An alternative approach is proposed here to investigate the problem of scattering surface water waves by a vertical permeable plate submerged in deep within framework linear wave theory. Using Havelock’s expansion potential, associated boundary value reduced second kind hypersingular integral equation order 2. The unknown function expressed as product suitable weight and an polynomial. 2 evalua...

Galerkin boundary element methods for the solution of novel first kind Steklov–Poincaré and hypersingular operator boundary integral equations with nonlinear perturbations are investigated to solve potential type problems in twoand three-dimensional Lipschitz domains with nonlinear boundary conditions. For the numerical solution of the resulting Newton iterate linear boundary integral equations...

For the first time, some hypersingular nonlinear boundary-value problems with a small parameter ε at the highest derivative are described. These problems essentially (qualitatively and quantitatively) differ from the usual linear and quasilinear singularly perturbed boundary-value problems and have the following unusual properties: (i) in hypersingular boundary-value problems, super thin bounda...

In the field of offshore renewable energy, impermeable plates are used as underwater lenses to amplify wave amplitude, and perforated can harness energy a power takeoff device. Within framework linear potential-flow theory, water scattering by horizontal is investigated in present study, both circular elliptical considered. The hypersingular integral equation constructed model interaction betwe...