Efficient Spectral-Galerkin Methods III: Polar and Cylindrical Geometries

Authors:
Jie Shen
Affiliations:
-
Venue:
SIAM Journal on Scientific Computing
Year:
1997

Citing 0
Cited 18

An efficient spectral-projection method for the Navier--Stokes equations in cylindrical geometries

Journal of Computational Physics
Formulation of a Galerkin spectral element-fourier method for three-dimensional incompressible flows in cylindrical geometries

Journal of Computational Physics
Spectral collocation schemes on the unit disc

Journal of Computational Physics
A fast iterative solver for the variable coefficient diffusion equation on a disk

Journal of Computational Physics
Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method

Journal of Computational Physics
An efficient direct parallel spectral-element solver for separable elliptic problems

Journal of Computational Physics
Spectral radial basis functions for full sphere computations

Journal of Computational Physics
Spectral Chebyshev-Fourier collocation for the Helmholtz and variable coefficient equations in a disk

Journal of Computational Physics
Efficient spectral-Galerkin methods for polar and cylindrical geometries

Applied Numerical Mathematics
Combinations of collocation and finite-element methods for Poisson's equation

Computers & Mathematics with Applications
Brinkman equation for a corrugated pipe using a spectral-Galerkin method

Computers & Mathematics with Applications
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

Journal of Computational Physics
Matrix decomposition algorithms for elliptic boundary value problems: a survey

Numerical Algorithms
A Fourier-Legendre spectral element method in polar coordinates

Journal of Computational Physics
Efficient spectral-Galerkin methods for systems of coupled second-order equations and their applications

Journal of Computational Physics
A 3D pseudospectral method for cylindrical coordinates. Application to the simulations of rotating cavity flows

Journal of Computational Physics
Modeling and simulations of drop pinch-off from liquid crystal filaments and the leaky liquid crystal faucet immersed in viscous fluids

Journal of Computational Physics
A Spectral-Element Method for Transmission Eigenvalue Problems

Journal of Scientific Computing

Quantified Score

Hi-index	0.06

Visualization

Abstract

We present in this paper several extremely efficient and accurate spectral-Galerkin methods for second- and fourth-order equations in polar and cylindrical geometries. These methods are based on appropriate variational formulations which incorporate naturally the pole condition(s). In particular, the computational complexities of the Chebyshev--Galerkin method in a disk and the Chebyshev--Legendre--Galerkin method in a disk or a cylinder are quasi-optimal (optimal up to a logarithmic term). As an indication of efficiency, the CPU time for the Poisson solver on a disk by our Chebyshev--Galerkin method is only about 70% of the corresponding finite-difference code in FISHPACK.