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  • Cited by 168
Publisher:
Cambridge University Press
Online publication date:
January 2010
Print publication year:
2009
Online ISBN:
9780511605345

Book description

The fast multipole method is one of the most important algorithms in computing developed in the 20th century. Along with the fast multipole method, the boundary element method (BEM) has also emerged as a powerful method for modeling large-scale problems. BEM models with millions of unknowns on the boundary can now be solved on desktop computers using the fast multipole BEM. This is the first book on the fast multipole BEM, which brings together the classical theories in BEM formulations and the recent development of the fast multipole method. Two- and three-dimensional potential, elastostatic, Stokes flow, and acoustic wave problems are covered, supplemented with exercise problems and computer source codes. Applications in modeling nanocomposite materials, bio-materials, fuel cells, acoustic waves, and image-based simulations are demonstrated to show the potential of the fast multipole BEM. Enables students, researchers, and engineers to learn the BEM and fast multipole method from a single source.

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Contents

References
Jaswon, M. A., “Integral equation methods in potential theory. I,” Proc. R. Soc. London A 275, 23–32 (1963).
Symm, G. T., “Integral equation methods in potential theory. II,” Proc. R. Soc. London A 275, 33–46 (1963).
Jaswon, M. A. and Ponter, A. R., “An integral equation solution of the torsion problem,” Proc. R. Soc. London A 273, 237–246 (1963).
Rizzo, F. J., “An integral equation approach to boundary value problems of classical elastostatics,” Q. Appl. Math. 25, 83–95 (1967).
Rizzo, F. J. and Shippy, D. J., “A formulation and solution procedure for the general non-homogeneous elastic inclusion problem,” Int. J. Solids Structures 4, 1161–1179 (1968).
Cruse, T. A. and Rizzo, F. J., “A direct formulation and numerical solution of the general transient elastodynamic problem – I,” J. Math. Anal. Appl. 22, 244–259 (1968).
Cruse, T. A., “A direct formulation and numerical solution of the general transient elastodynamic problem – II,” J. Math. Anal. Appl. 22, 341–355 (1968).
Cruse, T. A., “Numerical solutions in three dimensional elastostatics,” Int. J. Solids Structures 5, 1259–1274 (1969).
Rizzo, F. J. and Shippy, D. J., “A method for stress determination in plane anisotropic elastic bodies,” J. Composite Mater. 4, 36–61 (1970).
Rizzo, F. J. and Shippy, D. J., “A method of solution for certain problems of transient heat conduction,” AIAA J. 8, 2004–2009 (1970).
Rizzo, F. J. and Shippy, D. J., “An application of the correspondence principle of linear viscoelasticity theory,” SIAM J. Appl. Math. 21, 321–330 (1971).
Cruse, T. A. and Buren, W. V., “Three-dimensional elastic stress analysis of a fracture specimen with an edge crack,” Int. J. Fracture Mech. 7, 1–16 (1971).
Cruse, T. A. and Swedlow, J. L., “Formulation of boundary integral equations for three-dimensional elasto-plastic flow,” Int. J. Solids Structures 7, 1673–1683 (1971).
Cruse, T. A., “Application of the boundary-integral equation method to three-dimensional stress analysis,” Computers Structures 3, 509–527 (1973).
Cruse, T. A., “An improved boundary-integral equation method for three-dimensional elastic stress analysis,” Computers Structures 4, 741–754 (1974).
Cruse, T. A. and Rizzo, F. J., eds., Boundary-Integral Equation Method: Computational Applications in Applied Mechanics (AMD-ASME, New York 1975), Vol. 11.
Lachat, J. C. and Watson, J. O., “Effective numerical treatment of boundary integral equations: A formulation for three-dimensional elastostatics,” Int. J. Numer. Methods Eng. 10, 991–1005 (1976).
Rizzo, F. J. and Shippy, D. J., “An advanced boundary integral equation method for three-dimensional thermoelasticity,” Int. J. Numer. Methods Eng. 11, 1753–1768 (1977).
Stippes, M. and Rizzo, F. J., “A note on the body force integral of classical elastostatics,” Z. Angew. Math. Phys. 28, 339–341 (1977).
Wilson, R. B. and Cruse, T. A., “Efficient implementation of anisotropic three-dimensional boundary-integral equation stress analysis,” Int. J. Numer. Methods Eng. 12, 1383–1397 (1978).
Banerjee, P. K. and Butterfield, R., “Boundary element methods in geomechanics,” in Gudehus, G., ed., Finite Elements in Geomechanics (Wiley, London, 1976), Chap. 16, pp. 529–570.
Banerjee, P. K. et al., eds., Developments in Boundary Element Methods (Elsevier Applied Science, London, 1979–1991), Vols. I–VII.
Brebbia, C. A., The Boundary Element Method for Engineers (Pentech Press, London, 1978).
Banerjee, P. K., The Boundary Element Methods in Engineering, 2nd ed. (McGraw-Hill, New York, 1994).
Mukherjee, S., Boundary Element Methods in Creep and Fracture (Applied Science Publishers, New York, 1982).
Cruse, T. A., Boundary Element Analysis in Computational Fracture Mechanics (Kluwer Academic, Dordrecht, The Netherlands, 1988).
Brebbia, C. A. and Dominguez, J., Boundary Elements – An Introductory Course (McGraw-Hill, New York, 1989).
Kane, J. H., Boundary Element Analysis in Engineering Continuum Mechanics (Prentice-Hall, EnglewoodCliffs, NJ, 1994).
Bonnet, M., Boundary Integral Equation Methods for Solids and Fluids (Wiley, Chichester, UK, 1995).
Wrobel, L. C., The Boundary Element Method – Vol. 1, Applications in Thermo-Fluids and Acoustics (Wiley, Chichester, UK, 2002).
Aliabadi, M. H., The Boundary Element Method – Vol. 2, Applications in Solids and Structures (Wiley, Chichester, UK, 2002).
Mukherjee, S. and Mukherjee, Y. X., Boundary Methods: Elements, Contours, and Nodes (CRC, Boca Raton, FL, 2005).
Rokhlin, V., “Rapid solution of integral equations of classical potential theory,” J. Comput. Phys. 60, 187–207 (1985).
Greengard, L. F. and Rokhlin, V., “A fast algorithm for particle simulations,” J. Comput. Phys. 73, 325–348 (1987).
Greengard, L. F., The Rapid Evaluation of Potential Fields in Particle Systems (MIT Press, Cambridge, MA, 1988).
Peirce, A. P. and Napier, J. A. L., “A spectral multipole method for efficient solution of large-scale boundary element models in elastostatics,” Int. J. Numer. Methods Eng. 38, 4009–4034 (1995).
Gomez, J. E. and Power, H., “A multipole direct and indirect BEM for 2D cavity flow at low Reynolds number,” Eng. Anal. Boundary Elements 19, 17–31 (1997).
Fu, Y., Klimkowski, K. J., Rodin, G. J., Berger, E., Browne, J. C., Singer, J. K., Geijn, R. A. V. D., and Vemaganti, K. S., “A fast solution method for three-dimensional many-particle problems of linear elasticity,” Int. J. Numer. Methods Eng. 42, 1215–1229 (1998).
, N. Nishimura, Yoshida, K., and Kobayashi, S., “A fast multipole boundary integral equation method for crack problems in 3D,” Eng. Anal. Boundary Elements 23, 97–105 (1999).
Mammoli, A. A. and Ingber, M. S., “Stokes flow around cylinders in a bounded two-dimensional domain using multipole-accelerated boundary element methods,” Int. J. Numer. Methods Eng. 44, 897–917 (1999).
Nishimura, N., “Fast multipole accelerated boundary integral equation methods,” Appl. Mech. Rev. 55, 299–324 (2002).
Zemanian, A. H., Distribution Theory and Transform Analysis – An Introduction to Generalized Functions, with Applications (Dover, New York, 1987).
Fung, Y. C., A First Course in Continuum Mechanics, 3rd ed. (Prentice-Hall, Englewood Cliffs, NJ, 1994).
Hadamard, J., Lectures on Cauchy's Problem in Linear Partial Differential Equations (Yale University Press, New Haven, CT, 1923).
Martin, P. A. and Rizzo, F. J., “Hypersingular integrals: How smooth must the density be?Int. J. Numer. Methods Eng. 39, 687–704 (1996).
Liu, Y. J. and Rudolphi, T. J., “Some identities for fundamental solutions and their applications to weakly-singular boundary element formulations,” Eng. Anal. Boundary Elements 8, 301–311 (1991).
Liu, Y. J. and Rudolphi, T. J., “New identities for fundamental solutions and their applications to non-singular boundary element formulations,” Comput. Mech. 24, 286–292 (1999).
Liu, Y. J., “On the simple-solution method and non-singular nature of the BIE/BEM – A review and some new results,” Eng. Anal. Boundary Elements 24, 787–793 (2000).
Krishnasamy, G., Rizzo, F. J., and Liu, Y. J., “Boundary integral equations for thin bodies,” Int. J. Numer. Methods Eng. 37, 107–121 (1994).
Liu, Y. J. and Rizzo, F. J., “A weakly-singular form of the hypersingular boundary integral equation applied to 3-D acoustic wave problems,” Comput. Methods Appl. Mech. Eng. 96, 271–287 (1992).
Liu, Y. J. and Chen, S. H., “A new form of the hypersingular boundary integral equation for 3-D acoustics and its implementation with C° boundary elements,” Comput. Methods Appl. Mech. Eng. 173, 3–4, 375–386 (1999).
Liu, Y. J. and Rizzo, F. J., “Hypersingular boundary integral equations for radiation and scattering of elastic waves in three dimensions,” Comput. Methods Appl. Mech. Eng. 107, 131–144 (1993).
Liu, Y. J., Zhang, D. M., and Rizzo, F. J., “Nearly singular and hypersingular integrals in the boundary element method,” in: Brebbia, C. A. and Rencis, J. J., eds., Boundary Elements XV (Computational Mechanics Publications, Worcester, MA, 1993), pp. 453–468.
Chen, X. L. and Liu, Y. J., “An advanced 3-D boundary element method for characterizations of composite materials,” Eng. Anal. Boundary Elements 29, 513–523 (2005).
Partridge, P. W., Brebbia, C. A., and Wrobel, L. C., The Dual Reciprocity Boundary Element Method (Computational Mechanics Publications, Southampton, UK, 1992).
Kellogg, O. D., Foundations of Potential Theory (Dover, New York, 1953).
Liu, Y. J., “Dual BIE approaches for modeling electrostatic MEMS problems with thin beams and accelerated by the fast multipole method,” Eng. Anal. Boundary Elements 30, 940–948 (2006).
Hayt, W. H. and Buck, J. A., Engineering Electromagnetics (McGraw-Hill, London, 2001).
Liu, Y. J. and Shen, L., “A dual BIE approach for large-scale modeling of 3-D electrostatic problems with the fast multipole boundary element method,” Int. J. Numer. Methods Eng. 71, 837–855 (2007).
Cheng, H., Greengard, L., and Rokhlin, V., “A fast adaptive multipole algorithm in three dimensions,” J. Comput. Phys. 155, 468–498 (1999).
Shen, L. and Liu, Y. J., “An adaptive fast multipole boundary element method for three-dimensional potential problems,” Comput. Mech. 39, 681–691 (2007).
Liu, Y. J. and Nishimura, N., “The fast multipole boundary element method for potential problems: A tutorial,” Eng. Anal. Boundary Elements 30, 371–381 (2006).
Yoshida, K., “Applications of fast multipole method to boundary integral equation method,” Ph.D. dissertation, Department of Global Environment Engineering, Kyoto University (2001).
Beyer, W. H., CRC Standard Mathematical Tables and Formulae, 29th ed. (CRC, Boca Raton, FL, 1991).
Greengard, L. and Rokhlin, V., “A new version of the fast multipole method for the Laplace equation in three dimensions,” Acta Numerica 6, 229–269 (1997).
Yoshida, K., Nishimura, N., and Kobayashi, S., “Application of new fast multipole boundary integral equation method to crack problems in 3D,” Eng. Anal. Boundary Elements 25, 239–247 (2001).
Chen, X. L. and Zhang, H., “An integrated imaging and BEM for fast simulation of freeform objects,” Computer-Aided Design and Applications 5(1–4), 371–380 (2008).
Greengard, L. F., Kropinski, M. C., and Mayo, A., “Integral equation methods for Stokes flow and isotropic elasticity in the plane,” J. Comput. Phys. 125, 403–414 (1996).
Greengard, L. F. and Helsing, J., “On the numerical evaluation of elastostatic fields in locally isotropic two-dimensional composites,” J. Mech. Phys. Solids 46, 1441–1462 (1998).
Richardson, J. D., Gray, L. J., Kaplan, T., and Napier, J. A., “Regularized spectral multipole BEM for plane elasticity,” Eng. Anal. Boundary Elements 25, 297–311 (2001).
Fukui, T., “Research on the boundary element method – Development and applications of fast and accurate computations,” Ph.D. dissertation (in Japanese), Department of Global Environment Engineering, Kyoto University (1998).
Fukui, T., Mochida, T., and Inoue, K., “Crack extension analysis in system of growing cracks by fast multipole boundary element method (in Japanese),” in Proceedings of the Seventh BEM Technology Conference (JASCOME, Tokyo, 1997), pp. 25–30.
Liu, Y. J., “A new fast multipole boundary element method for solving large-scale two-dimensional elastostatic problems,” Int. J. Numer. Methods Eng. 65, 863–881 (2005).
Liu, Y. J., “A fast multipole boundary element method for 2-D multi-domain elastostatic problems based on a dual BIE formulation,” Comput. Mech. 42, 761–773 (2008).
Wang, P. and Yao, Z., “Fast multipole DBEM analysis of fatigue crack growth,” Comput. Mech. 38, 223–233 (2006).
Yamada, Y. and Hayami, K., “A multipole boundary element method for two dimensional elastostatics,” Report METR 95–07, Department of Mathematical Engineering and Information Physics, University of Tokyo (1995).
Popov, V. and Power, H., “An O(N) Taylor series multipole boundary element method for three-dimensional elasticity problems,” Eng. Anal. Boundary Elements 25, 7–18 (2001).
Yoshida, K., Nishimura, N., and Kobayashi, S., “Application of fast multipole Galerkin boundary integral equation method to crack problems in 3D,” Int. J. Numer. Methods Eng. 50, 525–547 (2001).
Lai, Y.-S. and Rodin, G. J., “Fast boundary element method for three-dimensional solids containing many cracks,” Eng. Anal. Boundary Elements 27, 845–852 (2003).
Liu, Y. J., Nishimura, N., and Otani, Y., “Large-scale modeling of carbon-nanotube composites by the boundary element method based on a rigid-inclusion model,” Comput. Mater. Sci. 34, 173–187 (2005).
Liu, Y. J., Nishimura, N., Otani, Y., Takahashi, T., Chen, X. L., and Munakata, H., “A fast boundary element method for the analysis of fiber-reinforced composites based on a rigid-inclusion model,” J. Appl. Mech. 72, 115–128 (2005).
Liu, Y. J., Nishimura, N., Qian, D., Adachi, N., Otani, Y., and Mokashi, V., “A boundary element method for the analysis of CNT/polymer composites with a cohesive interface model based on molecular dynamics,” Eng. Anal. Boundary Elements 32, 299–308 (2008).
Sladek, V. and Sladek, J., eds., Singular Integrals in Boundary Element Methods, Advances in Boundary Element Series, Brebbia, C. A. and Aliabadi, M. H., series eds. (Computational Mechanics Publications, Boston, 1998).
Mukherjee, S., “Finite parts of singular and hypersingular integrals with irregular boundary source points,” Eng. Anal. Boundary Elements 24, 767–776 (2000).
Liu, Y. J. and Rizzo, F. J., “Scattering of elastic waves from thin shapes in three dimensions using the composite boundary integral equation formulation,” J. Acoust. Soc. Am. 102, 926–932 (1997).
Muskhelishvili, N. I., Some Basic Problems of Mathematical Theory of Elasticity (Noordhoff, Groningen, The Netherlands, 1958).
Sokolnikoff, I. S., Mathematical Theory of Elasticity, 2nd ed. (McGraw-Hill, New York, 1956).
Timoshenko, S. P. and Goodier, J. N., Theory of Elasticity, 3rd ed. (McGraw-Hill, New York, 1987).
Gross, D. and Seelig, T., Fracture Mechanics with an Introduction to Micromechanics (Springer, Dordrecht, The Netherlands, 2006).
Ingber, M. S. and Papathanasiou, T. D., “A parallel-supercomputing investigation of the stiffness of aligned, short-fiber-reinforced composites using the boundary element method,” Int. J. Numer. Methods Eng. 40, 3477–3491 (1997).
Currie, I. G., Fundamental Mechanics of Fluids (McGraw-Hill, New York, 1974).
Pozrikidis, C., Boundary Integral and Singularity Methods for Linearized Viscous Flow (Cambridge University Press, New York, 1992).
Power, H. and Wrobel, L. C., Boundary Integral Methods in Fluid Mechanics (Computational Mechanics Publications, Southampton, UK, 1995).
Ding, J. and Ye, W., “A fast integral approach for drag force calculation due to oscillatory slip stokes flows,” Int. J. Numer. Methods Eng. 60, 1535–1567 (2004).
Frangi, A., “A fast multipole implementation of the qualocation mixed-velocity-traction approach for exterior Stokes flows,” Eng. Anal. Boundary Elements 29, 1039–1046 (2005).
Frangi, A. and Gioia, A. D., “Multipole BEM for the evaluation of damping forces on MEMS,” Comput. Mech. 37, 24–31 (2005).
Frangi, A. and Tausch, J., “A qualocation enhanced approach for Stokes flow problems with rigid-body boundary conditions,” Eng. Anal. Boundary Elements 29, 886–893 (2005).
Frangi, A., Spinola, G., and Vigna, B., “On the evaluation of damping in MEMS in the slip–flow regime,” Int. J. Numer. Methods Eng. 68, 1031–1051 (2006).
Liu, Y. J., “A new fast multipole boundary element method for solving 2-D Stokes flow problems based on a dual BIE formulation,” Eng. Anal. Boundary Elements 32, 139–151 (2008).
Frangi, A. and Novati, G., “Symmetric BE method in two-dimensional elasticity: Evaluation of double integrals for curved elements,” Comput. Mech. 19, 58–68 (1996).
Perez-Gavilan, J. J. and Aliabadi, M. H., “Symmetric Galerkin BEM for multi-connected bodies,” Commun. Numer. Methods Eng. 17, 761–770 (2001).
Shen, L. and Liu, Y. J., “An adaptive fast multipole boundary element method for three-dimensional acoustic wave problems based on the Burton–Miller formulation,” Comput. Mech. 40, 461–472 (2007).
Pozrikidis, C., Fluid Dynamics – Theory, Computation and Numerical Simulation (Kluwer Academic, Boston, 2001).
Power, H., “The interaction of a deformable bubble with a rigid wall at small Reynolds number: A general approach via integral equations,” Eng. Anal. Boundary Elements 19, 291–297 (1997).
Zhu, G., Mammoli, A. A., and Power, H., “A 3-D indirect boundary element method for bounded creeping flow of drops,” Eng. Anal. Boundary Elements 30, 856–868 (2006).
Mukherjee, S., Telukunta, S., and Mukherjee, Y. X., “BEM modeling of damping forces on MEMS with thin plates,” Eng. Anal. Boundary Elements 29, 1000–1007 (2005).
Schenck, H. A., “Improved integral formulation for acoustic radiation problems,” J. Acoust. Soc. Am. 44, 41–58 (1968).
Burton, A. J. and Miller, G. F., “The application of integral equation methods to the numerical solution of some exterior boundary-value problems,” Proc. R. Soc. London Ser. A 323, 201–210 (1971).
Ursell, F., “On the exterior problems of acoustics,” Proc. Cambridge Philos. Soc. 74, 117–125 (1973).
Kleinman, R. E. and Roach, G. F., “Boundary integral equations for the three-dimensional Helmholtz equation,” SIAM Rev. 16, 214–236 (1974).
Jones, D. S., “Integral equations for the exterior acoustic problem,” Q. J. Mech. Appl. Math. 27, 129–142 (1974).
Meyer, W. L., Bell, W. A., Zinn, B. T., and Stallybrass, M. P., “Boundary integral solutions of three-dimensional acoustic radiation problems,” J. Sound Vib. 59, 245–262 (1978).
Seybert, A. F., Soenarko, B., Rizzo, F. J., and Shippy, D. J., “An advanced computational method for radiation and scattering of acoustic waves in three dimensions,” J. Acoust. Soc. Am. 77, 362–368 (1985).
Kress, R., “Minimizing the condition number of boundary integral operators in acoustic and electromagnetic scattering,” Q. J. Mech. Appl. Math. 38, 323–341 (1985).
Seybert, A. F. and Rengarajan, T. K., “The use of CHIEF to obtain unique solutions for acoustic radiation using boundary integral equations,” J. Acoust. Soc. Am. 81, 1299–1306 (1987).
Cunefare, K. A. and Koopmann, G., “A boundary element method for acoustic radiation valid for all wavenumbers,” J. Acoust. Soc. Am. 85, 39–48 (1989).
Everstine, G. C. and Henderson, F. M., “Coupled finite element/boundary element approach for fluid structure interaction,” J. Acoust. Soc. Am. 87, 1938–1947 (1990).
Martinez, R., “The thin-shape breakdown (TSB) of the Helmholtz integral equation,” J. Acoust. Soc. Am. 90, 2728–2738 (1991).
Cunefare, K. A. and Koopmann, G. H., “A boundary element approach to optimization of active noise control sources on three-dimensional structures,” J. Vib. Acoust. 113, 387–394 (1991).
Ciskowski, R. D. and Brebbia, C. A., Boundary Element Methods in Acoustics (Kluwer Academic, New York, 1991).
Krishnasamy, G., Rudolphi, T. J., Schmerr, L. W., and Rizzo, F. J., “Hypersingular boundary integral equations: Some applications in acoustic and elastic wave scattering,” J. Appl. Mech. 57, 404–414 (1990).
Amini, S., “On the choice of the coupling parameter in boundary integral formulations of the exterior acoustic problem,” Appl. Anal. 35, 75–92 (1990).
Wu, T. W., Seybert, A. F., and Wan, G. C., “On the numerical implementation of a Cauchy principal value integral to insure a unique solution for acoustic radiation and scattering,” J. Acoust. Soc. Am. 90, 554–560 (1991).
Liu, Y. J., “Development and applications of hypersingular boundary integral equations for 3-D acoustics and elastodynamics,” Ph.D. dissertation, Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign (1992).
Yang, S.-A., “Acoustic scattering by a hard and soft body across a wide frequency range by the Helmholtz integral equation method,” J. Acoust. Soc. Am. 102, 2511–2520 (1997).
Rokhlin, V., “Rapid solution of integral equations of scattering theory in two dimensions,” J. Comput. Phys. 86, 414–439 (1990).
Rokhlin, V., “Diagonal forms of translation operators for the Helmholtz equation in three dimensions,” Appl. Comput. Harmon. Anal. 1, 82–93 (1993).
Epton, M. and Dembart, B., “Multipole translation theory for the three-dimensional Laplace and Helmholtz equations,” SIAM J. Sci. Comput. 16, 865–897 (1995).
Koc, S. and Chew, W. C., “Calculation of acoustical scattering from a cluster of scatterers,” J. Acoust. Soc. Am. 103, 721–734 (1998).
Greengard, L., Huang, J., Rokhlin, V., and Wandzura, S., “Accelerating fast multipole methods for the Helmholtz equation at low frequencies,” IEEE Comput. Sci. Eng. 5(3), 32–38 (1998).
Tournour, M. A. and Atalla, N., “Efficient evaluation of the acoustic radiation using multipole expansion,” Int. J. Numer. Methods Eng. 46, 825–837 (1999).
Gumerov, N. A. and Duraiswami, R., “Recursions for the computation of multipole translation and rotation coefficients for the 3-D Helmholtz equation,” SIAM J. Sci. Comput. 25, 1344–1381 (2003).
Darve, E. and Havé, P., “Efficient fast multipole method for low-frequency scattering,” J. Comput. Phys. 197, 341–363 (2004).
Fischer, M., Gauger, U., and Gaul, L., “A multipole Galerkin boundary element method for acoustics,” Eng. Anal. Boundary Elements 28, 155–162 (2004).
Chen, J. T. and Chen, K. H., “Applications of the dual integral formulation in conjunction with fast multipole method in large-scale problems for 2D exterior acoustics,” Eng. Anal. Boundary Elements 28, 685–709 (2004).
Gumerov, N. A. and Duraiswami, R., Fast Multipole Methods for the Helmholtz Equation in Three Dimensions (Elsevier, Amsterdam, 2004).
Cheng, H., Crutchfield, W. Y., Gimbutas, Z., Greengard, L. F., Ethridge, J. F., Huang, J., Rokhlin, V., Yarvin, N., and Zhao, J., “A wideband fast multipole method for the Helmholtz equation in three dimensions,” J. Comput. Phys. 216, 300–325 (2006).
Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 10th ed. (United States Department of Commerce, U.S. Government Printing Office, Washington, DC, 1972).
Marburg, S. and Wu, T. W., “Treating the phenomenon of irregular frequencies,” in Marburg, S. and Nolte, B., eds., Computational Acoustics of Noise Propagation in Fluids (Springer, Berlin, 2008), pp. 411–434.
Liu, Y. J. and Rizzo, F. J., “Application of Overhauser C(1) continuous boundary elements to ‘hypersingular’ BIE for 3-D acoustic wave problems,” in Brebbia, C. A. and Gipson, G. S., eds., Boundary Elements XIII (Computation Mechanics Publications, Tulsa, OK, 1991), pp. 957–966.
Messiah, A., “Clebsch–Gordan (C-G) Coefficients and ‘3j Symbols,’” in Quantum Mechanics, Appendix C.I. (North-Holland Amsterdam, The Netherlands, 1962), pp. 1054–1060.
Bapat, M., Shen, L., and Liu, Y. J., “An adaptive fast multipole boundary element method for 3-D half-space acoustic wave problems,” Eng. Anal. Boundary Elements, in press (2009).
Chen, S. H. and Liu, Y. J., “A unified boundary element method for the analysis of sound and shell-like structure interactions. I. Formulation and verification,” J. Acoust. Soc. Am. 103, 1247–1254 (1999).
Chen, S. H., Liu, Y. J., and Dou, X. Y., “A unified boundary element method for the analysis of sound and shell-like structure interactions. II. Efficient solution techniques,” J. Acoust. Soc. Am. 108, 2738–2745 (2000).
Wu, T. W., ed., Boundary Element Acoustics: Fundamentals and Computer Codes (WIT Press, Southampton, UK, 2000).

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