Тестирование численного решения задачи определения источников магнитостатического поля в намагничиваемой среде - Михайлов, Валерий Михайлович; Чунихин, Константин Вадимович (НТУ "ХПИ", 2017)
Выполнена проверка правильности интегрального уравнения второго рода для расчета распределения источников плоскомеридианного магнитостатического поля на границах раздела кусочно-однородной намагничиваемой среды и его численного решения. Для этого использованы электростатическая аналогия и аналитическое решение задачи о воздействии однородного электростатического поля на сферическую диэлектрическую оболочку в кусочно-однородной диэлектрической среде. Подтверждена правильность интегрального уравнения и его численного решения при помощи аппроксимирующей системы алгебраических уравнений. Сделан анализ влияния магнитных проницаемостей однородных областей среды на распределение фиктивных магнитных зарядов на поверхностях и напряженность магнитного поля внутри сферической оболочки.

Purpose. Testing of numerical solution algorithm for integral equation for calculation of plane meridian magnetostatic field source distribution at interfaces of piecewise homogeneous magnetized medium by means of electrostatic analogy. Methodology. The piecewise homogeneous medium consists of three regions with different magnetic permeabilities: the shell of arbitrary meridian section, external unlimited medium outside the shell, and the medium inside the shell. For testing external homogeneous magnetic field effect on spherical shell is considered. The analytical solution of this problem on the basis of electrostatic analogy from the solution of the problem uniform electrostatic field effect on dielectric shell is obtained. We have compared results of numerical solution of integral equation with the data obtained by means of analytical solution at the variation of magnetic permeabilities of regions of medium. Results. Integral equation and the algorithm of its numerical solution for calculation of source field distribution at the boundaries of piecewise homogeneous medium is validated. Testing of integral equations correctness for calculation of fictitious magnetic charges distribution on axisymmetric boundaries of piecewise homogeneous magnetized medium and algorithms of their numerical solutions can be carried out by means of analytical solutions of problems of homogeneous electrostatic field effect analysis on piecewise homogeneous dielectric medium with central symmetry of boundaries – single-layer and multilayer spherical shells. In the case of spherical shell in wide range of values of the parameter λk, including close to ± 1, numerical solution of integral equation is stable, and relative error in calculating of fictitious magnetic charges surface density and magnetic field intensity inside the shell is from tenths of a percent up to several percent except for the cases of very small values of these quantities. Originality. The use analytical solutions for problems of calculation of external electrostatic field effect on piecewise homogeneous dielectric bodies for testing integral equations of magnetostatics and algorithms for their numerical solutions. Practical value. The described method of testing integral equations of magnetostatics and their numerical solutions can be used for calculation of magnetic fields of spacecraft control system electromagnets.
Testing of numerical solution of the problem of determining sources of magnetostatic field in magnetized medium
Keywords: поле плоскомеридианное; среда кусочно-однородная; уравнение интегральное; аналогия электростатическая; заряд фиктивный; заряд магнитный; plane meridian field; piecewise homogeneous medium; integral equation; electrostatic analogy; fictitious magnetic charge