On indices of tangent fields with finite singularities

Author(s):  
Duane Randall
Keyword(s):  
2021 ◽  
Vol 47 (4) ◽  
pp. 1-24
Author(s):  
Quoc T. Le Gia ◽  
Ming Li ◽  
Yu Guang Wang

Vector spherical harmonics on the unit sphere of ℝ 3 have broad applications in geophysics, quantum mechanics, and astrophysics. In the representation of a tangent vector field, one needs to evaluate the expansion and the Fourier coefficients of vector spherical harmonics. In this article, we develop fast algorithms (FaVeST) for vector spherical harmonic transforms on these evaluations. The forward FaVeST evaluates the Fourier coefficients and has a computational cost proportional to N log √ N for N number of evaluation points. The adjoint FaVeST, which evaluates a linear combination of vector spherical harmonics with a degree up to ⊡ M for M evaluation points, has cost proportional to M log √ M . Numerical examples of simulated tangent fields illustrate the accuracy, efficiency, and stability of FaVeST.


2005 ◽  
Vol 18 (2) ◽  
pp. 481-497 ◽  
Author(s):  
Céline Lacaux
Keyword(s):  

2009 ◽  
Vol 75 (3) ◽  
pp. S224-S225 ◽  
Author(s):  
A.B. Hwang ◽  
J. Chen ◽  
E. Kinsey ◽  
B.L. Fowble ◽  
N.R. Schechter ◽  
...  

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