Computing with Functions in Spherical and Polar Geometries II. The Disk

DOI10.1137/16M1070207zbMath1368.65026arXiv1604.03061OpenAlexW1844026322MaRDI QIDQ5275046

Alex Townsend, Heather Wilber, Grady B. Wright

Publication date: 7 July 2017

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.03061

zbMATH Keywords

algorithmfast Fourier transformGaussian eliminationintegrationapproximation theorydifferentiationfunctionslow rank approximationPoisson solverpolar geometriesdouble Fourier sphere method

Mathematics Subject Classification ID

Numerical methods for discrete and fast Fourier transforms (65T50) Algorithms for approximation of functions (65D15) Numerical differentiation (65D25) Direct numerical methods for linear systems and matrix inversion (65F05) Numerical integration (65D30)

Related Items (12)

Fast algorithms using orthogonal polynomials ⋮ Approximation properties of the double Fourier sphere method ⋮ Rhodonea curves as sampling trajectories for spectral interpolation on the unit disk ⋮ Multidomain spectral method for the Gauss hypergeometric function ⋮ A double Fourier sphere method for \(d\)-dimensional manifolds ⋮ Tensor calculus in spherical coordinates using Jacobi polynomials. I: Mathematical analysis and derivations ⋮ Computing with Functions in the Ball ⋮ On the singular values of matrices with high displacement rank ⋮ Computing with Functions in Spherical and Polar Geometries I. The Sphere ⋮ Polar differentiation matrices for the Laplace equation in the disk under nonhomogeneous Dirichlet, Neumann and Robin boundary conditions and the biharmonic equation under nonhomogeneous Dirichlet conditions ⋮ Bounds on the Singular Values of Matrices with Displacement Structure ⋮ Spectral, tensor and domain decomposition methods for fractional PDEs

Uses Software

• Matlab
• DLMF
• Chebfun
• Chebfun2

Cites Work

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