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In marine offshore engineering, cost-efficient simulation of unsteady waterwaves and their nonlinear interaction with bodies are important to address abroad range of engineering applications at increasing fidelity and scale. Weconsider a fully nonlinear potential flow (FNPF) model discretized using aGalerkin spectral element method to serve as a basis for handling both wavepropagation and wave-body interaction with high computational efficiency withina single modellingapproach. We design and propose an efficientO(n)-scalablecomputational procedure based on geometric p-multigrid for solving the Laplaceproblem in the numerical scheme. The fluid volume and the geometric features ofcomplex bodies is represented accurately using high-order polynomial basisfunctions and unstructured meshes with curvilinear prism elements. The newp-multigrid spectralelement model can take advantage of the high-orderpolynomial basis and thereby avoid generating a hierarchy of geometric mesheswith changing number of elements as required in geometric h-multigridapproaches. We provide numerical benchmarks for the algorithmic and numericalefficiency of the iterative geometric p-multigrid solver. Results of numericalexperiments are presented for wave propagation and for wave-body interaction inan advanced case for focusing design waves interacting with a FPSO. Our studyshows, that the use of iterative geometric p-multigrid methods for theLaplaceproblem can significantly improve run-time efficiency of FNPF simulators.

Efficient p-multigrid spectral element model for water waves and marine offshore structures