The asymptotic behavior of conformal modules of quadrilaterals with applications to the estimation of resistance values
type: Item
instance of: scholarly article
title: The asymptotic behavior of conformal modules of quadrilaterals with applications to the estimation of resistance values
zbMATH Open document ID: 0917.30008
author: N. Papamichael
author: Nikos S. Stylianopoulos
published in: Constructive Approximation
publication date: 1999-08-16T00:00:00Z
review text: If a quadrilateral \(Q\) is subdivided by crosscuts in \(Q\) into component quadrilaterals \(Q_j\) and \(m(Q)\), \(m(Q_j)\) are their conformal modules, the composition law gives \(m(Q)\geq \sum_j m(Q_j)\). One aspect of the present paper is to present asymptotic error estimates for \(m(Q)-\sum_jm(Q_j)\) in case that \(Q\) is `long' in one or two directions. These error estimates use previous estimates by Gaier and Hayman (1991) for simpler geometries. A special feature is the comparison of the authors' results with engineering rules that are used in the construction of integrated circuit networks. This is possible because \(m(Q)\) can be interpreted as the resistance of a conducting plate. These rules can now be used with error estimates. In a numerical example, \(Q\) is a polygonal domain with 30 corners, and \(m(Q)\) is determined with six correct decimals.
reviewed by: Dieter Gaier
Mathematics Subject Classification ID: 30C30
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 30C35
zbMATH DE Number: 1271886
describes a project that uses: Schwarz-Christoffel
describes a project that uses: SC Toolbox
MaRDI profile type: Publication
full work available at URL: s003659900100
OpenAlex ID: W2166514023
DOI: 10.1007/S003659900100
description: scientific article; zbMATH DE number 1271886