A spectral coupled boundary element method for the simulation of nonlinear surface gravity waves

•A novel domain decomposition method called the spectral coupled boundary element method (SCBEM) is developed.•The SCBEM can efficiently simulate vast water bodies with complex structures.•With SCBEM, computational domains can be expanded to tens of times larger than traditional boundary element methods.•SCBEM is capable of accurately modeling strong nonlinear phenomena, including modulation wave trains, focused waves, and wave run-ups.