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

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

Abstract

A procedure for addressing the sign conflict issue for conforming hexahedral meshes.An efficient implementation of hierarchic hp-Nedelec elements in deal.II.Solution of a series of challenging 3D eddy current benchmark problems.Description of the extension to non-conforming hexahedral meshes. The eddy current approximation of Maxwells 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 Maxwells 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 Ndlec (edge element) discretisations are generally applied, but these require dense meshes to ensure that skin effects are properly captured. On the other hand, hpNdlec 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 hpNdlec 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 hpNdlec 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.

Citation

Kynch, R., & Ledger, P. (2017). Resolving the sign conflict problem for hp–hexahedral Nédélec elements with application to eddy current problems. Computers and Structures, 181, 41-54. https://doi.org/10.1016/j.compstruc.2016.05.021

• Journal Article Type: Article
• Publication Date: 2017-03
• Deposit Date: Jun 12, 2023
• Journal: Computers & Structures
• Print ISSN: 0045-7949
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 181
• Pages: 41-54
• DOI: https://doi.org/10.1016/j.compstruc.2016.05.021
• Keywords: Computer Science Applications; Mechanical Engineering; General Materials Science; Modeling and Simulation; Civil and Structural Engineering
• Additional Information: This article is maintained by: Elsevier; Article Title: Resolving the sign conflict problem for hp–hexahedral Nédélec elements with application to eddy current problems; Journal Title: Computers & Structures; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.compstruc.2016.05.021; Content Type: article; Copyright: © 2016 The Author(s). Published by Elsevier Ltd.