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 Zh. Vychisl. Mat. Mat. Fiz., 1999, Volume 39, Number 4, Pages 630–637 (Mi zvmmf1700)

On series solutions of the magnetostatic integral equation

J. F. Ahnera, V. V. Dyakinb, V. Ya. Raevskiib, R. Ritterc

a Dept. Math., Vanderbilt Univ., Nashville, Tennesse 37240, USA
b Inst. Metal Phys., Rus. Acad. Sci., Ekaterinburg, Russia
c Math. Inst. II, Univ. Karlsruhe, D-76128 Karlsruhe, Germany

Abstract: We consider the fundamental magnetostatic integral equation for homogeneous and isotropic solids. The construction of the orthogonal basis consisting of the eigenvectors of the magnetostatic operator is based on the coupling of the spectral characteristics of this operator and classic potential operators. Estimations of the error of the resulting field in terms of cut-off errors to the external magnetic field are given. Additionally we obtain explicit expressions for both the eigenvectors and eigenfunqtions of the magnetostatic operator for the case that the underlying body is a triaxial ellipsoid. These quantities are given in terms of Lame functions and ellipsoidal harmonics.

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English version:
Computational Mathematics and Mathematical Physics, 1999, 39:4, 601–608

Bibliographic databases:
UDC: 519.642
MSC: Primary 78A30; Secondary 33E10
Revised: 26.08.1998
Language:

Citation: J. F. Ahner, V. V. Dyakin, V. Ya. Raevskii, R. Ritter, “On series solutions of the magnetostatic integral equation”, Zh. Vychisl. Mat. Mat. Fiz., 39:4 (1999), 630–637; Comput. Math. Math. Phys., 39:4 (1999), 601–608

Citation in format AMSBIB
\Bibitem{AhnDyaRae99} \by J.~F.~Ahner, V.~V.~Dyakin, V.~Ya.~Raevskii, R.~Ritter \paper On series solutions of the magnetostatic integral equation \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 1999 \vol 39 \issue 4 \pages 630--637 \mathnet{http://mi.mathnet.ru/zvmmf1700} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1691382} \zmath{https://zbmath.org/?q=an:0963.78010} \transl \jour Comput. Math. Math. Phys. \yr 1999 \vol 39 \issue 4 \pages 601--608