Corpus ID: 199064286

# FaVeST: Fast Vector Spherical Harmonic Transforms

@article{Gia2019FaVeSTFV,
title={FaVeST: Fast Vector Spherical Harmonic Transforms},
author={Quoc Thong Le Gia and Ming Li and Yu Guang Wang},
journal={ArXiv},
year={2019},
volume={abs/1908.00041}
}
• Q. L. Gia, Yu Guang Wang
• Published 31 July 2019
• Physics, Mathematics, Computer Science
• ArXiv
Vector spherical harmonics on the unit sphere of $\mathbb{R}^3$ 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 paper, 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 $N… Expand 4 Citations #### Figures, Tables, and Topics from this paper Fast Tensor Needlet Transforms for Tangent Vector Fields on the Sphere • Ming Li, Yu Guang Wang • Computer Science, Mathematics • ArXiv • 2019 The proposed tight tensor needlets provide a multiscale representation of any square integrable tangent vector field on$\mathbb{S}^2$, which leads to a multiresolution analysis (MRA) for the field. Expand A Local Spectral Exterior Calculus for the Sphere and Application to the Shallow Water Equations • Physics, Computer Science • ArXiv • 2020 The numerical results demonstrate that a$\Psi\mathrm{ec}$-based discretization of the equations attains accuracy comparable to those of spectral methods while using a representation that is well localized in space and frequency. Expand Fractional stochastic partial differential equation for random tangent fields on the sphere • V. Anh, Yu Guang Wang • Mathematics • Theory of Probability and Mathematical Statistics • 2021 This paper develops a fractional stochastic partial differential equation (SPDE) to model the evolution of a random tangent vector field on the unit sphere. The SPDE is governed by a fractionalExpand A LOCAL SPECTRAL EXTERIOR CALCULUS FOR THE SPHERE AND APPLICATION TO THE ROTATING SHALLOW WATER EQUATIONS We introduce Ψec(S2), a local spectral exterior calculus for the two-sphere S2. Ψec(S2) provides a discretization of Cartan’s exterior calculus on S2 formed by spherical differential r-form waveletsExpand #### References SHOWING 1-10 OF 76 REFERENCES Fast Algorithms for Spherical Harmonic Expansions • Mathematics, Computer Science • SIAM J. Sci. Comput. • 2006 An algorithm is introduced for the rapid evaluation at appropriately chosen nodes on the two-dimensional sphere of functions specified by their spherical harmonic expansions (known as the inverse spherical harmonic transform); the performance of the algorithm is illustrated via several numerical examples. Expand Fast Tensor Needlet Transforms for Tangent Vector Fields on the Sphere • Ming Li, Yu Guang Wang • Computer Science, Mathematics • ArXiv • 2019 The proposed tight tensor needlets provide a multiscale representation of any square integrable tangent vector field on$\mathbb{S}^2$, which leads to a multiresolution analysis (MRA) for the field. Expand A fast transform for spherical harmonics AbstractSpherical harmonics arise on the sphere S2 in the same way that the (Fourier) exponential functions {eikθ}k∈ℤ arise on the circle. Spherical harmonic series have many of the same wonderfulExpand Accurate calculation of spherical and vector spherical harmonic expansions via spectral element grids • Bo Wang • Mathematics, Computer Science • Adv. Comput. Math. • 2018 A spectrally accurate numerical method for computing the spherical/vector spherical harmonic expansion of a function/vector field with given (elemental) nodal values on a spherical surface that is robust for high mode expansions. Expand Algorithm 888: Spherical Harmonic Transform Algorithms • Mathematics, Computer Science • TOMS • 2008 A collection of MATLAB classes for computing and using spherical harmonic transforms is presented and the use of the spectral synthesis and analysis algorithms using fast Fourier transforms and Legendre transforms with the associated Legendre functions is demonstrated. Expand Fast evaluation of quadrature formulae on the sphere • Computer Science, Mathematics • Math. Comput. • 2008 A new fast algorithm for the adjoint problem which can be used to compute expansion coefficients from sampled data by means of quadrature rules and results of numerical tests are provided showing the stability of the obtained algorithm. Expand Stability and Error Estimates for Vector Field Interpolation and Decomposition on the Sphere with RBFs • Mathematics, Computer Science • SIAM J. Numer. Anal. • 2009 A new numerical technique based on radial basis functions (RBFs) is presented for fitting a vector field tangent to the sphere from samples of the field at “scattered” locations on S2, providing a way to decompose the reconstructed field into its individual Helmholtz-Hodge components. Expand On the computation of spherical designs by a new optimization approach based on fast spherical Fourier transforms • Mathematics, Computer Science • Numerische Mathematik • 2011 This paper considers the problem of finding numerical spherical t-designs on the sphere for high polynomial degree t, and shows that by means of the nonequispaced fast spherical Fourier transforms, gradient and Hessian evaluations in arithmetic operations are performed. Expand Fully discrete needlet approximation on the sphere • Mathematics • 2015 Spherical needlets are highly localized radial polynomials on the sphere$\mathbb{S}^{d}\subset \mathbb{R}^{d+1}$,$d\ge 2\$, with centers at the nodes of a suitable cubature rule. The originalExpand
Generalized Discrete Spherical Harmonic Transforms
• Mathematics
• 2000
Two generalizations of the spherical harmonic transforms are provided. First, they are generalized to an arbitrary distribution of latitudinal points ?i. This unifies transforms for Gaussian andExpand