On the Kelvin Transformation in Finite Difference Implementations

On the Kelvin Transformation in Finite Difference Implementations

Finite difference operators were applied on a Delaunay mesh. This way it is possible to discretize a radial boundary that is used to perform a Kelvin mapping of an additional outer domain to virtually extend the computation domain to infinity. With an example two-wire problem, the performance of thi...

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Bibliographic Details
Main Author: Gerald Gold
Format: Article
Language:English
Published: MDPI AG 2020-03-01
Series:Electronics
Subjects:
delaunay mesh
fem mesh
finite differences
infinite differences
kelvin mapping
kelvin transformation
open boundary
unbounded grid
Online Access:https://www.mdpi.com/2079-9292/9/3/442
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spelling doaj-9f11927fed4b4c07ba25840a8f49d2572020-11-25T02:09:30ZengMDPI AGElectronics2079-92922020-03-019344210.3390/electronics9030442electronics9030442On the Kelvin Transformation in Finite Difference ImplementationsGerald Gold0Institute of Microwaves and Photonics, Friedrich-Alexander University Erlangen-Nuremberg (FAU), 91054 Erlangen, GermanyFinite difference operators were applied on a Delaunay mesh. This way it is possible to discretize a radial boundary that is used to perform a Kelvin mapping of an additional outer domain to virtually extend the computation domain to infinity. With an example two-wire problem, the performance of this approach is shown in comparison with a conventional calculation domain and with the analytical solution, respectively. The presented implementation delivers a more precise approximation to the real values and at the same time requires a smaller system of equations—i.e., allows for faster computations.https://www.mdpi.com/2079-9292/9/3/442delaunay meshfem meshfinite differencesinfinite differenceskelvin mappingkelvin transformationopen boundaryunbounded grid
collection DOAJ
language English
format Article
sources DOAJ
author Gerald Gold
spellingShingle Gerald Gold
On the Kelvin Transformation in Finite Difference Implementations
Electronics
delaunay mesh
fem mesh
finite differences
infinite differences
kelvin mapping
kelvin transformation
open boundary
unbounded grid
author_facet Gerald Gold
author_sort Gerald Gold
title On the Kelvin Transformation in Finite Difference Implementations
title_short On the Kelvin Transformation in Finite Difference Implementations
title_full On the Kelvin Transformation in Finite Difference Implementations
title_fullStr On the Kelvin Transformation in Finite Difference Implementations
title_full_unstemmed On the Kelvin Transformation in Finite Difference Implementations
title_sort on the kelvin transformation in finite difference implementations
publisher MDPI AG
series Electronics
issn 2079-9292
publishDate 2020-03-01
description Finite difference operators were applied on a Delaunay mesh. This way it is possible to discretize a radial boundary that is used to perform a Kelvin mapping of an additional outer domain to virtually extend the computation domain to infinity. With an example two-wire problem, the performance of this approach is shown in comparison with a conventional calculation domain and with the analytical solution, respectively. The presented implementation delivers a more precise approximation to the real values and at the same time requires a smaller system of equations—i.e., allows for faster computations.
topic delaunay mesh
fem mesh
finite differences
infinite differences
kelvin mapping
kelvin transformation
open boundary
unbounded grid
url https://www.mdpi.com/2079-9292/9/3/442
work_keys_str_mv AT geraldgold onthekelvintransformationinfinitedifferenceimplementations
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