Estimation of Fichera-Type Eigenvalues Using Standard Functions

• Published in: IEEE transactions on magnetics Vol. 45; no. 8; pp. 3046 - 3054
• Main Authors: McKirdy, D.M., Wilton, D.T., Shute, H.A.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Approximation; Associated Legendre functions; Boundary conditions; Conductors; corner singularities; Corners; Cross-disciplinary physics: materials science; rheology; Dirichlet problem; Eigenvalues; Eigenvalues and eigenfunctions; Electromagnetic fields; Exact sciences and technology; Geometry; Laplace equations; Legendre functions; Magnetic fields; Magnetic heads; Magnetic recording; Magnetic separation; Magnetism; Materials science; Other topics in materials science; Physics; potential theory; Power system modeling; Scalars; corner singularities; Potentials; potential theory; Magnetic properties; Associated Legendre functions
• ISSN: 0018-9464; 1941-0069
• DOI: 10.1109/TMAG.2009.2017198

Infinite series involving associated Legendre functions of general degree and order are used to describe the scalar potential in the vicinity of a cubic corner. The method of analysis closely follows methods used to describe the magnetic field in the gap of a ring head for magnetic recording and the degree of the Legendre functions can be approximated when the determinant of the derived matrix vanishes. We solve with both Dirichlet and Neumann boundary conditions, but study symmetric and antisymmetric solutions separately. Other geometries considered are the two-dimensional straight edge and the quarter-plane. We also discuss the degeneracy of higher order eigenvalues.