On the Tree Gauge in Magnetostatics
We recall the classical tree-cotree technique in magnetostatics. (1) We extend it in the frame of high-order finite elements in general domains. (2) We focus on its connection with the question of the invertibility of the final algebraic system arising from a high-order edge finite element discretiz...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | J |
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| Online Access: | https://www.mdpi.com/2571-8800/5/1/4 |
| _version_ | 1797470600500871168 |
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| author | Francesca Rapetti Ana Alonso Rodríguez Eduardo De Los Santos |
| author_facet | Francesca Rapetti Ana Alonso Rodríguez Eduardo De Los Santos |
| author_sort | Francesca Rapetti |
| collection | DOAJ |
| description | We recall the classical tree-cotree technique in magnetostatics. (1) We extend it in the frame of high-order finite elements in general domains. (2) We focus on its connection with the question of the invertibility of the final algebraic system arising from a high-order edge finite element discretization of the magnetostatic problem formulated in terms of the magnetic vector potential. With the same purpose of invertibility, we analyse another classically used condition, the Coulomb gauge. (3) We conclude by underlying that the two gauges can be naturally considered in a high order framework without any restriction on the topology of the domain. |
| first_indexed | 2024-03-09T19:38:42Z |
| format | Article |
| id | doaj.art-4c7aadc8ae9e476abe5d2c4999b01e32 |
| institution | Directory Open Access Journal |
| issn | 2571-8800 |
| language | English |
| last_indexed | 2024-03-09T19:38:42Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | J |
| spelling | doaj.art-4c7aadc8ae9e476abe5d2c4999b01e322023-11-24T01:45:38ZengMDPI AGJ2571-88002022-01-0151526310.3390/j5010004On the Tree Gauge in MagnetostaticsFrancesca Rapetti0Ana Alonso Rodríguez1Eduardo De Los Santos2Laboratoire Mathématiques & Interactions, Université Côte d’Azur, Parc Valrose, F-06108 Nice, FranceDipartimento di Matematica, Università degli Studi di Trento, Via Sommarive 14, Povo, I-38123 Trento, ItalyDipartimento di Matematica, Università degli Studi di Trento, Via Sommarive 14, Povo, I-38123 Trento, ItalyWe recall the classical tree-cotree technique in magnetostatics. (1) We extend it in the frame of high-order finite elements in general domains. (2) We focus on its connection with the question of the invertibility of the final algebraic system arising from a high-order edge finite element discretization of the magnetostatic problem formulated in terms of the magnetic vector potential. With the same purpose of invertibility, we analyse another classically used condition, the Coulomb gauge. (3) We conclude by underlying that the two gauges can be naturally considered in a high order framework without any restriction on the topology of the domain.https://www.mdpi.com/2571-8800/5/1/4magnetic vector potentialhigh order edge finite elementstree gaugeCoulomb gauge |
| spellingShingle | Francesca Rapetti Ana Alonso Rodríguez Eduardo De Los Santos On the Tree Gauge in Magnetostatics J magnetic vector potential high order edge finite elements tree gauge Coulomb gauge |
| title | On the Tree Gauge in Magnetostatics |
| title_full | On the Tree Gauge in Magnetostatics |
| title_fullStr | On the Tree Gauge in Magnetostatics |
| title_full_unstemmed | On the Tree Gauge in Magnetostatics |
| title_short | On the Tree Gauge in Magnetostatics |
| title_sort | on the tree gauge in magnetostatics |
| topic | magnetic vector potential high order edge finite elements tree gauge Coulomb gauge |
| url | https://www.mdpi.com/2571-8800/5/1/4 |
| work_keys_str_mv | AT francescarapetti onthetreegaugeinmagnetostatics AT anaalonsorodriguez onthetreegaugeinmagnetostatics AT eduardodelossantos onthetreegaugeinmagnetostatics |