The Hybrid FEM-DBCI for the Solution of Open-Boundary Low-Frequency Problems
This paper describes a particular use of the hybrid FEM-DBCI, for the computation of low-frequency electromagnetic fields in open-boundary domains. Once the unbounded free space enclosing the system has been truncated, the FEM is applied to the bounded domain thus obtained, assuming an unknown Diric...
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MDPI AG
2021-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/16/1968 |
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| author | Giovanni Aiello Salvatore Alfonzetti Santi Agatino Rizzo Nunzio Salerno |
| author_facet | Giovanni Aiello Salvatore Alfonzetti Santi Agatino Rizzo Nunzio Salerno |
| author_sort | Giovanni Aiello |
| collection | DOAJ |
| description | This paper describes a particular use of the hybrid FEM-DBCI, for the computation of low-frequency electromagnetic fields in open-boundary domains. Once the unbounded free space enclosing the system has been truncated, the FEM is applied to the bounded domain thus obtained, assuming an unknown Dirichlet condition on the truncation boundary. An integral equation is used to express this boundary condition in which the integration surface is selected in the middle of the most external layer of finite elements, very close to the truncation boundary, so that the integral equation becomes quasi-singular. The method is described for the computation of electrostatic fields in 3D and of eddy currents in 2D, but it is also applicable to the solution of other kinds of electromagnetic problems. Comparisons are made with other methods, concluding that FEM-DBCI is competitive with the well-known FEM-BEM and coordinate transformations for what concerns accuracy and computing time. |
| first_indexed | 2024-03-10T08:37:22Z |
| format | Article |
| id | doaj.art-b2d25e8b726f47c3b46f34abb0417f39 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T08:37:22Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b2d25e8b726f47c3b46f34abb0417f392023-11-22T08:34:35ZengMDPI AGMathematics2227-73902021-08-01916196810.3390/math9161968The Hybrid FEM-DBCI for the Solution of Open-Boundary Low-Frequency ProblemsGiovanni Aiello0Salvatore Alfonzetti1Santi Agatino Rizzo2Nunzio Salerno3Dipartimento di Ingegneria Elettrica, Elettronica e Informatica (DIEEI), Università di Catania, Viale A. Doria, 6, I-95125 Catania, ItalyDipartimento di Ingegneria Elettrica, Elettronica e Informatica (DIEEI), Università di Catania, Viale A. Doria, 6, I-95125 Catania, ItalyDipartimento di Ingegneria Elettrica, Elettronica e Informatica (DIEEI), Università di Catania, Viale A. Doria, 6, I-95125 Catania, ItalyDipartimento di Ingegneria Elettrica, Elettronica e Informatica (DIEEI), Università di Catania, Viale A. Doria, 6, I-95125 Catania, ItalyThis paper describes a particular use of the hybrid FEM-DBCI, for the computation of low-frequency electromagnetic fields in open-boundary domains. Once the unbounded free space enclosing the system has been truncated, the FEM is applied to the bounded domain thus obtained, assuming an unknown Dirichlet condition on the truncation boundary. An integral equation is used to express this boundary condition in which the integration surface is selected in the middle of the most external layer of finite elements, very close to the truncation boundary, so that the integral equation becomes quasi-singular. The method is described for the computation of electrostatic fields in 3D and of eddy currents in 2D, but it is also applicable to the solution of other kinds of electromagnetic problems. Comparisons are made with other methods, concluding that FEM-DBCI is competitive with the well-known FEM-BEM and coordinate transformations for what concerns accuracy and computing time.https://www.mdpi.com/2227-7390/9/16/1968finite element methodintegral equationsopen-boundary problemselectrostaticsskin effectGMRES |
| spellingShingle | Giovanni Aiello Salvatore Alfonzetti Santi Agatino Rizzo Nunzio Salerno The Hybrid FEM-DBCI for the Solution of Open-Boundary Low-Frequency Problems Mathematics finite element method integral equations open-boundary problems electrostatics skin effect GMRES |
| title | The Hybrid FEM-DBCI for the Solution of Open-Boundary Low-Frequency Problems |
| title_full | The Hybrid FEM-DBCI for the Solution of Open-Boundary Low-Frequency Problems |
| title_fullStr | The Hybrid FEM-DBCI for the Solution of Open-Boundary Low-Frequency Problems |
| title_full_unstemmed | The Hybrid FEM-DBCI for the Solution of Open-Boundary Low-Frequency Problems |
| title_short | The Hybrid FEM-DBCI for the Solution of Open-Boundary Low-Frequency Problems |
| title_sort | hybrid fem dbci for the solution of open boundary low frequency problems |
| topic | finite element method integral equations open-boundary problems electrostatics skin effect GMRES |
| url | https://www.mdpi.com/2227-7390/9/16/1968 |
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