To accurately obtain the radiation and propagation characteristics of the highly oscillating electromagnetic (EM) waves, the p-refinement method which expands the physical quantities by high-order basis functions has been proposed. Nevertheless, since the time-domain EM simulation is a dynamic process, a static refinement is not applicable. In this communication, an efficient dynamic p-adaptation method based on hierarchical vector basis functions having the property of nesting to facilitate the construction of basis functions has been developed for the discontinuous Galerkin time-domain (DGTD) method. In this approach, based on the relationship between the amplitude of the expansion coefficients of hierarchical vector basis functions and the corresponding expansion coefficients of the physical quantities captured by each element in the previous time step, an error estimator is proposed to determine the order of each element in the next time step. To reduce the computational overhead, the basis orders of each element can be dynamically adjusted when the pulse passes through or is dissipated. The numerical results demonstrate the accuracy and efficiency of the proposed approach.

The radio propagation loss prediction model is essential for maritime communication. The oceanic tropospheric duct is much more complicated than the atmospheric structure on land due to the rough sea surface influence, and it leads to difficulties in loss prediction. Classical radio wave propagation loss prediction models are either based on complicated electromagnetic wave theories or rely on empirical data. Consequently, they suffer from low accuracy and a limited range of application. To address this issue, a novel maritime propagation loss prediction approach is proposed, which fully exploits the data for training. In this new approach, 3D sea surface contour profiles are generated based on the Pierson–Moskowitz spectrum theory and the direction expansion formula Stereo Wave Observation Program (SWOP), by sweeping the parameters. The full-wave propagation procedure of radio signals over the sea surface is simulated by commercial EM analysis software CST Studio Suite. Based on the large quantity of simulated data, the BP neural network is employed to fit the radio propagation loss and obtain the sea surface radio wave propagation prediction model. Other classical machine learning methods are also compared to validate the proposed approach. Traditional empirical model construction relies on observation data. This approach, for the first time, proposed an automatic scheme which covers the whole procedure from the data generation to prediction model training. It avoids the requirements for on-site observation, as well as significantly decreases the cost of experiments. The application scope of the prediction model such as propagation distance range and working frequency range could be adaptive through adjustments for simulated sea size and simulated working frequency. This approach is validated to save 99% of prediction time in comparison with the full-wave simulations. The prediction model trained via our proposed method could obtain the coefficient of determination R² which is over 0.92, demonstrating the superiority of this method.

Composition-dependent interdiffusion coefficients are key parameters in many physical processes. However, finding such coefficients for a system with few components is challenging due to the underdetermination of the governing diffusion equations, the lack of data in practice, and the unknown parametric form of the interdiffusion coefficients. In this work, we propose InfPolyn, Infinite Polynomial, a novel statistical framework to characterize the component-dependent interdiffusion coefficients. Our model is a generalization of the commonly used polynomial fitting method with extended model capacity and flexibility and it is combined with the numerical inversion-based Boltzmann–Matano method for the interdiffusion coefficient estimations. We assess InfPolyn on ternary and quaternary systems with predefined polynomial, exponential, and sinusoidal interdiffusion coefficients. The experiments show that InfPolyn outperforms the competitors, the SOTA numerical inversion-based Boltzmann–Matano methods, with a large margin in terms of relative error (10× more accurate). Its performance is also consistent and stable, whereas the number of samples required remains small.