We present a Spectral Element Fully Nonlinear Potential Flow (FNPF-SEM) model developed for the simulation of wave-body interactions between nonlinear free surface waves and impermeable structures. The solver is accelerated using an iterative p-multigrid algorithm. Two cases are considered: (i) a surface piercing box forced into vertical motion creating radiated waves and (ii) a rectangular box released above its equilibrium resulting in freely decaying heave motion. The FNPF-SEM model is validated by comparing the computed hydrodynamic forces against those obtained by a Navier-Stokes solver. Although not perfect agreement is observed the results are promising, a significant speedup due to the iterative algorithm is however seen.