Fast spherical harmonic transforms

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August undefined, 2024

Webwith horizontal wavelength R⊙/ℓ of the observations, where ℓ is degree of spherical harmonic Yℓm(θ,φ). When applied to solar power spectra at frequencies below acous-tic … http://www.jasonmcewen.org/papers/fsht.pdf

High resolution spherical and ellipsoidal harmonic expansions by Fast …

WebOct 18, 2024 · This method can be used to reconstruct band limited spherical harmonic or Wigner D-function series (spherical harmonic series are a special case) with sparse … WebAbout this Title. Jens Gerlach Christensen, Colgate University, Hamilton, NY, Susanna Dann, Vienna University of Technology, Wien, Austria and Matthew Dawson, CIMAT, … henty postcode

(PDF) FaVeST: Fast Vector Spherical Harmonic Transforms

WebThe spectral synthesis and analysis algorithms using fast Fourier transforms and Legendre transforms with the associated Legendre functions are presented in detail. A set of methods associated with a spectral_field class provides spectral approximation to the differential operators ∇ ⋯, ∇ ×, ∇, and ∇ 2 in spherical geometry. Weboped asymptotically optimal spherical harmonic transforms with O(n2 logn) run times. The pre-computation was also asymptotically optimal, though this is anticipated only for absurdly high degrees. More recently, Slevinsky proposed two new fast spherical harmonic transforms, ﬁrst with backward stability, O(n2 log2 n) run-time and O(n3 logn) pre- WebM.P. Mohlenkamp, A fast transform for spherical harmonics, J. Fourier Anal. Appl. 5 (2/3) (1999) 159–184. Google Scholar S. Moore, Efficient stabilization methods for fast polynomial transforms, Ph.D. thesis, Department of Mathematics and Computer Science, Dartmouth College (1994). henty residential care

On-grid compressive sampling for spherical field measurements in ...

SHTns: High performance Spherical Harmonic Transform for

WebThe spherical harmonic transforms in SHTOOLS make use of integrations over longitude that involve fast Fourier transforms and integrations over latitude that utilize either Gauss-Legendre quadrature … WebAug 13, 2014 · High resolution transformations between regular geophysical data and harmonic model coefficients can be most efficiently computed by Fast Fourier Transform (FFT). However, a prerequisite is that the data grids are given in … henty road southamptonWebscipy.special.sph_harm(m, n, theta, phi, out=None) = # Compute spherical harmonics. The spherical harmonics are defined as Y n m ( θ, ϕ) = 2 n + 1 4 π ( n − m)! ( n + m)! e i m θ P n m ( cos ( ϕ)) where P n m are the associated Legendre functions; see lpmv. Parameters: marray_like Order of the harmonic (int); must have m … henty reef apollo bay

"WebJul 31, 2024 · 4 fast vector spherical harmonic transforms In Subsections 4.1 and 4.2 below, we prov e two theorems to represent the vector spherical harmonic transforms by scalar spherical harmonics and Clebsch ... " - Fast spherical harmonic transforms

Fast spherical harmonic transforms

Algorithm 888: Spherical Harmonic Transform Algorithms

WebMay 12, 2024 · Abstract Geophysical analyses are often performed in spherical geometry and require the use of spherical harmonic functions to express observables or physical quantities. When expanded to high degr... SHTools: Tools for Working with Spherical Harmonics - Wieczorek - 2024 - Geochemistry, Geophysics, Geosystems - Wiley Online … WebDec 1, 2003 · The discrete spherical Fourier transform (DSFT) plays an essential role in many applications. In particular, there is a growing need for the fast summation of spherical harmonic expansions (see [6], [26], [21], [32], [14]). Unfortunately, working with spherical harmonics is computationally complex in many respects [5].

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WebFeb 15, 2012 · The spherical harmonic transform (SHT) is the spherical analog of the Fourier transform and is an essential tool for data analysis and simulation on the … WebJan 21, 2013 · The fast Fourier transform (FFT) should be used for this part, as it improves accuracy and speed. SHTns uses the FFTW library [ Frigo & Johnson, 2005 ], a portable, …

WebNov 1, 1999 · 1 Introduction. Many geophysical problems involve spherical geometry. Some can be described as data processing while others involve the solution of partial differential equations in spherical coordinates; in both cases it is useful to transform between a spatial representation and a set of spherical harmonic coefficients.

WebThe spherical harmonic (SH) expansion technique maps a variable on a spherical surface to its representation in the SH function space in terms of SH expansion coefficients. This technique, also known as the spectral transform method, has been employed in global atmospheric modeling efforts (Williamson, 2007 ), including numerical weather ... WebJan 1, 2002 · Fast spherical harmonic transforms either accelerate synthesis and analysis, complementing the physical-and momentum-space representations of quantum …

WebFeb 15, 2012 · The spherical harmonic transform (SHT) is the spherical analog of the Fourier transform and is an essential tool for data analysis and simulation on the sphere. ... The discovery of fast Fourier transforms (FFTs) has been all important for signal analysis over the past half century, and there is no lack of high-quality commercial and open ...

WebJul 8, 2014 · An Optimal-Dimensionality Sampling Scheme on the Sphere With Fast Spherical Harmonic Transforms. Abstract: We develop a sampling scheme on the … henty respite trustWebspherical harmonic transform further reduces to the problem of performing a fast associated Legendre transform. First attempts to compute a scalar spherical harmonic through a fast Legendre transform were performed by Orszag [18] and were based on a Wentzel-Kramers-Brillouin (WKB) approximation. Alternative approaches using the fast … henty suit bagWebfast to compute, can be completely characterized theoretically, and empirically has superior angular resolution to the FRT, though also ... was modeled using a spherical harmonic representation, where the spherical harmonic coefficients were obtained using a regularized ... transforms in the new family of transforms introduced in (Haldar, 2012 ... henty tennis clubWebApr 24, 2024 · Mathematica's implementation of the Fast Fourier Transform is, naturally, much faster than computing the discrete transform yourself using Sum. The analog of … henty real estate nswWebAug 1, 2024 · Fast, nonuniform spherical harmonic transforms Any square integrable function distributed on the sphere can be decomposed into an infinite sum of Laplace spherical harmonic functions, , such that View Expanded where θ is latitude, ϕ is longitude, and l and m are the indices of the spectral coefficient matrix . henty showWebJul 8, 2014 · An Optimal-Dimensionality Sampling Scheme on the Sphere With Fast Spherical Harmonic Transforms Abstract: We develop a sampling scheme on the sphere that permits accurate computation of the spherical harmonic transform and its inverse for signals band-limited at L using only L 2 samples. henty roadWebJun 3, 2016 · SHTns is a high performance library for Spherical Harmonic Transform written in C, aimed at numerical simulation (fluid flows, mhd, ...) in spherical geometries. … hentys corporate