  In marine offshore engineering, cost-efficient simulation of unsteady water
waves and their nonlinear interaction with bodies are important to address a
broad range of engineering applications at increasing fidelity and scale. We
consider a fully nonlinear potential flow (FNPF) model discretized using a
Galerkin spectral element method to serve as a basis for handling both wave
propagation and wave-body interaction with high computational efficiency within
a single modellingapproach. We design and propose an efficientO(n)-scalable
computational procedure based on geometric p-multigrid for solving the Laplace
problem in the numerical scheme. The fluid volume and the geometric features of
complex bodies is represented accurately using high-order polynomial basis
functions and unstructured meshes with curvilinear prism elements. The new
p-multigrid spectralelement model can take advantage of the high-order
polynomial basis and thereby avoid generating a hierarchy of geometric meshes
with changing number of elements as required in geometric h-multigrid
approaches. We provide numerical benchmarks for the algorithmic and numerical
efficiency of the iterative geometric p-multigrid solver. Results of numerical
experiments are presented for wave propagation and for wave-body interaction in
an advanced case for focusing design waves interacting with a FPSO. Our study
shows, that the use of iterative geometric p-multigrid methods for theLaplace
problem can significantly improve run-time efficiency of FNPF simulators.
