A high-fidelity full-wave simulator is presented to perform numerical experiments for rough sea scattering problem by considering different polarizations, frequencies, grazing angles, wind speeds, and sea surface spectra. The simulator is based on a novel finite-element domain decomposition (FEDD) method for solving the problem of 2-D electromagnetic scattering over 1-D sea surface. This noniterative method partitions the computational domain into a number of overlapping subdomains and solves each domain individually by employing the locally conformal perfectly matched layer (LC-PML) at the truncation boundaries. LC-PML has a unique feature such that it can be applied to irregular domains on the contrary to standard PML methods, and hence inspired the birth of FEDD. The FEDD method is used at each Monte Carlo realization corresponding to a sample from random rough surfaces and decreases the computational load, especially for electrically large problems. The accuracy and computational efficiency of the method are investigated through several simulations. Using the FEDD method, the statistical behavior of the bistatic radar cross section (RCS) is obtained for both the horizontal and vertical polarizations. A special emphasis is given to forward-scattered RCS and the mean reflection coefficient for sea surface, especially at low grazing angles, and it is shown that the simulator produces results in agreement with the Ament and Miller-Brown approximations, and experimental data, proving the reliability of the simulation approach. The results are also compared with the standard finite-element method and method of moments. Rough sea surfaces are created by using both the Pierson-Moskowitz and Elfouhaily spectra.