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This paper presents a new simulation strategy based on the finite-difference time-domain (FDTD) method. This new approach aims at simulating efficiently a full-duplex link where both the transmitting and receiving antennas require a precise description, while their environment does not imply a particularly fine mesh. Typical application fields of the bilateral dual-grid-FDTD are the analysis of transmission between two on-body or implanted antennas. It can also be applied to the computation of specific absorption rate (SAR) in a precise location of the human body. The principle of this method consists in splitting the overall simulation into three FDTD simulations sequentially executed with an appropriate mesh. The radiator is first characterized using a fine mesh. All the elements of the problem are then represented using a coarse mesh. Finally, that element requiring a high resolution is finely described. This approach is applied to the analysis of a 2.4-GHz transmission between two on-body devices and to the computation of the SAR in the fetal brain of a pregnant woman at 900 MHz. The bilateral dual-grid-FDTD technique proves to be accurate compared to FDTD while being fast, stable, and simple to implement.