Enviar artigo por via de e-mail The 2D Magnetostatics Inverse Problem for Homogeneously Magnetized Bodies
- Autores: Dyakin V.V.1, Kudryashova O.V.1, Rayevsky V.Y.1
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Afiliações:
- Mikheev Institute of Metal Physics of the Ural Branch of the Russian Academy of Sciences
- Edição: Nº 2 (2025)
- Páginas: 39-52
- Seção: Electromagnetic methods
- URL: https://bakhtiniada.ru/0130-3082/article/view/276322
- DOI: https://doi.org/10.31857/S0130308225020049
- ID: 276322
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Resumo
We consider 2D magnetostatics inverse problem for uniformly magnetized body and reduce it to a nonlinear 1D integrodifferential equation determining body(cavity) shape based on the measured strength of the external magnetic field. We design an numerical algorithm for solution of this equation based on minimization of a function of several variables and develop a FORTRAN program implementing this algorithm. To test and illustrate our approach we find a solution for the cross-section of a homogeneous infinite cylinder in a non-magnetic and opaque medium based on the known strength of the external field.
Sobre autores
V. Dyakin
Mikheev Institute of Metal Physics of the Ural Branch of the Russian Academy of Sciences
Email: kudryashova_ov@imp.uran.ru
Rússia, 18, S. Kovalevskaya St., Yekaterinburg, 620108
O. Kudryashova
Mikheev Institute of Metal Physics of the Ural Branch of the Russian Academy of Sciences
Autor responsável pela correspondência
Email: kudryashova_ov@mail.ru
Rússia, 18, S. Kovalevskaya St., Yekaterinburg, 620108
V. Rayevsky
Mikheev Institute of Metal Physics of the Ural Branch of the Russian Academy of Sciences
Email: raevskii@imp.uran.ru
Rússia, 18, S. Kovalevskaya St., Yekaterinburg, 620108
Bibliografia
- Pechenkov A N., Shcherbinin V.E. Nekotorye pryamye i obratnye zadachi tekhnicheskoj magnitostatiki. Ekaterinburg: Izd-vo UrO RAN, 2004. 177s.
- Pechenkov A.N., Shcherbinin V.E. O reshenii obratnoj zadachi magnitostaticheskoj tomografii // Defectoskopiya. 2009. No 3. P. 37—55.
- Pechenkov A.N., Shcherbinin V.E. K voprosu o needinstvennosti resheniya obratnoj zadachi magnitostaticheskoj defektoskopii // Kontrol’. Diagnostika. 2006. No. 9. P. 59—60.
- Pechenkov A.N. O vliyanii formy tela na edinstvennost’ resheniya obratnoj zadachi magnitostaticheskoj defektoskopii // Defectoskopiya. 2006. № 10. P. 24—26.
- Dyakin V.V. Pryamaya i obratnaya zadacha magnitostatiki // Defectoskopiya. 1996. No. 3. P. 3—6.
- Dyakin V.V., Kudryashova O.V., Raevskij V.Ya. K voprosu o korrektnosti pryamoj i obratnoj zadachi magnitostatiki. Chast’ 2 // Defectoskopiya. 2018. No. 10. P. 15—24.
- Reutov Yu.Ya., Gobov Yu.L., Loskutov V.E. O vozmozhnostyah ispol’zovaniya programmy ELCUT v raschetah po defektoskopii // Defectoskopiya. 2002. No. 6. P. 34—40.
- Zagidulin R.V., Dyakin V.V., Dudarev M.S., Shcherbinin V.E. K opredeleniyu geometricheskih razmerov poverhnostnogo defekta / Fizicheskie metody i pribory NK. Tezisy dokladov X Ural’skoj nauchnoj tekhnicheskoj konferencii. Izhevsk. 1989. P. 83.
- Novoslugina A.P., Smorodinskij Ya.G. Raschetnyj sposob ocenki parametrov defektov v stalyah // Defectoskopiya. 2017. No. 11. P. 13—19.
- Dyakin V.V., Raevskij V.Ya., Kudryashova O.V. Pole konechnogo defekta v plastine // Defectoskopiya. 2009. No. 3. P. 67—79.
- Krotov L.N. Rekonstrukciya granicy razdela sred po prostranstvennomu raspredeleniyu magnitnogo polya rasseyaniya. 1. Issledovanie svojstv resheniya vspomogatel’noj pryamoj zadachi // Defectoskopiya. 2004. No. 2. P. 76—82.
- Krotov L.N. Rekonstrukciya granicy razdela sred po prostranstvennomu raspredeleniyu magnitnogo polya rasseyaniya. 2. Postanovka i metod resheniya obratnoj geometricheskoj zadachi magnitostatiki // Defectoskopiya. 2004. No. 6. P. 76—82.
- Slesarev D.A., Barat V.A., Chobanu P.M. Snizhenie pogreshnosti statisticheskogo metoda ocenki parametrov defektov v magnitnoj defektoskopii // Defectoskopiya. 2012. No. 1. P. 69—74.
- Gobov Yu.L., Nikitin A.V., Popov S.E. Reshenie obratnoj geometricheskoj zadachi magnitostatiki dlya defektov korrozii // Defectoskopiya. 2018. No. 10. P. 51—57.
- Dyakin V.V., Kudryashova O.V., Raevskij V.Ya. Obratnaya zadacha magnitostatiki v polyah nasyshcheniya // Defectoskopiya. 2019. No. 10. P. 35—44.
- Ahiezer A.I. Obshchaya fizika. Elektricheskie i magnitnye yavleniya. Kiev: Naukova dumka, 1981. 471 p.
- Pechenkov A.N., Shcherbinin V.E. Metod sozdaniya odnorodnoj namagnichennosti i opredeleniya magnitnoj vospriimchivosti // Defectoskopiya. 2002. No. 7. P. 47—50.
- Hizhnyak N.A. Integral’nye uravneniya makroskopicheskoj elektrodinamiki. Kiev: Naukova dumka, 1986. 279 p.
- Friedman M.J. Mathematical Study of the Nonlinear Singular Integral Magnetic Field Equation. 1. // SIAM J. Appl. Math. 1980. V. 39. No. 1. P. 14—20.
- Friedman M.J. Mathematical Study of the Nonlinear Singular Integral Magnetic Field Equation. 2. // SIAM J. Numer. Anal. 1981. V. 18. No. 4. P. 644—653.
- Friedman M.J. Mathematical Study of the Nonlinear Singular Integral Magnetic Field Equation. 3. // SIAM J. Math. Analys. 1981. V. 12. No. 4. P. 536—540.
- Dyakin V.V. Matematicheskie osnovy klassicheskoj magnitostatiki. Ekaterinburg: RIO UrO RAN, 2016. 403 p.
- Raevskij V.Ya. O svojstvah kvaziermitovyh operatorov i ih primenenii k issledovaniyu operatorov teorii potenciala i osnovnogo uravneniya elektro- i magnitostatiki / Preprint № 24/48(01). Ekaterinburg: IFM UrO RAN, 2001.
- Raevskij V.Ya. Nekotorye svojstva operatorov teorii potenciala i ih primenenie k issledovaniyu osnovnogo uravneniya elektro- i magnitostatiki // Teoreticheskaya i matematicheskaya fizika. 1994. V. 3. No. 100. P. 323—331.
- Fihtengol’c G.M. Kurs differencial’nogo i integral’nogo ischisleniya. T. 3. M.: Nauka, 1966. 656 p.
- Prudnikov A.P., Brychkov Yu.A., Marichev O.I. Integraly i ryady. T. 1. M.: Fizmatlit, 2003. 632 p.
- Dyakin V.V., Kudryashova O.V., Raevskij V.Ya. Raschet napryazhennosti magnitnogo polya vnutri i vne beskonechnogo cilindra, pomeshchennogo v proizvol’noe vneshnee pole // Defectoskopiya. 2024. No. 3. P. 33—46.
- Panteleev A.V., Letova T.A. Metody optimizacii v primerah i zadachah. M.: Vyssh. shk., 2002. 544 p.
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