Geodesic
One approach to a magnetostatic problem for bodies with inclusions in an inhomogeneous external field
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 1, pp. 178-188

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A direct magnetostatic problem for magnets with a finite-size inclusion is considered in an integrodifferential form. An approach is used that, under certain conditions, reduces the problem to a single integral equation on a two-dimensional manifold-the inclusion surface. As an important illustrative example, finite formulas are derived to compute the resulting field of a magnetic half-space with a spherical cavity in an arbitrary external field. 
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     title = {One approach to a magnetostatic problem for bodies with inclusions in an inhomogeneous external field},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_1_a11/}
}
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V. V. Dyakin; V. Ya. Raevskii; O. V. Umergalina. One approach to a magnetostatic problem for bodies with inclusions in an inhomogeneous external field. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 1, pp. 178-188. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_1_a11/