Chebyshev approximation of the steel magnetization characteristic by the sum of a linear expression and an arctangent function

Malachivskyy, P. S.; Pizyur, Ya. V.

doi:10.23939/mmc2019.01.077

Cited by 4 publications

(8 citation statements)

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“…In physics, such scalar quantities formed by mathematical operations on vectors, the content of which can change their values (such as projections of vectors), are classifi ed as non-true scalars -pseudoscalars [26]. Therefore, the sources (15) have no physical certainty, they are fi ctitious or virtual, that is, they exist only as a calculated functional from μ(H) when modeling of MF.…”

Section: The Novel Mathematical Model and Methodology For Computer Si...mentioning

confidence: 99%

“…The nonlinearity of the characteristics of the magnetic materials from which the MS is made complicates such calculations even more, because the original fi eld equations become nonlinear, and for their solution it is necessary to use iterative methods, the convergence of which often turns out to be uncertain [13,14]. Therefore, in some articles various forms of analytical approximation of the magnetization curve [6,15] are proposed to improve computer models of MS, which are declared as means of achieving high accuracy of results. However, the variability of this…”

Section: Relevance and Objectives Of The Studymentioning

confidence: 99%

“…The volumetric integral in formula ( 17) is obviously a potential of volumetric charges with a density of ρ m = -divJ = divH, i.e. virtual secondary sources known from (15):…”

Section: Variants Of Ie-models Of Mf Proceeds On Equations (mentioning

confidence: 99%

“…2.1.1. In order to avoid the accumulation of errors in the iterative process of solving the MF equations, it is advisable to fi nd a rational way to transform the structure of the functional (15), containing the nonlinear dependence μ(H), into the form invariant with respect to the way of its approximation. Actually, the premises for such a transformation are clearly laid down in the very expression of this functional.…”

Section: Transformation Of the Virtual Volume Source Functionalmentioning

confidence: 99%

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The Novel Mathematical Model and Methodology for Computer Simulation of Magnetic Field in a Nonlinear Medium

ZAPOROZHETS

2024

Sci. innov.

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Introduction. Magnetic devices of various types are used in production equipment. Designing and modernizing such equipment requires a signifi cant bulk of calculations of magnetic fi elds and parameters of magnetic devices. This task is diffi cult due to large dimensionality of the system of equations and nonlinear properties of magnetic materials.Problem Statement. Due to the nonlinearity of diff erential and integral equations on which these calculations are based, they need to be solved numerically by iterative methods, the convergence of which is often uncertain. This requires powerful computing tools and considerable time. Therefore, the problem of improving mathematical mo dels and increasing the computational effi ciency of the corresponding algorithms is relevant.Purpose. To develop a mathematical model of a magnetic fi eld in a nonlinear medium in the form of a surface integral equation for a quasilinear space and a computer modeling technique with increased computational effi ciency.Material and Methods. The material of the study is the mathematical models of the magnetic fi eld in a nonlinear medium of magnetic materials and the computational properties of the corresponding algorithms. The methods of vector analysis of diff erential operators and synthesis of modifi ed formulas in the magnetic fi eld equations have been used in the work.Results. The newest mathematical model of the magnetic fi eld in which the volumetric equation for a nonlinear medium is reduced to a surface equation in quasi-linear space, which reduces the dimensionality of data arrays by one order of magnitude and the number of computational operations by two orders of magnitude, has been substantiated. On this basis, a methodology for computer modeling of fi elds with the use of a unifi ed magnetization curve has been developed.Conclusions. The applicability of this methodology to various magnetic materials and its effi ciency have been confi rmed by the example of a model problem of practical importance for improving the algorithms for calculating and analyzing magnetic fi elds in magnetic systems with nonlinear elements.

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Section: The Novel Mathematical Model and Methodology For Computer Si...mentioning

confidence: 99%

Section: Relevance and Objectives Of The Studymentioning

confidence: 99%

“…The volumetric integral in formula ( 17) is obviously a potential of volumetric charges with a density of ρ m = -divJ = divH, i.e. virtual secondary sources known from (15):…”

Section: Variants Of Ie-models Of Mf Proceeds On Equations (mentioning

confidence: 99%

Section: Transformation Of the Virtual Volume Source Functionalmentioning

confidence: 99%

See 2 more Smart Citations

The Novel Mathematical Model and Methodology for Computer Simulation of Magnetic Field in a Nonlinear Medium

ZAPOROZHETS

2024

Sci. innov.

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“…Для цього використовують ермітові сплайни [1,2]. З метою покращення точності наближення функцій сплайнами як ланки можна використовувати не тільки многочлени, а й нелінійні за параметрами вирази [3][4][5][6][7][8] ) ; , , ,…”

Section: ермітові сплайни з ланками у вигляді суми многочлена та експоненти з непарною кількістю параметрівunclassified

Hermitian splines with links in the form of the sum of the polynomial and exponents with an odd number of parameters

Pizyur

Hnativ

2021

Fìz.-mat. model. ìnf. tehnol.

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Conditions for the existence of a unique approximation of functions by Hermitian splines with a link in the form of a sum of a polynomial and an exponent with five parameters are established. Formulas for the parameters of the links of these Hermitian splines are derived. A formula for calculating the error and an expression for the kernel of the error of the balance approximation of functions by Hermitian splines with a link in the form of a sum of a polynomial and an exponent are given. Results of approximations are given.

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Hermitian splines with exponential power links with an odd number of parameters

Pizyur,

Karas

2023

PMMIT

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Chebyshev approximation of the steel magnetization characteristic by the sum of a linear expression and an arctangent function

Cited by 4 publications

References 1 publication

The Novel Mathematical Model and Methodology for Computer Simulation of Magnetic Field in a Nonlinear Medium

The Novel Mathematical Model and Methodology for Computer Simulation of Magnetic Field in a Nonlinear Medium

Hermitian splines with links in the form of the sum of the polynomial and exponents with an odd number of parameters

Hermitian splines with exponential power links with an odd number of parameters

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