integral equation method using auxiliary interior surface approach for acoustic radiation and scattering in two dimensions . J. Acoust. Soc. Am. , 112 ( 4 ) : 1307 – 1317 .
   Web of Science ®Google Scholar
• Chen , JT , Lee , YT and Lin , YJ . 2009 . Interaction of water waves with arbitrary vertical cylinders using null-field integral equations . Appl. Ocean Res. , 31 : 101 – 110 .
   Web of Science ®Google Scholar
• Chen , JT , Lee , JW and Leu , SY . 2011 . Analytical investigation for spurious eigensolutions of multiply-connected membranes containing elliptical boundaries using the dual BIEM . Int. J. Solids Struct. , 48 : 729 – 744 .
   Web of Science ®Google Scholar
• Chatjigeorgiou , IK and Mavrakos , SA . 2010 . An analytical approach for the solution of the hydrodynamic diffraction by arrays of elliptical cylinders . Appl. Ocean Res. , 32 ( 2 ) : 242 – 251 .
   Web of Science ®Google Scholar
• Linton , CM and Evans , DV . 1990 . The interaction of waves with arrays of vertical circular cylinders . J. Fluid Mech. , 215 : 549 – 569 .
   Web of Science ®Google Scholar
• B.H. Spring and P.L. Monkmeyer, Interaction of Plane Waves with Vertical Cylinders, Proceedings of the 14th Coastal Engineering Conference Vol. III, pp. 1828–1845, Copenhagen, Denmark, 1974
   Google Scholar
• Twersky , V . 1952 . Multiple scattering of radiation by an arbitrary configuration of parallel cylinders . J. Acoust. Soc. Am. , 24 ( 1 ) : 42 – 46 .
   Web of Science ®Google Scholar
• Chen , JT , Chen , IL and Chen , KH . 2006 . Treatment of rank deficiency in acoustics using SVD . J. Comput. Acoust. , 14 ( 2 ) : 157 – 183 .
   Web of Science ®Google Scholar
• Chen , IL , Chen , JT and Liang , MT . 2001 . Analytical study and numerical experiments for radiation and scattering problems using the CHIEF method . J. Sound Vib. , 248 ( 5 ) : 809 – 828 .
   Web of Science ®Google Scholar
• Chen , JT , Lin , SR and Tsai , JJ . 2009 . Fictitious frequency revisited . Eng. Anal. Bound. Elem. , 33 : 1289 – 1301 .
   Web of Science ®Google Scholar
• Schenck , HA . 1986 . Helmholtz integral formulation of the sonar equations . J. Acoust. Soc. Am. , 79 ( 5 ) : 1423 – 1433 .
   Web of Science ®Google Scholar
• Dokumaci , E and Sarigul , AS . 1995 . Analysis of the near field acoustic radiation characteristics of two radially vibrating spheres by the Helmholtz integral equation formulation and a critical study of the efficacy of the “CHIEF” over determination method in two-body problems . J. Sound Vib. , 187 ( 5 ) : 781 – 798 .
   Web of Science ®Google Scholar
• Morse , P and Feshbach , H . 1953 . Method of Theoretical Physics , New York : McGraw-Hill .
   Google Scholar
• Abramowitz , M and Stegun , IA . 1965 . Handbook of mathematical functions with formulas, graphs and mathematical tables , New York : Dover .
   Google Scholar
• Chen , JT , Kao , SK , Lee , WM and Lee , YT . 2009 . Eigenproblems of a multiply-connected domain with circular boundaries using the multipole Trefftz method . Eng. Anal. Bound. Elem. , 34 : 463 – 470 .
   Web of Science ®Google Scholar
• Lee , WM and Chen , JT . 2009 . Free vibration analysis of a circular plate with multiple circular holes by using multipole Trefftz method . CMES, , 50 ( 2 ) : 141 – 159 .
   Web of Science ®Google Scholar
• Lee , WM and Chen , JT . 2009 . Scattering of flexural wave in thin plate with multiple circular holes by using the multiple Trefttz method . Int. J. Solids Struct. , 47 : 1118 – 1129 .
   Web of Science ®Google Scholar