This study presents a spectral-fundamental solution (SFS) method which enables efficient simulation of large-scale nonlinear wave-body interactions. The SFS method combines spectral basis functions and fundamental solutions to achieve both global efficiency and local accuracy. Based on the linearity of the Laplace equation, it decomposes large-scale boundary-value problems into independent subproblems, enabling efficient full-domain computation. Numerical validations show that SFS achieves higher accuracy than the high-order spectral method for short, steep waves and outperforms the method of fundamental solutions in long-wave conditions. Applications to nonlinear ship waves in large-scale domains yield results in good agreement with experimental data, successfully capturing higher-order nonlinear effects. The simulations reveal the physical origins of distinct energy bands in the wave spectrogram and demonstrate how ship acceleration influences the ship-generated wake field. Furthermore, the simulations explain why high-speed ships exhibit wake angles that are narrower than classical predictions. Beyond ship waves, this efficient SFS framework can be extended to a wide range of unsteady wave-structure interaction problems in ocean engineering.

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• Hydrodynamic waves
• Surface gravity waves
• Wave-structure interactions