scholarly journals Application of Vector Spherical Harmonics to the Magnetisation of Mars’ Crust

2021 ◽  
Author(s):  
David Gubbins ◽  
Yi Jiang ◽  
Simon E. Williams ◽  
Keke Zhang
Keyword(s):  
Spherical Harmonics ◽  
Vector Spherical Harmonics

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.

scholarly journals Vector spherical harmonics and their application to magnetostatics

1985 ◽  
Vol 6 (4) ◽  
pp. 287-294 ◽  
Author(s):  
R G Barrera ◽  
G A Estevez ◽  
J Giraldo
Keyword(s):  
Spherical Harmonics ◽  
Vector Spherical Harmonics

scholarly journals Active compensation of magnetic field distortions based on vector spherical harmonics field description

AIP Advances ◽  
2017 ◽  
Vol 7 (3) ◽  
pp. 035216
Author(s):  
G. Wyszyński ◽  
K. Bodek ◽  
S. Afach ◽  
G. Bison ◽  
Z. Chowdhuri ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Spherical Harmonics ◽  
Vector Spherical Harmonics ◽  
Active Compensation
Sign in / Sign up

Export Citation Format

Share Document