Tensor calculus in spherical coordinates using Jacobi polynomials. I: Mathematical analysis and derivations
DOI10.1016/j.jcpx.2019.100013arXiv1804.10320OpenAlexW2963863319WikidataQ128303399 ScholiaQ128303399MaRDI QIDQ6145375
Jeffrey S. Oishi, Daniel Lecoanet, Keaton J. Burns, Geoffrey M. Vasil, Benjamin P. Brown
Publication date: 9 January 2024
Published in: Journal of Computational Physics: X (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1804.10320
spherical geometryJacobi polynomialsspectral methodssparse operatorscoordinate singularitiesspin-weighted spherical harmonics
Numerical approximation and computational geometry (primarily algorithms) (65Dxx) Numerical methods for ordinary differential equations (65Lxx) Numerical methods for partial differential equations, boundary value problems (65Nxx)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Spectral integration of linear boundary value problems
- An optimal Galerkin scheme to solve the kinematic dynamo eigenvalue problem in a full sphere
- Comparing seven spectral methods for interpolation and for solving the Poisson equation in a disk: Zernike polynomials, Logan-Shepp ridge polynomials, Chebyshev-Fourier series, cylindrical Robert functions, Bessel-Fourier expansions, square-to-disk conformal mapping and radial basis functions
- A Chebyshev method for the solution of boundary value problems
- An application of one-sided Jacobi polynomials for spectral modeling of vector fields in polar coordinates
- A numerical comparison of Chebyshev methods for solving fourth order semilinear initial boundary value problems
- Fast algorithms for spherical harmonic expansions. III
- Efficient multi-dimensional solution of PDEs using Chebyshev spectral methods
- A modified tau spectral method that eliminates spurious eigenvalues
- The Tau method as an analytic tool in the discussion of equivalence results across numerical methods
- The origin and nature of spurious eigenvalues in the spectral tau method
- Computational harmonic analysis for tensor fields on the two-sphere
- The ubiquitous Kronecker product
- Tensor calculus in polar coordinates using Jacobi polynomials
- A spectral method for polar coordinates
- A spectral method for nonlocal diffusion operators on the sphere
- Recurrence relations for a family of orthogonal polynomials on a triangle
- Galerkin orthogonal polynomials
- Efficient spectral ultraspherical-dual-Petrov-Galerkin algorithms for the direct solution of \((2n + 1)\)th-order linear differential equations
- A fully spectral methodology for magnetohydrodynamic calculations in a whole sphere
- Fast algorithms for spherical harmonic expansions. II.
- Efficient spectral-Galerkin algorithms for direct solution for second-order differential equations using Jacobi polynomials
- Spectral radial basis functions for full sphere computations
- Elimination of spurious eigenvalues in the Chebyshev tau spectral method
- A Fast and Well-Conditioned Spectral Method
- Representations of the group of rotations of 3-dimensional space and their applications
- Spectral Integration and Two-Point Boundary Value Problems
- On the Spectral Approximation of Discrete Scalar and Vector Functions on the Sphere
- New tensor spherical harmonics, for application to the partial differential equations of mathematical physics
- Spectral Methods in MATLAB
- On the use of Hahn’s asymptotic formula and stabilized recurrence for a fast, simple and stable Chebyshev–Jacobi transform
- Edth-a differential operator on the sphere
- Beugungstheorie des schneidenver-fahrens und seiner verbesserten form, der phasenkontrastmethode
- Representation of the Elastic - Gravitational Excitation of a Spherical Earth Model by Generalized Spherical Harmonics
- Efficient Spectral-Galerkin Algorithms for Direct Solution of Second-Order Equations Using Ultraspherical Polynomials
- An efficient spectral method for ordinary differential equations with rational function coefficients
- Computing with Functions in Spherical and Polar Geometries II. The Disk
- Gegenbauer Tau Methods With and Without Spurious Eigenvalues
- Numerical evolutions of fields on the 2-sphere using a spectral method based on spin-weighted spherical harmonics
- A Fast, Simple, and Stable Chebyshev--Legendre Transform Using an Asymptotic Formula
- Orthogonal Polynomials of Several Variables
- The Tau Method
- Bochner-Weitzenböck formulas and curvature actions on Riemannian manifolds
- Computing with Functions in Spherical and Polar Geometries I. The Sphere
- Trigonometric Interpolation of Empirical and Analytical Functions
- Quasi-\(L^{p}\) norm orthogonal Galerkin expansions in sums of Jacobi polynomials
This page was built for publication: Tensor calculus in spherical coordinates using Jacobi polynomials. I: Mathematical analysis and derivations