## 1 Introduction  
With the rapid development of computing technology, numerical simulation methods are increasingly being used in computational electromagnetics. As a powerful electromagnetic simulation tool, the finite-difference time-domain (FDTD) method is widely favored for its intuitive, versatile, and flexible nature [1, 2, 3, 4]. However, the FDTD method generally uses structural grids to discretize the problem being solved, which have significant step errors [5]. To reduce errors, the grid size in the FDTD method is generally less than one-twelfth of the wavelength. For some structures, such as holes, slots, and wedges, finer grids are required to ensure a better simulation of geometric shapes. In practical large-scale and complex electromagnetic problems, the target structure, material, etc., are becoming increasingly complex, and the calculated frequency is also increasing, which inevitably leads to a sharp increase in the sizes of computational grids. Due to the limitations of computer hardware resources, the traditional single-machine serial FDTD calculation scheme can no longer meet the actual computational needs. Fortunately, the FDTD method does not require solving matrix equations, which means its computational efficiency can be improved significantly through parallel processing. An FDTD algorithm exhibits inherent parallelism, allowing for the division of the computational domain into multiple subdomains. By facilitating data exchange solely between adjacent subdomains, this approach achieves the parallelization of the FDTDalgorithm while significantly enhancing its computational efficiency. At the hardware level, the parallelization of the FDTD algorithm can generally be divided into two categories: central processing unit (CPU) parallelism and graphics processing unit (GPU) parallelism. A CPU is good at handling sequential and complex computational tasks, and its core count is generally low (typically tens of cores), but each core has a relatively high computational power. To meet the needs of large-scale computing, many CPUs are required for collaborative computing, which is costly. A GPU, on the other hand, is good at parallel processing many simple computational tasks, and it has thousands of cores that can handle multiple threads and tasks simultaneously. With the same computational power, the computational cost of a CPU is much higher than that of a GPU. Therefore, developing GPU-based FDTD algorithms can improve their computational efficiency and applicability significantly and economically. Nowadays, GPU-based FDTD algorithms are emerging in an endless stream, and the computational power and efficiency of FDTD algorithms are being continuously improved. FDTD algorithms based on a GPU are also widely used in ground-penetrating radar [6], electromagnetic scattering [7], magnetic resonance imaging [8], transmission line calculation [9], and other related fields [10; 11]. For different computational requirements, researchers have developed FDTD parallel algorithms based on a single GPU [6; 7; 12; 13], multi-GPUs at one node [9; 10; 11; 14; 15; 16; 17], and multi-GPUs at multi-nodes [18; 19; 20; 21]. In multi-GPU parallel FDTD algorithms, the communication efficiency between the GPUs, especially inter-node GPUs, is critical to the computational efficiency. The existing intra-node GPU communication requires data exchange through a PCIe bus, and inter-node GPU communication requires data forwarding through a CPU. The limitations of the I/O bandwidth and CPU forwarding speed have hindered the improvement of multi-GPU parallel efficiency. The NVLink communication protocol proposed by NVIDIA provides high-bandwidth, low-latency direct communication between GPUs [22]. Compared to CPU forwarding and PCIe communication, NVLink delivers better performance and efficiency of the data transmission and collaboration between GPUs. Furthermore, NVIDIA has also developed the NVIDIA Collective Communications Library (NCCL) for high-speed data transmission and communication between multiple GPUs [23].