This study presents a comprehensive procedure to calculate the exact dynamic Green's function of a harmonic semi-infinite solid and the time trajectories of the atoms, in the framework of the Green's function molecular dynamics. This Green's function properly describes the energy dissipation caused by excitations of the surface phonons, and the simulated atoms serve as well-defined thermo- and barostats for the nonequilibrium surface and interface systems. Moreover, the use of the exact dynamic Green's function coupled with a fast convolution algorithm significantly improves both the accuracy and the computing speed. The presented method is applied to a diamond (001) surface, and the results demonstrate that the properties of the nonreflecting boundary, the thermal fluctuations, and the energy dissipations involving long-wavelength phonons are correctly reproduced. These distinctive performances potentially allow us to reveal the nonequilibrium phenomena in a wide spectrum of applications such as catalysis, thermal transport, fracture mechanics, mechanochemistry, and tribology.