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Bibliography

1
Rokhlin, V.: Rapid solution of integral equations of classical potential theory, J. Comp. Phys., 60, pp.187-207, 1985.

2
Greengard, L.: The rapid evaluation of potential fields in particle systems, The MIT Press, 1987.

3
Nishimura, N., Yoshida, K. and Kobayashi, S.: A fast multipole boundary integral equation method for crack problems in 3D, Eng. Anal. Boundary Elements, 23, pp.97-105, 1999.

4
Fu, Y., Klimkowski, K.J., Rodin, G.J., Berger, E., Browne, J.C., Singer, J.K., van de Geijin, R.A. and Vemaganti, K.S.: A fast solution method for three-dimensional many-particle problems of linear elasticity, Int. J. Num. Meth. Eng., 42, pp.1215-1229, 1998.

5
Fukui, T. and Kutsumi, T.: Fast multipole boundary element method in three dimensional elastostatic problems, Proc. 15th Japan Nat. Symp. BEM, 15, pp.99-104, 1998 (in Japanese).

6
Takahashi, T., Kobayashi, S. and Nishimura, N.: Fast multipole BEM simulation of overcoring in an improved conical-end borehole strain measurement method, Mechanics and Engineering in Honor of Professor Qinghua Du's 80th Anniversary, Tsinghua University Press, pp.120-127, 1999.

7
Yoshida, K., Nishimura, N. and Kobayashi, S.: Analysis of three dimensional elastostatic crack problems with fast multipole boundary integral equation method, J. Appl. Mech. JSCE, 1, pp.365-372, 1998 (in Japanese).

8
Yoshida, K., Nishimura, N. and Kobayashi, S.: Application of fast multipole Galerkin boundary integral equation method to elastostatic crack problems in 3D, Int. J. Numer. Meth. Engng., 50, pp.525-547, 2001.

9
Fujiwara, H.: The fast multipole method for solving integral equations of three-dimensional topography and basin problems, Geophys. J. Int., 140, pp.198-210, 2000.

10
Yoshida, K., Nishimura, N. and Kobayashi, S.: Analysis of three dimensional scattering of elastic waves by a crack with fast multipole bounday integral equation method, J. Appl. Mech. JSCE, 3, pp.143-150, 2000 (in Japanese).

11
Rokhlin, V.: Rapid solution of integral equations of scattering theory in two dimensions, J. Comp. Phys., 86, pp.414-439, 1990.

12
Rokhlin, V.: Diagonal forms of translation operator for the Helmholtz equation in three dimensions, Appl. Comp. Harmon. Anal., 1, pp.82-93, 1993.

13
Koc, S. and Chew, W.C.: Calculation of acoustical scattering from a cluster of scatterers, J. Acoust. Soc. Am., 103, pp.721-734, 1998.

14
Epton, M.A. and Dembart, B.: Multipole translation theory for the three-dimensional Laplace and Helmholtz equations, SIAM J. Sci. Comp., 16, pp.865-897, 1995.

15
Elliot, W.D. and Board, J.A. JR.: Fast Fourier transform accelerated fast multipole algorithm, SIAM J. Sci. Comp., 17, pp.398-415, 1995.

16
Dembart, B. and Yip, E.: The accuracy of fast multipole methods for Maxwell's equations, IEEE Comp. Sci. Eng., 5, pp.48-56, 1998.

17
Hrycak, T. and Rokhlin, V.: An improved fast multipole algorithm for potential fields, SIAM J. Sci. Comp. 19, pp.1804-1826, 1998.

18
Greengard, L. and Rokhlin, V.: A new version of the fast multipole method for the Laplace equation in three dimensions. Acta Numerica, 6, pp.229-270, 1997.

19
Cheng, H., Greengard, L. and Rokhlin, V.: A fast adaptive multipole algorithm in three dimensions, J. Comp. Phys., 155, pp.468-498, 1999. [.5cm]17cm

20
Greengard, L., Huang, J., Rokhlin, V. and Wandzura, S.: Accelerating fast multipole methods for the Helmholtz equation at low frequencies, IEEE Comp. Sci. Eng., 5, pp.32-38, 1998.

21
Nishimura, N., Miyakoshi, M. and Kobayashi, S.: Application of new multipole boundary integral equation method to crack problems, Proc. BTEC-99, pp.75-78, 1999 (in Japanese).

22
Fu, Y., Overfelt, J.R. and Rodin, G.J.: Fast summation methods and integral equations: Mathematical Aspects of Boundary Element Methods (Eds. M. Bonnet, A.M. Saendig and W. Wendland), CRC Press, pp.128-139, 1999.

23
Yarvin, N. and Rokhlin, V.: Generalized Gaussian quadratures and singular value decomposition of integral operators, SIAM J. Sci. Comp., 20, pp.699-718, 1998.

24
Perez-Jorda, J.M. and Yang, W.: A concise redefinition of the solid spherical harmonics and its use in fast multipole methods, J. Chem. Phys., 104, pp.8003-8006, 1996.

25
Biedenharn, L.C. and Louck, J.D.: Angular momentum in quantum physics: theory and application, Addison Wesley, London, 1981.

26
Nishida, T. and Hayami, K.: Application of the fast multipole method to the 3D BEM analysis of electron guns, Boundary Elements XIX, Computational Mechanics Publications, pp.613-622, 1997.

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Ken-ichi Yoshida
2001-03-26