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The contribution of this work is twofold: the authors developed an accurate model to solve the vector wave equation of radiallylayered inhomogeneous waveguides based on spline function expansions and automated grid construction by genetic programming, and thenemployed this model to analyse the propagation of electromagnetic waves within oil wells. The developed model uses a spline expansion of the fields to convert the wave equation into a quadratic eigenvalue problem where eigenvectors represent the coefficients of the splines and eigenvalues represent the propagation constant of the eigenmode. The present study compared the proposed model using the classical winding number technique. The results obtained for the first eigenmodes of a typical oil well geometry were more accurate than those obtained by the winding number method. Moreover, the authors model could find a larger amount of eigenmodes for a fixed azimuthal parameter than the standard approach.
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