An Efficient Harmonic Balance Method for Nonlinear Eddy-Current Problems. Außerhofer, S., Bíró, O., & Preis, K. IEEE Transactions on Magnetics, 43(4):1229–1232, IEEE, April, 2007.
A method is presented which determines the steady-state solution of nonlinear eddy current problems. The unknown potentials are represented by Fourier-series and the nonlinear behavior of the material is split into a linear and a nonlinear term using a fixed-point technique. This approach leads to decoupled linear equations for each harmonic component. To take the nonlinearity into account, several fixed-point iterations have to be made. The method avoids calculating transient processes which normally have to be stepped through if using time-stepping methods. The present method is illustrated by two 2-D examples
@Article{         Auserhofer_2007aa,
abstract      = {A method is presented which determines the steady-state solution of nonlinear eddy current problems. The unknown potentials are represented by Fourier-series and the nonlinear behavior of the material is split into a linear and a nonlinear term using a fixed-point technique. This approach leads to decoupled linear equations for each harmonic component. To take the nonlinearity into account, several fixed-point iterations have to be made. The method avoids calculating transient processes which normally have to be stepped through if using time-stepping methods. The present method is illustrated by two 2-D examples},
author        = {Außerhofer, Stefan and Bíró, Oszkár and Preis, Kurt},
doi           = {10.1109/TMAG.2006.890961},
file          = {Auserhofer_2007aa.pdf},
group         = {pels},
issn          = {0018-9464},
journal       = {IEEE Transactions on Magnetics},
keywords      = {Fourier series,eddy currents,fixed point arithmetic,harmonic analysis,transient analysis,Fourier series,fixed-point iteration,harmonic balance method,harmonic components,nonlinear behavior,nonlinear eddy-current problems,steady-state methods,time-stepping methods,transient process,Differential equations,Eddy currents,Electromagnetic forces,Electromagnetic transients,Magnetic flux,Magnetic materials,Magnetic separation,Nonlinear equations,Nonlinear magnetics,Steady-state,Eddy currents,nonlinear equations,nonlinear magnetics,periodic functions},
month         = apr,
number        = {4},
pages         = {1229--1232},
publisher     = {IEEE},
title         = {An Efficient Harmonic Balance Method for Nonlinear Eddy-Current Problems},
volume        = {43},
year          = {2007},
shortjournal  = {IEEE Trans. Magn.}
}