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A dispersion hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) method is proposed for simulating the graphene-based absorber at terahertz frequencies. The surface conductivity of the graphene derived from the Kubo formula is incorporated into the conventional HIE-FDTD algorithm by using the auxiliary differential equation technique. The time step size of this method is not related with the fine cells inside the graphene layer. The simulation result of the infinite graphene sheet shows that the dispersion HIE-FDTD method has high computational accuracy and the computational time is greatly reduced compared with the dispersion FDTD method. By using the dispersion HIEFDTD method, it is validated that the graphene sheet can be used as a broadband absorber. [ABSTRACT FROM AUTHOR]