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Resolving the sign conflict problem for hp–hexahedral Nédélec elements with application to eddy current problems

R.M. Kynch, P.D. Ledger, Paul Ledger

Computers & Structures, Volume: 181, Pages: 41 - 54

Swansea University Author: Paul Ledger

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DOI (Published version): 10.1016/j.compstruc.2016.05.021

Abstract

The eddy current approximation of Maxwell’s equations is relevant for Magnetic Induction Tomography (MIT), which is a practical system for the detection of conducting inclusions from measurements of mutual inductance with both industrial and clinical applications. An MIT system produces a conductivi...

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Published in: Computers & Structures
ISSN: 0045-7949
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa29408
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first_indexed 2016-08-02T19:01:23Z
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spelling 2020-10-19T12:55:39.7997233 v2 29408 2016-08-02 Resolving the sign conflict problem for hp–hexahedral Nédélec elements with application to eddy current problems 068dd31af167bcda33878951b2a01e97 Paul Ledger Paul Ledger true false 2016-08-02 FGSEN The eddy current approximation of Maxwell’s equations is relevant for Magnetic Induction Tomography (MIT), which is a practical system for the detection of conducting inclusions from measurements of mutual inductance with both industrial and clinical applications. An MIT system produces a conductivity image from the measured fields by solving an inverse problem computationally. This is typically an iterative process, which requires the forward solution of a Maxwell’s equations for the electromagnetic fields in and around conducting bodies at each iteration. As the (conductivity) images are typically described by voxels, a hexahedral finite element grid is preferable for the forward solver. Low order Nédélec (edge element) discretisations are generally applied, but these require dense meshes to ensure that skin effects are properly captured. On the other hand, hp–Nédélec finite elements can ensure the skin effects in conducting components are accurately captured, without the need for dense meshes and, therefore, offer possible advantages for MIT. Unfortunately, the hierarchic nature of hp–Nédélec basis functions introduces edge and face parameterisations leading to sign conflict issues when enforcing tangential continuity between elements. This work describes a procedure for addressing this issue on general conforming hexahedral meshes and an implementation of a hierarchic hp–Nédélec finite element basis within the deal.II finite element library. The resulting software is used to simulate Maxwell forward problems, including those set on multiply connected domains, to demonstrate its potential as an MIT forward solver. Journal Article Computers & Structures 181 41 54 0045-7949 31 3 2017 2017-03-31 10.1016/j.compstruc.2016.05.021 2016 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license(http://creativecommons.org/licenses/by/4.0/). COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University RCUK, EP/K023950/1 2020-10-19T12:55:39.7997233 2016-08-02T13:49:02.4688761 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised R.M. Kynch 1 P.D. Ledger 2 Paul Ledger 3 0029408-07022017141310.pdf kynch2017.pdf 2017-02-07T14:13:10.8100000 Output 1194135 application/pdf Version of Record true 2017-02-07T00:00:00.0000000 false
title Resolving the sign conflict problem for hp–hexahedral Nédélec elements with application to eddy current problems
spellingShingle Resolving the sign conflict problem for hp–hexahedral Nédélec elements with application to eddy current problems
Paul Ledger
title_short Resolving the sign conflict problem for hp–hexahedral Nédélec elements with application to eddy current problems
title_full Resolving the sign conflict problem for hp–hexahedral Nédélec elements with application to eddy current problems
title_fullStr Resolving the sign conflict problem for hp–hexahedral Nédélec elements with application to eddy current problems
title_full_unstemmed Resolving the sign conflict problem for hp–hexahedral Nédélec elements with application to eddy current problems
title_sort Resolving the sign conflict problem for hp–hexahedral Nédélec elements with application to eddy current problems
author_id_str_mv 068dd31af167bcda33878951b2a01e97
author_id_fullname_str_mv 068dd31af167bcda33878951b2a01e97_***_Paul Ledger
author Paul Ledger
author2 R.M. Kynch
P.D. Ledger
Paul Ledger
format Journal article
container_title Computers & Structures
container_volume 181
container_start_page 41
publishDate 2017
institution Swansea University
issn 0045-7949
doi_str_mv 10.1016/j.compstruc.2016.05.021
college_str Faculty of Science and Engineering
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hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
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description The eddy current approximation of Maxwell’s equations is relevant for Magnetic Induction Tomography (MIT), which is a practical system for the detection of conducting inclusions from measurements of mutual inductance with both industrial and clinical applications. An MIT system produces a conductivity image from the measured fields by solving an inverse problem computationally. This is typically an iterative process, which requires the forward solution of a Maxwell’s equations for the electromagnetic fields in and around conducting bodies at each iteration. As the (conductivity) images are typically described by voxels, a hexahedral finite element grid is preferable for the forward solver. Low order Nédélec (edge element) discretisations are generally applied, but these require dense meshes to ensure that skin effects are properly captured. On the other hand, hp–Nédélec finite elements can ensure the skin effects in conducting components are accurately captured, without the need for dense meshes and, therefore, offer possible advantages for MIT. Unfortunately, the hierarchic nature of hp–Nédélec basis functions introduces edge and face parameterisations leading to sign conflict issues when enforcing tangential continuity between elements. This work describes a procedure for addressing this issue on general conforming hexahedral meshes and an implementation of a hierarchic hp–Nédélec finite element basis within the deal.II finite element library. The resulting software is used to simulate Maxwell forward problems, including those set on multiply connected domains, to demonstrate its potential as an MIT forward solver.
published_date 2017-03-31T03:35:45Z
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