Spectral collocation methods and polar coordinate singularities
Journal of Computational Physics
Splitting techniques for the pseudospectral approximation of the unsteady Stokes equations
SIAM Journal on Numerical Analysis
Pole condition for singular problems: the pseudospectral approximation
Journal of Computational Physics
Conforming spectral methods for Poisson problems in cuboidal domains
Journal of Scientific Computing
A pseudospectral approach for polar and spherical geometries
SIAM Journal on Scientific Computing
A spectral method for polar coordinates
Journal of Computational Physics
Efficient Spectral-Galerkin Methods III: Polar and Cylindrical Geometries
SIAM Journal on Scientific Computing
Splitting Techniques for the Unsteady Stokes Equations
SIAM Journal on Numerical Analysis
Spectral collocation on triangular elements
Journal of Computational Physics
Pseudospectral Solution of the Two-Dimensional Navier--Stokes Equations in a Disk
SIAM Journal on Scientific Computing
Spectral methods in MatLab
A new fast Chebyshev—Fourier algorithm for Poisson-type equations in polar geometries
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
A direct spectral collocation Poisson solver in polar and cylindrical coordinates
Journal of Computational Physics
Splitting techniques with staggered grids for the Navier—Stokes equations in the 2D case
Journal of Computational Physics
Spectral schemes on triangular elements
Journal of Computational Physics
A fast iterative solver for the variable coefficient diffusion equation on a disk
Journal of Computational Physics
Spectral radial basis functions for full sphere computations
Journal of Computational Physics
Direct Minimization of the least-squares spectral element functional - Part I: Direct solver
Journal of Computational Physics
Efficient spectral-Galerkin methods for polar and cylindrical geometries
Applied Numerical Mathematics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
A Fourier-Legendre spectral element method in polar coordinates
Journal of Computational Physics
Journal of Computational Physics
Discrete geometric approach for modelling quantization effects in nanoscale electron devices
Journal of Computational Electronics
Computers & Mathematics with Applications
Hi-index | 31.48 |
Two spectral collocation schemes on the unit disc are presented. The first one is based on the mapping of Gordon and Hall. Here the unit square is directly mapped onto the unit disc by means of an interpolation technique. Unlike other Poisson solvers on the unit disc no polar coordinates are involved. Hence the usual problems with the singularity of polar coordinates are avoided. This is also shown for more complex geometries. The second method is based on a diameter approach where the collocation nodes are no more clustering in the center. Numerical results are presented which demonstrate the high accuracy of our new spectral collocation schemes.