Regularization of an external boundary value problem for open axisymmetric magnetic systems


  • O. Spivak
  • V. Tkachenko



magnetic field tension, scalar magnetic potential, boundary conditions, quasi-random method


Important characteristic of magnetic-field with the high measure of intensity and heterogeneity in the swept volume of the electromagnetic systems is a size of tension of the field Н. Calculation of tension in the field H in these systems, characterized by relatively large air interval, given its three-dimensionalty, presents a very difficult task.

Analytical decision of equalization of Laplace that describes distribution of magnetic-field in the interpolar volume of the axisymmetrical magnetic systems, difficultly from difficult geometry of bodies that is included in a calculation area, that is why for research of distribution of tension the expedient use of numeral methods of calculation - to the method of eventual differences, method of eventual elements, method of maximum integral equalizations.

The calculation of distribution of scalar magnetic potential in open magnetic systems with the use of numeral methods of calculation causes the difficulties related to limitation of calculation  area in which the calculation is conducted.

The static magnetic fields, analysed in this research, obey one of basic equalizations of mathematical physics, and namely, to equalization of Laplace in partial differential.

In case of calculation of magnetic field of the axisymmetrical magnetic systems it is necessary to resolve the Cauchy problem for equalization of Laplace. It is known, that this task does not have characteristic of steadyness, and thus does not obey Hadamars third condition of correctness and, therefore, is considered incorrectly defined.

For the number of unsteady tasks of mathematical physics of R.Lattes and ZH.Lions developed the quasi-random method, that can be applied both for evolutional tasks, as well as for constant. The basic idea of quasi-random method lays in proper update of differential operators that are part of the task. This change is done by introducing additional differential elements. Application of this method allows to use effectively the numeral methods of calculation of regional task for  open axisymmetrical systems.


Буль О.Б. Методы расчета магнитных систем электрических аппаратов. Магнитные цепи, поля и программа FEMM. М.: Академия, 2005. 336 с.

Андреева Е.Г., Татевосян А.А., Семина И.А. Исследование осесимметричной модели магнитной системы открытого типа. Омский научный вестник. 2010. Вып.1(87). С.110-113.

Alternative method to calculate the magnetic field of permanent magnets with azimuthal symmetry / Camacho J.M., Sosa V. // Revista Mexicana de F´ısica. 2013. Vol. 59. P. 8–17.

Steinbach O. Numerical approximation methods for elliptic boundary value problems. New York: Springer, 2008.

Sivak S. Boundary Element Method for eddy current problem // Actual Problems of Electronics Instrument Engineering (APEIE), 2014 12th International Conference on. IEEE. 2014. С. 207—214.

Kuczmann M. Potential formulations in magnetics applying the finite element method // Lecture notes, Laboratory of Electromagnetic Fields,“Sz´echenyi Istv´an” University, Gyor, Hungary. 2009.

Самарский А.А., Вабищев П.Н. Численные методы решения обратных задач математической физики: Учебное пособие. Изд.3-е. М.: Издательство ЛКИ, 2009. 480с.

Тихонов А.Н., Самарский А.А. Уравнения математической физики. 7-е изд. М.: Наука, 2004. 798 с.

Кабанихин С. И. Обратные и некорректные задачи. Новосибирск: Издательство СО РАН, 2018. 511с.

Воронин А.Ф. , Ковтанюк А.Е. , Лаврентьев М.М. Краевая задача Римана в исследовании корректности линейных и нелинейных задач математической физики. Сиб. электрон. матем. изв. 2010. Вып.7. С. 112–122.

Султанов М.А., Калматаева Б.Б. О решении граничной обратной задачи для параболического уравнения методом квазиобращения. Научные труды ЮКГУ им.М.Ауэзова. 2016. Вып.1(36). С. 63-67.

Gorobchenko O., Tkachenko V. Statistical analysis of locomotives traction motors performance. // MATEC Web of Conferences. 2019. Vol. 287, p. 04002. EDP Sciences.

Goolak S., Gerlici J., Sapronova S., Tkachenko V., Lack T., & Kravchenko K. Determination of Parameters of Asynchronous Electric Machines with Asymmetrical Windings of Electric Locomotives. // Communications-Scientific letters of the University of Zilina, 2019. 21(2), 24-31. ISSN 2585-7878.

Finite element formulation with coupled vector-scalar magnetic potentials for eddy current problems // 11th International Forum on Strategic Technology (IFOST-2016). IEEE. 2016. С. 456–460.

Yufeng L., Fengtao Y. Research progress and development trend of permanent magnetic separators in China and abroad // Proceedings of 3rd International Conference on Vehicle, Mechanical and Electrical Engineering (ICMVEE). U.S.A. 2016. https://doi:10.12783/dtetr/icvmee2016/4873.



How to Cite

Spivak, O., & Tkachenko, V. (2020). Regularization of an external boundary value problem for open axisymmetric magnetic systems. Transport Systems and Technologies, (35), 80–88.



Technics and techology

Most read articles by the same author(s)

1 2 > >>