An Accelerated Kernel-Independent Fast Multipole Method in One Dimension
YALE UNIV NEW HAVEN CT DEPT OF MATHEMATICS
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A version of the fast multipole method FMM is described for charge distributions on the line. Previously published schemes of this type relied either on analytical representations of the potentials to be evaluated multipoles, Legendre expansions, Taylor series, etc., or on the Singular Value Decomposition SVD in contrast, the algorithm of this paper utilizes the matrix compression scheme described in H. Cheng, Z. Gimbutas, P. G. Martinsson, and V. Rokhlin. On the compression of low rank matrices SIAM J. Sci. Comput. 2641389-1404, 2005., resulting in substantial improvements in the CPU time requirements. Furthermore, the scheme of this paper is applicable to a wide variety of potentials in this respect, it is similar to the SVD-based FMMs. The performance of the scheme is illustrated with several numerical examples.
- Numerical Mathematics