An accelerated kernel-independent fast multipole method in one dimension

SIAM Journal on Scientific Computing

Volumn 29, Issue 3, 2007, Pages 1160-1178

  Martinsson, P G ^a   Rokhlin, V ^b  

^a UNIVERSITY OF COLORADO   (United States)

^b YALE UNIVERSITY   (United States)

Author keywords

Fast multipole method; Fast summation; Matrix interpolation; Skeletonization

Indexed keywords

ALGORITHMS; MATRIX ALGEBRA; NUMERICAL METHODS;

FAST MULTIPOLE METHOD; FAST SUMMATION; MATRIX INTERPOLATION; SKELETONIZATION;

CHARGE DISTRIBUTION;

EID: 40249106214     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/060662253     Document Type: Article

References (26)

1. C. R. ANDERSON, An implementation of the fast multipole method without multipoles, SIAM J. Sci. Statist. Comput., 13 (1992), pp. 923-947.
2. J. BARNES AND P. HUT, A hierarchical o(n log n) force calculation algorithm, Nature, 324 (1986), pp. 446-449.
3. J. P. BOYD, A fast algorithm for Chebyshev, Fourier, and sinc interpolation onto an irregular grid, J. Comput. Phys., 103 (1992), pp. 243-257.
4. H. CHENG, W. CRUTCHFIELD, Z. GIMBUTAS, L. GREENGARD, F. ETHRIDGE, V. ROKHLIN, N. YARVIN, AND J. ZHAO, A Wideband Fast Multipole Method for the Helmholtz Equation in Three Dimensions, Technical report 514, MadMax Optics, Inc., Hamden, CT, 2005.
5. H. CHENG, Z. GIMBUTAS, P. G. MARTINSSON, AND V. ROKHLIN, On the compression of low rank matrices, SIAM J. Sci. Comput., 26 (2005), pp. 1389-1404.
6. W. C. CHEW, J. M. JIN, E. MICHIELSEN, AND J. SONG, Fast and Efficient Algorithms in Computational Electromagnetics, Artech House, Norwood, MA, 2001.
7. L. DEBNATH, Integral Transforms and their Applications, CRC Press, Boca Raton, FL, 1995.
8. Z. GIMBUTAS AND V. ROKHLIN, A generalized fast multipole method for nonoscillatory kernels, SIAM J. Sci. Comput., 24 (2002), pp. 796-817.
9. L. GREENGARD, The Rapid Evaluation of Potential Fields in Particle Systems, MIT Press, Cambridge, MA, 1988.
10. L. GREENGARD AND V. ROKHLIN, A fast algorithm for particle simulations, J. Comput. Phys., 73 (1987), pp. 325-348.
11. 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.
12. M. GU AND S. C. EISENSTAT, A divide-and-conquer algorithm for the bidiagonal SVD, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 79-92.
13. M. GU AND S. C. EISENSTAT, Efficient algorithms for computing a strong rank-revealing QR factorization, SIAM J. Sci. Comput., 17 (1996), pp. 848-869.
14. R. JAKOB-CHIEN AND B. ALPERT, A fast spherical filter with uniform resolution, J. Comput. Phys., 136 (1997), pp. 580-584.
15. 3: Efficient electrostatic and electromagnetic simulation, IEEE Comput. Sci. Eng., 5 (1998), pp. 60-67.
16. J. MAKINO, Yet another fast multipole method without multipoles - pseudoparticle multipole method, J. Comput. Phys., 151 (1999), pp. 910-920.
17. P. G. MARTINSSON, V. ROKHLIN, AND M. TYGERT, On Interpolation and Integration in Finitedimensional Spaces of Bounded Functions, Technical report YALEU/DCS/RR-1317, Department of Computer Science, Yale, New Haven, CT, 2005.
18. P. G. MARTINSSON AND V. ROKHLIN, A fast direct solver for boundary integral equations in two dimensions, J. Comput. Phys., 205 (2005), pp. 1-23.
19. E. MICHIELSSEN AND A. BOAG, A multilevel matrix decomposition algorithm for analyzing scattering from large structures, IEEE Trans. Antennas Propagat., 44 (1996), pp. 1086-1093.
20. 2 N) operations, IEEE Proc. Microwaves Antennas Propagat., 143 (1996), pp. 277-283.
21. K. NABORS, F. T. KORSMEYER, F. T. LEIGHTON, AND J. WHITE, Preconditioned, adaptive, multipole-accelerated iterative methods for three-dimensional first-kind integral equations of potential theory, Iterative Methods in Numerical Linear Algebra (Copper Mountain Resort, CO, 1992), SIAM J. Sci. Comput., 15 (1994), pp. 713-735.
22. V. ROKHLIN AND M. TYGERT, Fast algorithms for spherical harmonic expansions, SIAM J. Sci. Comput., 27 (2006), pp. 1903-1928.
23. D. SLEPIAN AND H. O. POLLAK, Prolate spheroidal wave functions, Fourier analysis, and uncertainty, I, Bell System Tech. J., (1961), pp. 43-63.
24. R. SUDA AND S. KURIYAMA, Another preprocessing algorithm for generalized one-dimensional fast multipole method, J. Comput. Phys., 195 (2004), pp. 790-803.
25. 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.
26. L. YING, G. BIROS, AND D. ZORIN, A kernel-independent adaptive fast multipole algorithm in two and three dimensions, J. Comput. Phys., 196 (2004), pp. 591-626.