A generalized fast multipole method for nonoscillatory kernels

SIAM Journal on Scientific Computing

Volumn 24, Issue 3, 2003, Pages 796-817

  Gimbutas, Zyndrunas ^a   Rokhlin, Vladimir ^b  

^a MadMax Optics Inc   (United States)

^b Yale University   (United States)

Author keywords

Arbitrary kernels; Fast multipole method; Potential theory

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; FORTRAN (PROGRAMMING LANGUAGE); INTEGRAL EQUATIONS; INTEGRATION; INTERPOLATION; NUMERICAL METHODS; POLYNOMIALS; TENSORS; THEOREM PROVING;

ARBITRARY KERNELS; FAST MULTIPOLE METHOD; NONOSCILLATORY KERNELS; POTENTIAL THEORY; SINGULAR VALUE DECOMPOSITION;

APPROXIMATION THEORY;

EID: 0038070202     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827500381148     Document Type: Article

References (18)

1. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, Applied Mathematics Series 55, U.S. Government Printing Office, Washington, DC, 1964.
2. B. K. Alpert and V. Rokhlin, A fast algorithm for the evaluation of Legendre expansions, SIAM J. Sci. Comput., 12 (1991), pp. 158-179.
3. J. Carrier, L. Greengard, and V. Rokhlin, A fast adaptive multipole algorithm for particle simulations, SIAM J. Sci. Comput., 9 (1988), pp. 669-686.
4. H. Cheng, L. Greengard, and V. Rokhlin, A fast multipole algorithm in three dimensions, J. Comput. Phys., 155 (1999), pp. 468-498.
5. A. Dutt, M. Gu, and V. Rokhlin, Fast algorithms for polynomial interpolation, integration, and differentiation, SIAM J. Numer. Anal., 33 (1996), pp. 1689-1711.
6. Z. Gimbutas. Generalized FMM for Nonoscillatory Kernels Ph.D. disseration, Yale University, New Haven CT, 1999.
7. L. Greengard and V. Rokhlin, A fast algorithm for particle simulations, J. Comput. Phys., 73 (1987), pp. 325-348.
8. L. Greengard, The Rapid Evaluation of Potential Fields in Particle Systems, MIT Press. Cambridge, MA, 1988.
9. L. Greengard and V. Rokhlin, A new version of the fast multipole method for the Laplace equation in three dimensions, Acta Numer., 6 (1997), pp. 229-269.
10. T. Hrycak and V. Rokhlin, An improved fast multipole algorithm for potential fields, SIAM J. Sci. Comput., 19 (1998), pp. 1804-1826.
11. S. Kapur and D. E. Long, IES3: Efficient electrostatic and electromagnetic simulation, IEEE Comput. Sci. Engrg., 5 (1998), pp. 60-67.
12. M. J. D. Powell, Approximation Theory and Methods, Cambridge University Press, Cambridge, UK, 1981.
13. J. R. Phillips and J. K. White, A precorrected-FFT method for electrostatic analysis of complicated 3-D structures, IEEE Trans. Comput. Aided Design, 16 (1997), pp. 1059-1072.
14. V. Rokhlin, Rapid solution of integral equations of classical potential theory, J. Comput. Phys., 60 (1986), pp. 187-207.
15. M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 1, Academic Press. 1980.
16. G. Szego, Orthogonal Polynomials, AMS, Providence, RI, 1978.
17. N. Yarvin and V. Rokhlin, Generalized Gaussian quadratures and singular value decomposition of integral operators, SIAM J. Sci. Comput., 20 (1998), pp. 699-718.
18. N. Yarvin and V. Rokhlin, An improved fast multipole algorithm for potential fields on the line, SIAM J. Numer. Anal., 36 (1999), pp 629-666.