Performance of the Impedance Boundary Conditions for Eddy-Current Problems
Impedance boundary conditions are used to derive approximate expressions for the magnetic vector potential, field quantities, Joule losses and forces for conducting spheroids in the presence of circular turns carrying sinusoidal with time currents. Numerical results are generated to determine, by comparison with the results obtained applying the exact boundary conditions, the improvement achieved with the surface impedance model with respect to the simpler perfect conductor model and the range of validity of these models. The study performed is useful for evaluating various approximate numerical solutions for real world conductors
First order conditions
The authors consider only time harmonic electromagnetic fields with a time dependence specified by the factor ejωt which is omitted. In a stationary, linear, isotropic, homogeneous medium which is free of sources, the field is described by Maxwell's equations.
Computation of special functions
Bernoulli and Euler Numbers Orthogonal Polynomials Gamma, Beta, and Psi Functions Legendre Functions Bessel Functions Modified Bessel Functions Integrals of Bessel Functions Spherical Bessel Functions Kelvin Functions Airy Functions Struve Functions Hypergeometric and Confluent Hypergeometric Functions Parabolic Cylinder Functions Mathieu Functions Spheroidal Wave Functions Error Function and Fresnel Integrals Cosine and Sine Integrals Elliptic Integrals and Jacobian Elliptic Functions Exponential Integrals Summary of Methods for Computing Special Functions Appendices Indexes.