Yantao Wang

Minghua Chen, Yantao Wang, Xiao Cheng et al.

We propose a locally one dimensional (LOD) finite difference method for multidimensional Riesz fractional diffusion equation with variable coefficients on a finite domain. The numerical method is second-order convergent in both space and time directions, and its unconditional stability is strictly proved. Comparing with the popular first-order finite difference method for fractional operator, the form of obtained matrix algebraic equation is changed from $(I-A)u^{k+1}=u^k+b^{k+1}$ to $(I-{\widetilde A})u^{k+1}=(I+{\widetilde B})u^k+{\tilde b}^{k+1/2}$; the three matrices $A$, ${\widetilde A}$ and ${\widetilde B}$ are all Toeplitz-like, i.e., they have completely same structure and the computational count for matrix vector multiplication is $\mathcal{O}(N {log} N)$; and the computational costs for solving the two matrix algebraic equations are almost the same. The LOD-multigrid method is used to solve the resulting matrix algebraic equation, and the computational count is $\mathcal{O}(N {log} N)$ and the required storage is $\mathcal{O}(N)$, where $N$ is the number of grid points. Finally, the extensive numerical experiments are performed to show the powerfulness of the second-order scheme and the LOD-multigrid method.

Minghua Chen, Weiping Bu, Wenya Qi et al.

In this article a theoretical framework for the Galerkin finite element approximation to the time-dependent Riesz tempered fractional problem is provided without the fractional regularity assumption. Because the time-dependent problems should become easier to solve as the time step $τ\rightarrow 0$, which correspond to the mass matrix dominant [R. E. Bank and T. Dupont, {\em Math. Comp.}, 153 (1981), pp. 35--51]. Based on the introduced and analysis of the fractional $τ$-norm, the uniform convergence estimates of the V-cycle multigrid method with the time-dependent fractional problem is strictly proved, which means that the convergence rate of the V-cycle MGM is independent of the mesh size $h$ and the time step $τ$. The numerical experiments are performed to verify the convergence with only $\mathcal{O}(N \mbox{log} N)$ complexity by the fast Fourier transform method, where $N$ is the number of the grid points. To the best of our knowledge, this is the first proof for the convergence rate of the V-cycle multigrid finite element method with $τ\rightarrow 0$.

Tingwei Chen, Yantao Wang, Hanzhi Chen et al.

The introduction of 5G technology has revolutionized communications, enabling unprecedented capacity, connectivity, and ultra-fast, reliable communications. However, this leap has led to a substantial increase in energy consumption, presenting a critical challenge for network sustainability. Accurate energy consumption modeling is essential for developing energy-efficient strategies, enabling operators to optimize resource utilization while maintaining network performance. To address this, we propose a novel deep learning model for 5G base station energy consumption estimation based on a real-world dataset. Unlike existing methods, our approach integrates the Base Station Identifier (BSID) as an input feature through an embedding layer, capturing unique energy patterns across different base stations. We further introduce a masked training method and an attention mechanism to enhance generalization and accuracy. Experimental results show significant improvements, reducing Mean Absolute Percentage Error (MAPE) from 12.75% to 4.98%, achieving over 60% performance gain compared to existing models. The source code for our model is available at https://github.com/RS2002/ARL.