Incompressible free-surface flows involving highly complex and violent phenomena are of great importance to the engineering industry. Applications such as breaking-wave impacts, fluid-structure interaction, and sloshing tanks demand an accurate and noise-free pressure field, and require large-scale simulations involving millions of computation points. This thesis addresses the need with the novel use of a graphics processing unit (GPU) to accelerate the incompressible smoothed particle hydrodynamics (ISPH) method for highly non-linear and violent free-surface flows using millions of particles in three dimensions. Compared to other simulation techniques, ISPH is robust in predicting a highly accurate pressure field, through the solution of a pressure Poisson equation (PPE), whilst capturing the complex behaviour of violent free-surface flows. However, for large-scale engineering applications the solution of extremely large PPE matrix systems on a GPU presents multiple challenges: constructing a PPE matrix every time step on the GPU for moving particles, overcoming the GPU memory limitations, establishing a robust and accurate ISPH solid boundary condition suitable for parallel processing on the GPU, and exploiting fast linear algebra GPU libraries. A new GPU-accelerated ISPH algorithm is presented by converting the highly optimised weakly-compressible SPH (WCSPH) code DualSPHysics and combining it with the open-source ViennaCL linear algebra library for fast solutions of the ISPH PPE. The challenges are addressed with new methodologies: a parallel GPU algorithm for population of the PPE matrix, mixed precision storage and computation, and extension of an existing WCSPH boundary treatment for ISPH. Taking advantage of a GPU-based algebraic multigrid preconditioner for solving the PPE matrix required modification for ISPH's Lagrangian particle system. The new GPU-accelerated ISPH solver, Incompressible-DualSPHysics, is validated through a variety of demanding test cases and shown to achieve speed ups of up to 25.3 times and 8.1 times compared to single and 16-threaded CPU computations respectively. The influence of free-surface fragmentation on the PPE matrix solution time with different preconditioners is also investigated. A profiling study shows the new code to concentrate the GPUâs processing power on solving the PPE. Finally, a real-engineering 3-D application of breaking focused-wave impacting a surface-piercing cylindrical column is simulated with ISPH for the first time. Extensions to the numerical model are presented to enhance the accuracy of simulating wave-structure impact. Simulations involving over 5 million particles show agreement with experimental data. The runtimes are similar to volume-of-fluid and particle-in-cell solvers running on 8 and 80 processors respectively. The 3-D model enables post-processing analysis of the wave mechanics around the cylinder. This study provides a substantial step for ISPH. Incompressible-DualSPHysics achieves resolutions previously too impractical for a single device allowing for the simulation of many industrial free-surface hydrodynamic applications.