[1] JAWSON M A, SYMM G T. Integral equation methods in potential theory-I, Ⅱ[C]//Proceedings of the Royal Society A Mathematical Physical & Engineering Sciences, 1963, 275A:23-46. [2] CHEN L H, SCHWEIKERT D G. Sound radiation from an arbitrary body[J]. Journal of the Acoustical Society of America, 1963, 35(10):1626-1632. [3] CHERTOCK G. Sound radiation from vibrating surfaces[J]. Journal of the Acoustical Society of America, 1963, 35(5):1305-1313. [4] SCHENCK H A. Improved integral formulation for the acoustic radiation problem[J]. Journal of the Acoustical Society of America, 1968, 44(1):41-58. [5] KLEINMAN R E, ROACH G F. Boundary integral equation for the three-dimensional Helmholtz equation[J]. Siam Review, 1974, 16(2):214-236. [6] BURTON A J, MILLER G F. The application of integral equation methods to numerical solution of some exterior boundary value problem[J]. Proceedings of the Royal Society of London, 1971, 323(1553):201-210. [7] CHIEN C C, RAJIYAH H, ATLURI S N. An effective method for solving the strongly singular integral equations in 3D acoustics[J]. Journal of the Acoustical Society of America, 1990, 88(2):918-937. [8] LIU Y J, RUDOLPHI T J. Some identities for fundamental solutions and their applications to non-singular boundary element formulations[J]. Engineering Analysis with Boundary Elements, 1991, 8(6):301-311. [9] LIU Y J, RIZZO F J. A weakly-singular form of the hypersingular boundary integral equation applied the 3D acoustic wave problem[J]. Computer Methods in Applied Mechanics & Engineering, 1992, 96:271-287. [10] LIU Y J, CHEN S H. A new form of the hyper-singular boundary integral equation for 3D acoustics and its implementation with C0 boundary element[J]. Computer Methods in Applied Mechanics & Engineering, 1999, 173:375-386. [11] RUDOLPHI T J. The use of simple solutions in the regularization of hypersingular boundary integral equations[J]. Mathematical & Computer Modelling An International Journal, 1991, 15(3-5):269-278. [12] GUIGGIANI M. Formulation and numerical treatment of boundary integral equations with hypersingular kernels[M]//Sladek V, Sladek J, Eds. Singular Integrals in Boundary Element Methods, Computational Mechanics Publications, Southampton, 1998:85-124. [13] HWANG W S. Hypersingular boundary integral equations for exterior acoustic problems[J]. Journal of the Acoustical Society of America, 1997, 101(6):3336-3342. [14] CHEN L L, ZHENG C J, CHEN H B. A wideband FMBEM for 2D acoustic design sensitivity analysis based on direct differentiation method[J]. Computational Mechanics, 2013, 52(3):631-648. [15] MATSUMOTO T, ZHENG C J, HARADA S, TAKAHASHI T. Explicit evaluation of hypersingular boundary integral equation for 3-D Helmholtz equation discretized with constant triangular element[J]. Journal of Computational Science & Technology, 2010, 4(3):194-206. [16] LIU Y J, RUDOLPHI T J. New identities for fundamental solutions and their applications to non-singular boundary element formulations[J]. Computational Mechanics, 1999, 24(4):286-292. [17] MEYER W L, BELL W A, STALLYBRASS M P, et al. Prediction of the sound field radiated from axisymmetric surfaces[J]. Journal of the Acoustical Society of America, 1979, 65(3):631-638. [18] LI S, HUANG Q. An improved form of the hypersingular boundary integral equation for exterior acoustic problems[J]. Engineering Analysis with Boundary Elements, 2010, 34(3):189-195. [19] LEE C H, SCLAVOUNOS P D. Removing the irregular frequencies from integral equations in wave-body interactions[J]. Journal of Fluid Mechanics, 1989, 207:393-418. [20] LIU Y J. Fast multipole boundary element method:Theory and applications in engineering[M]. Cambrige:Cambrige University Press, 2009. [21] ABRAMOWITZ M, STEGUN I A. Handbook of mathematical functions[M]. National Bureau of Standards, Washington DC, 1964. [22] MEYER W L, BELL W A, ZINN B T, et al. Boundary integral solutions of three-dimensional acoustic radiation problems[J]. Journal of Sound & Vibration, 1978, 59(2):245-262. [23] 王竹溪,郭敦仁.特殊函数概论[M].北京:北京大学出版社,2001. [24] CHEN J T, CHEN K H. Applications of the dual integral formulation in conjunction with fast multipole method in large-scale problems for 2D exterior acoustics[J]. Engineering Analysis with Boundary Elements, 2004, 28(6):685-709. [25] YOSHIDA K. Applications of fast multipole method to boundary integral equation method[D]. Ph D Dissertation, Department of Global Environment Engineering, Kyoto University, 2001. [26] BEBENDORF M. Approximation of boundary element matrices[J]. Numerische Mathematik, 2000, 86(4):565-589. |