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A direct spectral collocation Poisson solver in polar and cylindrical coordinates

TitleA direct spectral collocation Poisson solver in polar and cylindrical coordinates
Publication TypeJournal Article
Year of Publication2000
AuthorsChen, HL, Su, YH, Shizgal, BD
JournalJournal of Computational Physics
Volume160
Pagination453-469
Date PublishedMay
Type of ArticleArticle
ISBN Number0021-9991
KeywordsARBITRARY ORDER ACCURACY, coordinates, cylindrical, EXPANSION, METHOD QDM, NONCLASSICAL BASIS FUNCTIONS, Poisson solver, polar coordinates, QUADRATURE DISCRETIZATION METHOD, SCHRODINGER-EQUATION, SINGULARITIES, spectral collocation, TSCHEBYSCHEFF POLYNOMIALS
Abstract

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. (C) 2000 Academic Press.
URL<Go to ISI>://000087093200002