Using the method of fundamental solutions in conjunction with the degenerate kernel in cylindrical acoustic problems

References

• Atluri , S.N. and Zhu , T. 1998 . “A New Meshless Local Petrov‐Galerkin (MLPG) Approach in Computational Mechanics,” . Computational Mechanics , 22 : 117 – 127 .
   Web of Science ®Google Scholar
• Belystcho , T. , Lu , Y. and Gu , L. 1994 . “Element Free Galerkin Methods,” . International Journal for Numerical Methods in Engineering , 37 : 229 – 256 .
   Web of Science ®Google Scholar
• Burton , A.J. and Miller , G.F. “The Aplication of Integral Equation Methods to Numerical Solutions of Some Exterior Boundary Value Problems,” . Proceedings of the Royal Society London Ser A . Vol. 323 , pp. 201 – 210 .
   Google Scholar
• Chen , C.S. , Rashed , Y.F. and Golberg , M.A. 1998 . “A Mesh‐Free Method for Linear Diffusion Equations,” . Numerical Heat Transfer, Part B , 33 : 469 – 486 .
   Web of Science ®Google Scholar
• Chen , J.T. 1998 . “On Fictitious Frequencies Using Dual Series Representation,” . Mechanics Research Communications , 25 ( 5 ) : 529 – 534 .
   Web of Science ®Google Scholar
• Chen , J.T. , Chen , I.L. and Lee , Y.T. 2005 . “Eigensolutions of Multiply‐Connected Membranes Using Method of Fundamental Solution,” . Engineering Analysis with Boundary Elements , 29 : 166 – 174 .
   Web of Science ®Google Scholar
• Chen , J.T. , Chen , K. H. , Chen , I.L. and Liu , L.W. 2003 . “A New Concept of Modal Participation Factor for Numerical Instability in the Dual BEM for Exterior Acoustics,” . Mechanics Research Communications , 30 : 161 – 174 .
   Google Scholar
• Chen , J.T. and Kuo , S.R. 2000 . “On Fictitious Frequencies Using Circulants for Radiation Problems of a Cylinder,” . Mechanics Research Communications , 27 ( 3 ) : 49 – 58 .
   Google Scholar
• Chen , J.T. , Kuo , S.R. , Chen , K.H. and Cheng , Y.C. 2000 . Comments on Vibration Analysis of Arbitrary Shaped Membranes Using Nondimensional Dynamic Influence Function,” . Journal of Sound and Vibration , 235 ( 1 ) : 156 – 171 .
   Google Scholar
• Cisilino , A.P. and Sensale , B. 2002 . “Application of a Simulated Annealing Algorithm in the Optimal Placement of the Source Points in the Method of the Fundamental Solutions,” . Computational Mechanics , 28 : 129 – 136 .
   Web of Science ®Google Scholar
• Dokumaci , E. 1990 . “A Study of the Failure of Numerical Solutions in Boundary Element Analysis of Acoustic Radiation Problems,” . Journal of Sound and Vibration , 139 ( 1 ) : 83 – 97 .
   Web of Science ®Google Scholar
• Fairweather , G. and Karageorghis , A. 1998 . “The Method of Fundamental Solutions for Elliptic Boundary Value Problems,” . Advances in Computational Mathematics , 9 : 69 – 95 .
   Web of Science ®Google Scholar
• Fairweather , G. , Karageorghis , A. and Martin , P.A. 2003 . “The Method of Fundamental Solutions for Scattering and Radiation Problems,” . Engineering Analysis with Boundary Elements , 27 : 759 – 769 .
   Web of Science ®Google Scholar
• Gingold , R.A. and Maraghan , J.J. 1977 . “Smoothed Particle Hydrodynamics: Theory and Applications to Non‐Spherical Stars,” . Monthly Notices of the Royal Astronomical Society , 181 : 375 – 389 .
   Web of Science ®Google Scholar
• Golberg , M.A. , Chen , C.S. and Ganesh , M. 2000 . “Particular Solutions of 3D Helmholtz‐Type Equations Using Compactly Supported Radial Basis Functions,” . Engineering Analysis with Boundary Element , 24 : 539 – 547 .
   Google Scholar
• Harari , I. , Barbone , P.E. , Slavutin , M. and Shalom , R. 1998 . “Boundary Infinite Elements for the Helmholtz Equation in Exterior Domains,” . International Journal for Numerical Methods in Engineering , 41 : 1105 – 1131 .
   Web of Science ®Google Scholar
• Harari , I. , Barbone , P.E. and Montgomery , J.M. 1997 . “Finite Element Formulations for Exterior Problems: Application to Hybrid Methods, Non‐Reflecting Boundary Conditions, and Infinite Elements,” . International Journal for Numerical Methods in Engineering , 40 : 2791 – 2805 .
   Google Scholar
• Hwang , J.Y. and Chang , S.C. 1991 . “A Retracted Boundary Integral Equation for Exterior Acoustic Problem with Unique Solution for All Wave Numbers,” . Journal of the Acoustical Society of America , 90 : 1167 – 1180 .
   Google Scholar
• Kondapalli , P.S. , Shippy , D.J. and Fairweather , G. 1992 . “Analysis of Acoustic Scattering in Fluids and Solids by the Method of Fundamental Solutions,” . The Journal of Acoustical Society of America , 91 ( 4 ) : 1844 – 1854 .
   PubMedGoogle Scholar
• Kuo , S.R. , Chen , J.T. and Huang , C.X. 2000 . “Analytical Study and Numerical Experiments for True and Spurious Eigensolutions of a Circular Cavity Using the Real‐Part Dual BEM,” . International Journal for Numerical Methods in Engineering , 48 ( 9 ) : 1401 – 1422 .
   Google Scholar
• Lee , C.‐H. , Newman , J.N. and Zhu , X. 1996 . “An Extended Boundary Integral Equation Method for the Removal of Irregular Frequency Effects,” . International Journal for Numerical Methods in Fluids , 23 : 637 – 660 .
   Google Scholar
• Lee , C.‐H. and Sclavounos , P.D. 1989 . “Removing the Irregular Frequencies from Integral Equation in Wave‐Body Interactions,” . Journal of Fluid Mechanics , 207 : 393 – 418 .
   Google Scholar
• Liu , W.K. , Jun , S. and Zhang , Y.F. 1995 . “Reproducing Kernel Particle Methods,” . International Journal for Numerical Methods in Engineering , 20 : 1081 – 1106 .
   Web of Science ®Google Scholar
• Malenica , S. and Chen , X.B. 1998 . “On the Irregular Frequencies Appearing in Wave Diffraction‐Radiation Solutions,” . International Journal of Offshore and Polar Engineering , 8 ( 2 ) : 110 – 114 .
   Google Scholar
• Mukherjee , Y.X. and Mukherjee , S. 1997 . “The Boundary Node Method for Potential Problems,” . International Journal for Numerical Methods in Engineering , 40 : 797 – 815 .
   Web of Science ®Google Scholar
• Ohmatsu , S. 1983 . “ A New Simple Method to Eliminate the Irregular Frequencies in the Theory of Water Wave Radiation Problems,” . Papers of Ship Research Institute , 70
   Google Scholar
• Poullikkas , A. , Karageorghis , A. and Georgiou , G. 2002 . “The Method of Fundamental Solutions for Three‐Dimensional Elastostatics Problems,” . Computers and Structures , 80 : 365 – 370 .
   Google Scholar
• Ramachandran , P.A. 2002 . “Method of Fundamental Solutions: Singular Value Decomposition Analysis,” . Communications in Numerical Methods in Engineering , 18 : 789 – 801 .
   Web of Science ®Google Scholar
• Sladek , V. , Sladek , J. , Atluri , S.N. and Van Keer , R. 2000 . “Numerical Integration of Singularities in Meshless Implementation of Local Boundary Integral Equations,” . Computational Mechanics , 25 : 394 – 403 .
   Google Scholar
• Ursell , F. 1981 . “Irregular Frequencies and the Motions of the Floating Bodies,” . Journal of Fluid Mechanics , 143 : 143 – 156 .
   Google Scholar
• Zhang , X. , Song , K.Z. , Lu , M.W. and Liu , X. 2000 . “Meshless Methods Based on Collocation with Radial Basis Functions,” . Computational Mechanics , 26 : 333 – 343 .
   Web of Science ®Google Scholar