Error Analysis for the Numerical Evaluation of the Diagonal Forms of the Scalar Spherical Addition Theorem

Authors:
S. Koc;Jiming Song;W. C. Chew
Affiliations:
-;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
1999

Citing 0
Cited 4

Coupling of fast multipole method and microlocal discretization for the 3-D Helmholtz equation

Journal of Computational Physics
Efficient fast multipole method for low-frequency scattering

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Volumetric fast multipole method for modeling Schrödinger's equation

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Iterative Near-Field Preconditioner for the Multilevel Fast Multipole Algorithm

SIAM Journal on Scientific Computing

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Abstract

The numerical solution of wave scattering from large objects or from a large cluster of scatterers requires excessive computational resources and it becomes necessary to use approximate---but fast---methods such as the fast multipole method; however, since these methods are only approximate, it is important to have an estimate for the error introduced in such calculations. An analysis of the error for the fast multipole method is presented and estimates for truncation and numerical integration errors are obtained. The error caused by polynomial interpolation in a multilevel fast multipole algorithm is also analyzed. The total error introduced in a multilevel implementation is also investigated numerically.