Basic differential models for coordinate generation
type: Item
instance of: scholarly article
title: Basic differential models for coordinate generation
zbMATH Open document ID: 0539.65084
DOI: 10.1016/0096-3003(82)90187-4
published in: Applied Mathematics and Computation
publication date: 1982-01-01T00:00:00Z
review text: This paper examines in detail the analytical aspects of three distinct methods of coordinate generation based on partial differential equations, in either two or three dimensions. The first method is based on the Gauss equations of a surface under the constraint of the Beltrami's second order equations. These equations have been structured in such a way that an automatic connection is established between the succeeding generated surfaces. The second method is a re-examination of those equations which are based on the inhomogeneous Laplace equations. This analysis reveals a new form for the terms which play a role in the concentration of coordinate lines and in the adaptive coordinate system generation. The third method pertains to a set of equations in the metric coefficients which is obtained by setting the Riemann's curvature tensor to zero.
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 3858359
zbMATH Keywords: Gauss equations
zbMATH Keywords: Laplace equations
zbMATH Keywords: Riemann tensor
zbMATH Keywords: coordinate generation
zbMATH Keywords: Beltrami's second order equations
author: Zahir U. A. Warsi
MaRDI profile type: Publication
full work available at URL: 0096-3003(82)90187-4
OpenAlex ID: W2054862223
cites work: Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary two-dimensional bodies
cites work: A multi-surface method of coordinate generation
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description: scientific article; zbMATH DE number 3858359