Métodos numéricos de integração aplicados ao cálculo da impedância e admitância de retorno pelo solo em cabos submarinos

Abstract

The calculation of ground-return impedance and admittance in submarine cables pose complex challenges, often requiring the solution of integrals involving functions with different degrees of smoothness. This study examines the effectiveness of two numerical methods, namely Gauss-Laguerre quadrature and the Tanh-Sinh quadrature (Double exponential formula), in accurately computing these integrals. We investigate their performance under different seabed conditions where cables are buried. To verify this accuracy, the results were compared with well-approximated closed-form equations suitable for the specific scenario analyzed. It was observed that, unlike the Gauss-Laguerre method, the Tanh-Sinh method is less sensitive to irregularities in functions and exhibits good performance, making it a method to be utilized, explored, and refined in such applications. This is particularly relevant as it offers a viable option in cases where approximate analytical equations have limitations.