... employed here validates with different previous literatures as special cases. Then, numerical solutions of the reflection and transmission coefficients, hydrodynamic forces are graphically illustrated across various dimensionless structural parameters. In summary, the present paper offers valuable insights...

...-third singularity. Graphical representations are employed to depict the numerical evaluations of reflection and transmission coefficients across various non-dimensional parameters. These visualizations offer insight into the behavior and dependencies of these coefficients under different conditions...

... over a horizontal flat plate without any bottom undulation are considered. Both the permeable and impermeable cases have been taken into account. Figures 3( a ) and 3( b ) demonstrate the variation of reflection and transmission coefficients against relative submergence for impermeable...

... singularities with suitable weight functions have been taken into consideration. The numerical examples of both reflection and transmission coefficients are presented to examine the hydrodynamic performance of breakwater. Some fascinating results like resonant frequencies are obtained for practical engineering...

... integral equation boundary element method Galerkin approximation ultraspherical Gegenbauer polynomials reflection and transmission coefficients fluid–structure interaction The problem of water wave diffraction by some obstacles of different geometrical shapes has been studied substantially...

... and the unknowns are obtained numerically. The reflection and transmission coefficients are computed, respectively, as follows: (38) K r = | R 0 | and K t = | T 0 | The dissipation coefficient is defined as (39) K d = 1 − K r 2 − K t 2 The free-surface elevation...