A new closed-form formula for calculating a weakly singular static potential integral with linear current source distribution on a triangle
The article presents a closed-form formula for solving a weakly singular surface integral with a linear current source distribution associated with the SIE-MoM formulation used for solving electromagnetic (EM) problems. The analytical formula was obtained by transforming the surface integral over a...
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| Format: | Article |
| Language: | English |
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Polish Academy of Sciences
2023-02-01
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| Series: | Bulletin of the Polish Academy of Sciences: Technical Sciences |
| Subjects: | |
| Online Access: | https://journals.pan.pl/Content/126045/PDF/BPASTS_2023_71_1_3115.pdf |
| _version_ | 1797862388528054272 |
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| author | Anna Grytsko Piotr Słobodzian |
| author_facet | Anna Grytsko Piotr Słobodzian |
| author_sort | Anna Grytsko |
| collection | DOAJ |
| description | The article presents a closed-form formula for solving a weakly singular surface integral with a linear current source distribution associated with the SIE-MoM formulation used for solving electromagnetic (EM) problems. The analytical formula was obtained by transforming the surface integral over a triangular domain into a double integral, and then directly determining formulas for the inner and outer integrals. The solution obtained is marked by high computational efficiency, high accuracy, and very simple implementation. The derived formula, in contrast to the currently available formulas, consists of quantities that have a clear and simple geometric interpretation, related to the geometry of the computational domain. |
| first_indexed | 2024-04-09T22:19:40Z |
| format | Article |
| id | doaj.art-8ea53ecd981443b29b380c2fc3af83ef |
| institution | Directory Open Access Journal |
| issn | 2300-1917 |
| language | English |
| last_indexed | 2024-04-09T22:19:40Z |
| publishDate | 2023-02-01 |
| publisher | Polish Academy of Sciences |
| record_format | Article |
| series | Bulletin of the Polish Academy of Sciences: Technical Sciences |
| spelling | doaj.art-8ea53ecd981443b29b380c2fc3af83ef2023-03-22T17:47:55ZengPolish Academy of SciencesBulletin of the Polish Academy of Sciences: Technical Sciences2300-19172023-02-01711https://doi.org/10.24425/bpasts.2022.143645A new closed-form formula for calculating a weakly singular static potential integral with linear current source distribution on a triangleAnna Grytsko0https://orcid.org/0000-0002-1107-6575Piotr Słobodzian1https://orcid.org/0000-0003-3545-9228Wroclaw University of Science and Technology, Faculty of Information and Communication Technology, Wybrzeze Wyspiańskiego 27, 50-370 Wrocław, PolandWroclaw University of Science and Technology, Faculty of Information and Communication Technology, Wybrzeze Wyspiańskiego 27, 50-370 Wrocław, PolandThe article presents a closed-form formula for solving a weakly singular surface integral with a linear current source distribution associated with the SIE-MoM formulation used for solving electromagnetic (EM) problems. The analytical formula was obtained by transforming the surface integral over a triangular domain into a double integral, and then directly determining formulas for the inner and outer integrals. The solution obtained is marked by high computational efficiency, high accuracy, and very simple implementation. The derived formula, in contrast to the currently available formulas, consists of quantities that have a clear and simple geometric interpretation, related to the geometry of the computational domain.https://journals.pan.pl/Content/126045/PDF/BPASTS_2023_71_1_3115.pdfstatic vector potential integrallinear current source distributionanalytic integrationweakly singular integralsisoparametric transformationintegration over a triangular domain |
| spellingShingle | Anna Grytsko Piotr Słobodzian A new closed-form formula for calculating a weakly singular static potential integral with linear current source distribution on a triangle Bulletin of the Polish Academy of Sciences: Technical Sciences static vector potential integral linear current source distribution analytic integration weakly singular integrals isoparametric transformation integration over a triangular domain |
| title | A new closed-form formula for calculating a weakly singular static potential integral with linear current source distribution on a triangle |
| title_full | A new closed-form formula for calculating a weakly singular static potential integral with linear current source distribution on a triangle |
| title_fullStr | A new closed-form formula for calculating a weakly singular static potential integral with linear current source distribution on a triangle |
| title_full_unstemmed | A new closed-form formula for calculating a weakly singular static potential integral with linear current source distribution on a triangle |
| title_short | A new closed-form formula for calculating a weakly singular static potential integral with linear current source distribution on a triangle |
| title_sort | new closed form formula for calculating a weakly singular static potential integral with linear current source distribution on a triangle |
| topic | static vector potential integral linear current source distribution analytic integration weakly singular integrals isoparametric transformation integration over a triangular domain |
| url | https://journals.pan.pl/Content/126045/PDF/BPASTS_2023_71_1_3115.pdf |
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