Premium
On the Computation of Lamé Functions, of Eigenvalues and Eigenfunctions of Some Potential Operators
Author(s) -
Ritter Stefan
Publication year - 1998
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(199801)78:1<66::aid-zamm66>3.0.co;2-v
Subject(s) - eigenfunction , eigenvalues and eigenvectors , ellipsoid , computation , mathematics , operator (biology) , mathematical analysis , spherical harmonics , physics , algorithm , quantum mechanics , biochemistry , chemistry , astronomy , repressor , transcription factor , gene
Eigenvalue problems for the double‐layer potential operator and the electrostatic integral operator are of considerable interest in some models for permanent magnetization of compact bodies. For 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 Lamé functions and surface ellipsoidal harmonics. Since only few Lamé functions can be written in closed form numerical methods are required. We provide an effective scheme for the computation these functions.