On series solutions of the magnetostatic integral equation

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.