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A generalized one-dimensional fast multipole method with application to filtering of spherical harmonics. (English) Zbl 0927.65138
The authors introduce a generalized fast multipole method that leads to an accelerated version of the filtering process. It is described as a set of modifications of the fast multipole method presented by L. Greengard and V. Rokhlin [J. Comput. Phys. 73, No. 2, 325-348 (1987; Zbl 0629.65005)] and by A. Dutt, M. Gu and V. Rokhlin [SIAM J. Numer. Anal. 33, No. 5, 1689-1711 (1996; Zbl 0862.65005)].
Furthermore, the authors describe an accelerated version of the algorithm presented by R. Jacob-Chien and B. Alpert [J. Comput. Phys. 136, No. 2, 580-584 (1997; Zbl 0885.65016)] in which two calls to the original one-dimensional fast multipole method are replaced by one call to the new generalized fast multipole method.
The performance of the proposed algorithms is illustrated by several numerical examples.
Reviewer: M.Jung (Chemnitz)

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35Q72 Other PDE from mechanics (MSC2000)
65C35 Stochastic particle methods
82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
Full Text: DOI
[1] Abramowitz, M.; Stegun, I., Handbook of mathematical functions, (1964) · Zbl 0171.38503
[2] Alpert, B.; Beylkin, G.; Coifman, R.; Rokhlin, V., Wavelet-like bases for the fast solution of second-kind integral equations, SIAM J. sci. comput., 14, 159, (1993) · Zbl 0771.65088
[3] Dutt, A.; Gu, M.; Rokhlin, V., Fast algorithms for polynomial interpolation, integration, and differentiation, SIAM J. numer. anal., 33, (1996) · Zbl 0862.65005
[4] Epton, M.A.; Dembart, B., Multipole translation theory for the three-dimensional Laplace and Helmholtz equations, SIAM J. sci. comput., 16, 865, (1995) · Zbl 0852.31006
[5] Gradshteyn, I.S.; Ryzhik, I.M., Table of integrals, series, and products, (1994) · Zbl 0918.65002
[6] Greengard, L.; Rokhlin, V., A fast algorithm for particle simulations, J. comput. phys., 73, 325, (1987) · Zbl 0629.65005
[7] Greengard, L.; Rokhlin, V., A new version of the fast multipole method for the Laplace equation in three dimensions, Acta numer., 229, (1997) · Zbl 0889.65115
[8] Golub, V.H.; Van Loan, C.H., Matrix computations, (1983) · Zbl 0559.65011
[9] Hrycak, T.; Rokhlin, V., An improved fast multipole algorithm for potential fields, (1995)
[10] Jakob-Chien, R.; Alpert, B., A fast spherical filter with uniform resolution, J. comput. phys., 136, 580, (1997) · Zbl 0885.65016
[11] S. Kapur, D. E. Long, IES^3, 37th International Conference on Computer Aided Design, Nov. 1997
[12] S. Kapur, D. E. Long, J. Zhao, Efficient full-wave simulation in layered, lossy media, Proceedings of the IEEE Custom Integrated Circuits Conference, May 1998
[13] Orszag, S.A., Fourier series on spheres, Mon. weather rev., 102, 56, (1974)
[14] Stoer, J.; Bulirsch, R., Introduction to numerical analysis, (1993) · Zbl 0771.65002
[15] N. Yarvin, V. Rokhlin, An improved fast multipole algorithm for potential fields on the line, SIAM J. Numer. Anal. · Zbl 0973.65106
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