Reliable computation of eigenvalues of the magnetostatic integral operator

✍ Scribed by H.-J. Dobner; S. Ritter

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 646 KB
• Volume: 27
• Category: Article
• ISSN: 0895-7177
• DOI: 10.1016/s0895-7177(98)00040-5

✦ Synopsis

variational problems in magnetostatics can be reformulated as eigenvalue problems for vector surface integral operators in appropriate function spaces, e.g., the magnetostatic integral operator is of considerable interest in the theory of permanent magnetization of compact bodies. In the case that the underlying surface is either a sphere, a spheroid, or a triaxial ellipsoid, explicit expressions for eigenvalues and eigenfunctions are well known. For the ellipsoid, these quantities are given in terms of Lam6 functions and surface ellipsoidal harmonics. Since there is an apparent lack in literature we provide an new effective scheme for the reliable computation of these functions and of the corresponding eigenvalues of the magnetostatic operator.