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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)

MSC:
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)
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