  The thermal conductance in graphene nanoribbon with a vacancy or silicon
point defect (substitution of C by Si atom) is investigated by non-equilibrium
Green's function (NEGF) formalism combined with first-principle calculations
density-functional theory with local density approximation. An efficient
correction to the force constant matrix is presented to solve the conflict
between the long-range character of the {\it ab initio} approach and the
first-nearest-neighboring character of the NEGF scheme. In nanoribbon with a
vacancy defect, the thermal conductance is very sensitive to the position of
the vacancy defect. A vacancy defect situated at the center of the nanoribbon
generates a saddle-like surface, which greatly reduces the thermal conductance
by strong scattering to all phonon modes; while an edge vacancy defect only
results in a further reconstruction of the edge and slightly reduces the
thermal conductance. For the Si defect, the position of the defect plays no
role for the value of the thermal conductance, since the defective region is
limited within a narrow area around the defect center.
