A spectral method for unbounded domains
type: Item
instance of: scholarly article
title: A spectral method for unbounded domains
zbMATH Open document ID: 0887.65103
author: J. Ning
published in: Journal of Computational Physics
publication date: 1998-05-25T00:00:00Z
review text: The spectral method for an unbounded domain is developed and presented. For the expansion in the radial direction of polar coordinates \((r,\varphi)\) or \((r, \varphi, z)\) rational basis functions which are algebraically mapped Legendre functions are used. These functions satisfy the pole condition exactly at the coordinate singularity and their behavior as \(r\to\infty\) is suitable for expanding smooth functions which decay algebraically or exponentially as \(r\to\infty\). This method is not stiff when it is applied to an initial value problem despite the presence of coordinate singularity. Solenoidal vector fields are treated efficiently by the toroidal and poloidal decomposition which reduces the number of dependent variables from 3 to 2. Examples which include the computation of vortex dynamics in two and three dimensions are also given.
Mathematics Subject Classification ID: 65M70
zbMATH DE Number: 1100739
zbMATH Keywords: numerical examples
zbMATH Keywords: toroidal decomposition
zbMATH Keywords: spectral method
zbMATH Keywords: unbounded domain
zbMATH Keywords: vector fields
zbMATH Keywords: poloidal decomposition
zbMATH Keywords: vortex dynamics
reviewed by: Jiří Vaníček
MaRDI profile type: Publication
OpenAlex ID: W1974210344
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DOI: 10.1006/JCPH.1997.5804
description: scientific article; zbMATH DE number 1100739