相关论文: SHarmonic: A fast and accurate implementation of s…
Spherical harmonics provide a smooth, orthogonal, and symmetry-adapted basis to expand functions on a sphere, and they are used routinely in physical and theoretical chemistry as well as in different fields of science and technology, from…
We introduce a new basis function (the spherical gaussian) for electronic structure calculations on spheres of any dimension $D$. We find \alert{general} expressions for the one- and two-electron integrals and propose an efficient…
Computing spherical harmonic decompositions is a ubiquitous technique that arises in a wide variety of disciplines and a large number of scientific codes. Because spherical harmonics are defined by integrals over spheres, however, one must…
The spherical harmonic transform is a powerful tool in the analysis of spherical data sets, such as the cosmic microwave background data. In this work, we present a new scheme for the spherical harmonic transforms that supports both CPU and…
Recent microscopy imaging techniques allow to precisely analyze cell morphology in 3D image data. To process the vast amount of image data generated by current digitized imaging techniques, automated approaches are demanded more than ever.…
We demonstrate a fast spin-s spherical harmonic transform algorithm, which is flexible and exact for band-limited functions. In contrast to previous work, where spin transforms are computed independently, our algorithm permits the…
3D image processing constitutes nowadays a challenging topic in many scientific fields such as medicine, computational physics and informatics. Therefore, development of suitable tools that guaranty a best treatment is a necessity.…
In this short note we propose a new method for construction new nice arrangement on the sphere $S^d$ using the spaces of spherical harmonic.
In this pedagogically structured article, we describe a generalized harmonic formulation of the Einstein equations in spherical symmetry which is regular at the origin. The generalized harmonic approach has attracted significant attention…
We present a method for electronic structure calculations that retains all of the advantages of real space and addresses the inherent inefficiency of a regular grid, which has equal precision everywhere. The computations are carried out on…
A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…
We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics are used surprisingly infrequently, considering their…
We develop a systematic framework for constructing spherical harmonics on the two-dimensional unit sphere as superpositions of Gaussian beams whose poles form well-separated point configurations. The distributional and analytic properties…
We propose SHARC, a novel framework that synthesizes arbitrary, genus-agnostic shapes by means of a collection of Spherical Harmonic (SH) representations of distance fields. These distance fields are anchored at optimally placed reference…
We describe an algorithm for computing an inverse spherical harmonic transform suitable for graphic processing units (GPU). We use CUDA and base our implementation on a Fortran90 routine included in a publicly available parallel package,…
Associated Legendre polynomials and spherical harmonics are central to calculations in many fields of science and mathematics - not only chemistry but computer graphics, magnetic, seismology and geodesy. There are a number of algorithms for…
In this paper, we compare two optimization algorithms using full Hessian and approximation Hessian to obtain numerical spherical designs through their variational characterization. Based on the obtained spherical design point sets, we…
Most of the digital signal processing applications performs operations like multiplication, addition, square-root calculation, solving linear equations etc. The physical implementation of these operations consumes a lot of hardware and,…
Harmonic inversion techniques have been shown to be a powerful tool for the semiclassical quantization and analysis of quantum spectra of both classically integrable and chaotic dynamical systems. Various computational procedures have been…
In this paper, we report on very efficient algorithms for the spherical harmonic transform (SHT). Explicitly vectorized variations of the algorithm based on the Gauss-Legendre quadrature are discussed and implemented in the SHTns library…