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We present JefiAtten, a novel neural network model employing the attention mechanism to solve Maxwell's equations efficiently. JefiAtten uses self-attention and cross-attention modules to understand the interplay between charge density, current density, and electromagnetic fields. Our results indicate that JefiAtten can generalize well to a range of scenarios, maintaining accuracy across various spatial distribution and handling amplitude variations. The model showcases an improvement in computation speed after training, compared to traditional integral methods. The adaptability of the model suggests potential for broader applications in computational physics, with further refinements to enhance its predictive capabilities and computational efficiency. Our work is a testament to the efficacy of integrating attention mechanisms with numerical simulations, marking a step forward in the quest for data-driven solutions to physical phenomena., Comment: 29 pages, 11 figures

This paper presents the RBG-Maxwell framework, a relativistic collisional plasma simulator on GPUs. We provide detailed discussions on the fundamental equations, numerical algorithms, implementation specifics, and key testing outcomes. The RBG-Maxwell framework is a robust numerical code designed for simulating the evolution of plasma systems through a kinetic approach on large-scale GPUs. It offers easy adaptability to a wide range of physical systems. Given the appropriate initial distributions, particle masses, charges, differential cross-sections, and external forces (which are not confined to electromagnetic forces), the RBG-Maxwell framework can direct the evolution of a particle system from a non-equilibrium state to a thermal state., Comment: 21 pages, 10 figures

We have implemented a GPU version of the Jefimenko's equations -- JefiGPU. Given the proper distributions of the source terms $\rho$ (charge density) and $\mathbf{J}$ (current density) in the source volume, the algorithm gives the electromagnetic fields in the observational region (not necessarily overlaps the vicinity of the sources). To verify the accuracy of the GPU implementation, we have compared the obtained results with that of the theoretical ones. Our results show that the deviations of the GPU results from the theoretical ones are around 5\%. Meanwhile, we have also compared the performance of the GPU implementation with a CPU version. The simulation results indicate that the GPU code is significantly faster than the CPU version. Finally, we have studied the parameter dependence of the execution time and memory consumption on one NVIDIA Tesla V100 card. Our code can be consistently coupled to RBG (Relativistic Boltzmann equations on GPUs) and many other GPU-based algorithms in physics., Comment: 21 pages, 8 figures, 4 tables

We have numerically studied the evolution of the heavy ions that expand in a cold background plasma at a large scale. Two typical collective behaviors of the heavy ions are identified with the conditions where only the traversing heavy ion's initial total mass is different. Our work has demonstrated that a difference in the initial total mass of the moving heavy ions is able to induce completely different collective behaviors of the plasma. The simulation is performed via the hybrid model, in which the ions and electrons are treated as classical particles and mass-less fluid, respectively. Due to the imbalance of the electric and magnetic force on the heavy ions, these particles will evolve into different collective patterns at the later time. These patterns manifest a rather different stopping behavior of the moving ions and an opposite drifting direction of the electron fluid at the rim of the expanding plasma. Further numerical and analytical calculations show that the imbalance depends not only on the number densities of the plasma ions, but also on the spatial variations of the magnetic fields. Our work reveals that the collective behavior of the heavy ions is highly non-linear, and the non-linearity is able to induce different phenomena in the evolution of the system at a large scale., Comment: 8 pages, 8 figures