In intermediate and deep waters, third-order resonant wave–wave interactions play a crucial role in sea state simulations. These interactions are described by a complex, multidimensional integral that must be evaluated accurately. The widely used Discrete Interaction Approximation (DIA) provides computational efficiency, but at the expense of limited accuracy.

To address this limitation, quasi-exact methods have been developed, among which the Gaussian Quadrature Method (GQM) stands out. This approach was initially implemented in the TOMAWAC model for infinite depth by M. Benoit and Gagnaire-Renou. More recently, thanks to the work of A. Guerri, this implementation has been successfully extended to finite depth conditions.