Single Level Multipole Expansions and Operators for Potentials of the Form $r^-\lambda$
Copyright policy )Single Level Multipole Expansions and Operators for Potentials of the Form $r^-\lambda$
Summary: This paper presents the generalized multipole, local, and translation operators for three-dimensional static potentials of the form \(r^{-\lambda}\), where \(\lambda\) is any real number. Addition theorems are developed using Gegenbauer polynomials. Multipole expansions and error bounds are presented in a manner similar to those for truncated classical multipole expansions. Numerical results showing error behavior versus number of terms, distance, and \(\lambda\) are presented. For \(\lambda=1\) cf. \textit{L. Greengard}, The rapid evaluation of potential fields in particle systems, Cambridge MA (1988; Zbl 1001.31500).
fast multipole method, Computational methods for problems pertaining to mechanics of particles and systems, van der Waals force, Harmonic, subharmonic, superharmonic functions in higher dimensions, \(n\)-body problems, Potentials and capacities, extremal length and related notions in higher dimensions, Probabilistic models, generic numerical methods in probability and statistics, Software, source code, etc. for problems pertaining to potential theory, Gegenbauer polynomials, Discrete potential theory
fast multipole method, Computational methods for problems pertaining to mechanics of particles and systems, van der Waals force, Harmonic, subharmonic, superharmonic functions in higher dimensions, \(n\)-body problems, Potentials and capacities, extremal length and related notions in higher dimensions, Probabilistic models, generic numerical methods in probability and statistics, Software, source code, etc. for problems pertaining to potential theory, Gegenbauer polynomials, Discrete potential theory
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