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A Direct Spectral Collocation Poisson Solver in Polar and Cylindrical Coordinates

✍ Scribed by Heli Chen; Yuhong Su; Bernie D. Shizgal

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 125 KB
Volume: 160
Category: Article
ISSN: 0021-9991
DOI: 10.1006/jcph.2000.6461

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✦ Synopsis

In this paper, we present a direct spectral collocation method for the solution of the Poisson equation in polar and cylindrical coordinates. The solver is applied to the Poisson equations for several different domains including a part of a disk, an annulus, a unit disk, and a cylinder. Unlike other Poisson solvers for geometries such as unit disks and cylinders, no pole condition is involved for the present solver. The method is easy to implement, fast, and gives spectral accuracy. We also use the weighted interpolation technique and nonclassical collocation points to improve the convergence.

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