A finite element method for the solution of the up-to-second-order wave diffraction-radiation problem in the time-domain is proposed. The solver has been validated against experimental data available for the HiPRWind semisubmersible platform (designed for floating wind turbines). To perform the validation, the wave diffraction-radiation solver is coupled to a body dynamics and mooring solvers in the time-domain. The HiPRWind movements and mooring forces have been compared for a large number of test cases, including decay tests, bichromatic, and irregular waves. Good agreement has been found for both, body movements and mooring forces