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We present a general harmonic formulation that takes into account, explicitly, the effects of micromagnetics for modeling the magnetic fields in a magnetoimpedance (MI) sensor element. We first relax assumptions commonly made to derive closed form solutions from a decoupled set of linear equations. We then solve numerically (using a meshless method formulated in point-collocation) the Maxwell and the Landau-Lifshitz-Gilbert equations simultaneously for the real and imaginary parts of the magnetic fields and magnetization in the context of a cylindrical amorphous MI sensor element. Comparing our results of the effects of coupling the equations of motion against published experimental data, we found striking differences both quantitatively and qualitatively between the coupled nonlinear and decoupled linear models. The coupled nonlinear harmonic formulation presented here results in improved accuracy and more consistent qualitative behavior in accordance to reported experimental observations, particularly in the weak field regime. Also presented here are spin wave amplitude distributions showing spatial dispersion within MI elements structures, which represents information lost in decoupled formulations.