In this paper we describe algorithms for the numerical computation of Fourier transforms of tensor fields on the two-sphere, S 2 . These algorithms reduce the computation of an expansion on tensor spherical harmonics to expansions in scalar spherical harmonics, and hence can take advantage of recent
Note on the computation of the multiple tensor in spherical harmonics
β Scribed by Werner W. Schulz
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 195 KB
- Volume
- 254
- Category
- Article
- ISSN
- 0009-2614
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β¦ Synopsis
A simple formula for the spherical multipole tensor which has better scaling behaviour than those based on a cartesian formulation is presented. The interaction energy calculation scales as ~'(L 4) for a multipole expansion up to rank L. A new derivation of the bipolar multipole expansion for well-separated charge distributions is given.
π SIMILAR VOLUMES
A growth lemma for certain discrete symmetric Laplacians defined on a lattice Z d Ξ΄ = Ξ΄Z d β R d with spacing Ξ΄ is proved. The lemma implies a De Giorgi theorem, that the harmonic functions for these Laplacians are equi-HΓΆlder continuous, Ξ΄ β 0. These results are then applied to establish regularity