Институт вычислительной математики
и математической геофизики

Тезисы докладов

Численное решение дифференциальных и интегральных уравнений

In the report some problems of calculation of Electromagnetic field in an original wire are discussed. Design features of the wire were worked out to obstruct spreading of high-frequency currents.

The calculations deal with a cross-section of the wire. To make use of Finite Element Method the 2-dimentional harmonic statement is formed for this problem. The statement also includes the zero Newmann's boundary condition at the outermost bound and the zero Derichlet's boundary condition at the bound of an ideal conductor to set a backward current. Since the studied current frequency is not higher than 2 MHz the displacement currents are eliminated.

During the researches the main attention has been focused at a resistance and reactance dependence on the current frequency, therefore the primary desired characteristics are the peak values of in-phase and out-of-phase components of the total current of this system and their dependence on frequency of the exterior current.

To control the accuracy of the calculations the total current is computed using two approaches, as a circulation of a magnetic intensity vector around the wire and as a current flux through the cross-section of the wire. These two approaches give the value of the one current component using two different components of the Electromagnetic field. Due to this fact one has an opportunity to control the accuracy of both components of the electromagnetic field. It becomes very important when high-frequency processes are being studied, in such case out-of-phase component is several orders greater than in-phase one.

During the finite element approximation a problem of building an appropriate triangulation mesh has arisen because the working area has quite complicated geometry and includes adjoining mediums with contrast characteristic. Among other methods for studying the quality of a mesh an original method is used. Its’ main idea is to measure circulations of a magnetic intensity vector around different areas. This approach enables a rough estimate of mesh approximation.

With a help of developed method some researches of the wire have been done. The characteristics of the wire were studied not only for the different values of the exterior current but also for different constructions of the wire and for the cases of its mechanical damage. After the researches had been completed the appropriate experiments were carried out and the results of the measurement of the characteristics were compared with the results of finite element simulating. The close similarity of these results shows that the right model has been chosen for description of the experimental construction and that the calculations has been done with the sufficient accuracy.

Примечание. Тезисы докладов публикуются в авторской редакции

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