This paper presents the development of a numerical wave basin for violent hydrodynamics of free-surface waves interacting with vertical cylindrical structures using the incompressible smoothed particle hydrodynamics (ISPH) method accelerated with a graphics processing unit (GPU). ISPH has been implemented on a single GPU based on the open-source DualSPHysics software and using the ViennaCL linear algebra library for solving the pressure Poisson equation. Extensions to the code are presented for a numerical wave basin including development of the solid boundary condition, based on a mirror image particle and moving least squares interpolation approach, for improved accuracy at the free and solid surface interfaces during wave-structure impact. This is applied to focused waves, including breaking for which SPH is well suited, interacting with a cylindrical column to compare with experimental data. Convergence is demonstrated within the limit of 5 million particles for a single GPU. Acceptable agreement with experiment is achieved for force measurements, and variation of free-surface elevation around the column is shown to be significant particularly in larger waves with a correspondingly large force contribution from hydrostatic pressure. While breaking does not have a marked effect on total force, associated high particle velocities amplify local pressures considerably on the column near the water surface. The computer runtime is similar to that for volume-of-fluid and particle-in-cell solvers running on 8 and 80 processors respectively.