Numerical techniques for conformal mapping onto a rectangle

Papamichael, N.; Kokkinos, C. A.; Warby, M. K.

doi:10.1016/0377-0427(87)90152-x

Cited by 17 publications

(7 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…g . [4], [32] and [35]. For this reason, in theory at least, the problem of approximating F may be regarded as solved once a suitable approximation t o f :…”

Section: Can Be Determined By Computing T H E R a T I O O F T W O C Omentioning

confidence: 99%

Numerical conformal mapping onto a rectangle with applications to the solution of Laplacian problems

Papamichael

1989

Journal of Computational and Applied Mathematics

Self Cite

View full text Add to dashboard Cite

Let F be the function which maps conformally a simple-connected domain Ω onto a rectangle R, so that four specified points on are mapped Ω ∂ respectively onto the four vertices of R. In this paper we consider the problem of approximating the conformal map F, and present a survey of the available numerical methods. We also illustrate the practical significance of the conformal map, by presenting a number of applications involving the solution of Laplacian boundary value problems.

show abstract

“…g . [4], [32] and [35]. For this reason, in theory at least, the problem of approximating F may be regarded as solved once a suitable approximation t o f :…”

Section: Can Be Determined By Computing T H E R a T I O O F T W O C Omentioning

confidence: 99%

Numerical conformal mapping onto a rectangle with applications to the solution of Laplacian problems

Papamichael

1989

Journal of Computational and Applied Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…(ii) The method can be used to overcome the "crowding" difficulties associated with the numerical conformal mapping of "long" quadrilaterals of the form (1.3). (Full details of the crowding phenomenon and its damaging effects on numerical procedures for the mapping of "long" -7quadrilaterals can be found in [12], [13] and [10]; see also [4:p.l79 and let E h and E g { j }, E X { j }, j = 1,2, denote the following domain decomposition errors:…”

Section: Introductionmentioning

confidence: 99%

On the numerical performance of a domain decomposition method for conformal mapping

Papamichael

Stylianopoulos

1990

Computational Methods and Function Theory

Self Cite

View full text Add to dashboard Cite

“…The theory of conformal mapping is rich and mature. Comprehensive treatments can be found in [5,6,13]. In any case, a brief introduction to the notion of conformality and mapping composition is provided in the appendix.…”

Section: Conformal Mappingmentioning

confidence: 99%

Looking at Cellular Networks Through Canonical Domains and Conformal Mapping

Gonzalez

Hämäläinen

2016

IEEE Trans. Wireless Commun.

View full text Add to dashboard Cite

In order to cope with the rapidly increasing service demand in cellular networks, more cells are needed with better resource usage efficiency. This poses challenges for the network planning since service demand in practical networks is not geographically uniform and, to cope with the non-uniform service demand, network deployments are becoming increasingly irregular. This paper introduces a new idea to deal with the non-uniform network topology. Rather than capturing the network character (e.g. load distribution) by means of stochastic methods, the proposed novel approach aims at transforming the analysis from the physical (irregular) domain to a canonical/dual (uniform) domain that simplifies the work due to its symmetry. To carry out this task, physical and canonical domains are connected using the conformal (Schwarz-Christoffel) mapping, that makes the rich and mature theory of Complex Analysis available. The main contribution of this paper is to introduce and validate the usability of conformal mapping in the load coupling analysis of cellular networks.

show abstract

Numerical techniques for conformal mapping onto a rectangle

Abstract: This paper is concerned with the problem of determining approximations to the function F which maps conformally a simply-connected domain Ω onto a rectangle R, so that four specified points on are mapped Ω ∂

Cited by 17 publications

References 13 publications

Numerical conformal mapping onto a rectangle with applications to the solution of Laplacian problems

Numerical conformal mapping onto a rectangle with applications to the solution of Laplacian problems

On the numerical performance of a domain decomposition method for conformal mapping

Looking at Cellular Networks Through Canonical Domains and Conformal Mapping

Contact Info

Product

Resources

About