A 3D fully nonlinear potential flow (FNPF) model based on an Eulerian formulation is presented. The model is discretized using high-order prismatic – possibly curvi-linear – elements using a spectral element method (SEM) that has support for adaptive unstructured meshes. The paper presents details of the FNPF-SEM development and the model is illustrated to exhibit exponential convergence. The model is then applied to the case of focused waves impacting on a surface-piecing fixed FPSO-like structure. Good agreement was found between numerical and experimental wave elevations and pressures.