On indices of tangent fields with finite singularities

1988 ◽  
pp. 213-240 ◽  
Author(s):  
Duane Randall
Keyword(s):  
Tangent Fields

Algorithm 1018: FaVeST—Fast Vector Spherical Harmonic Transforms

2021 ◽  
Vol 47 (4) ◽  
pp. 1-24
Author(s):  
Quoc T. Le Gia ◽  
Ming Li ◽  
Yu Guang Wang
Keyword(s):  
Spherical Harmonics ◽  
Spherical Harmonic ◽  
Fourier Coefficients ◽  
Computational Cost ◽  
Tangent Vector ◽  
Tangent Vector Field ◽  
Vector Spherical Harmonics ◽  
Numerical Examples ◽  
Vector Spherical Harmonic ◽  
Tangent Fields

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.

Fields with Exceptional Tangent Fields

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

Effect of Photon Energy on Superficial Dose in the Treatment of Breast Cancer with Tangent Fields

2009 ◽  
Vol 75 (3) ◽  
pp. S224-S225 ◽  
Author(s):  
A.B. Hwang ◽  
J. Chen ◽  
E. Kinsey ◽  
B.L. Fowble ◽  
N.R. Schechter ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Photon Energy ◽  
Tangent Fields
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