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Advances in Applied Mathematics and Mechanics 2021年第1期13卷 101-118页

作者： Hongliang Liu Jingwen Song Huini Liu Jie Xu Lijuan Li School of Mathematics and Computational Science&Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtanHunan 411105China School of Automation and Electronic Information Xiangtan UniversityXiangtanHunan 411105China

In this paper,we propose a novel Legendre neural network combined with the extreme learning machine algorithm to solve variable coefficients linear delay differential-algebraic equations with weak ***,the solution interval is divided into multiple subintervals by weak discontinuity ***,Legendre neural network is used to eliminate the hidden layer by expanding the input pattern using Legendre polynomials on each ***,the parameters of the neural network are obtained by training with the extreme learning *** numerical examples show that the proposed method can effectively deal with the difficulty of numerical simulation caused by the discontinuities.

关键词： Convergence delay differential-algebraic equations Legendre activation function,neural network.

A Reinforcement Learning Method to Trajectory Design for Manned Lunar Mission via Reshaping Rewards

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A Reinforcement Learning Method to Trajectory Design for Man...

International Conference on Guidance, Navigation and Control, ICGNC 2022

作者： Yang, Luyi Li, Haiyang Li, Xingyong Li, Zeyue Lu, Lin College of Aerospace Science and Engineering National University of Defense Technology Changsha410073 China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Hunan Changsha410073 China

ISBN: (纸本)9789811966125

This paper applies the reinforcement learning (RL) to multi-stage impulsive trajectory design of the manned lunar mission. The manned spacecraft is modeled as the agent and the nonlinear dynamics in the cislunar space is the interaction environment of the agent. Then the Markov decision model is mathematically built for the spacecraft and the optimization goal is to minimize the total impulses in the whole mission. The Q-learning method is used to learn the optimal policy and to better train the agent to explore and exploit the environment, a reshaping reward is designed to improve the convergency and effectiveness of the algorithm. Numerical results give the integrated designs of the lunar transfer orbit, Earth transfer orbit and three-impulsive lunar injection/ejection orbit. The proposed reshaping reward function shows better performance compared with the non-reshaping reward. The conclusions could provide a reference for China’s future manned lunar project. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

关键词： Reinforcement learning

THREE-PRECISION ITERATIVE REFINEMENT WITH PARAMETER REGULARIZATION AND PREDICTION FOR SOLVING LARGE SPARSE LINEAR SYSTEMS

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arXiv 2025年

作者： Ge, Jifeng Zhang, Juan Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Hunan KeyLaboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

This study presents a novel mixed-precision iterative refinement algorithm, GADI-IR, within the general alternating-direction implicit (GADI) framework, designed for efficiently solving large-scale sparse linear systems. By employing low-precision arithmetic, particularly half-precision (FP16), for computationally intensive inner iterations, the method achieves substantial acceleration while maintaining high numerical accuracy. key challenges such as overflow in half-precision and convergence issues for low precision are addressed through careful backward error analysis and the application of a regularization parameter α. Furthermore, the integration of low-precision arithmetic into the parameter prediction process, using Gaussian Process Regression (GPR), significantly reduces computational time without degrading performance. The method is particularly effective for large-scale linear systems arising from discretized partial differential equations and other high-dimensional problems, where both accuracy and efficiency are critical. Numerical experiments demonstrate that the use of mixed-precision strategies not only accelerates computation but also ensures robust convergence, making the approach advantageous for various applications. The results highlight the potential of leveraging lower-precision arithmetic to achieve superior computational efficiency in high-performance computing. © 2025, CC BY.

关键词： Convergence of numerical methods

Analysis of a two-grid method for semiconductor device problem

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Applied Mathematics and Mechanics(English Edition) 2021年第1期42卷 143-158页

作者： Ying LIU Yanping CHEN Yunqing HUANG Qingfeng LI School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtan 411105Hunan ProvinceChina College of Information and Intelligence Hunan Agricultural UniversityChangsha 410128China School of Mathematical Sciences South China Normal UniversityGuangzhou 510631China

The mathematical model of a semiconductor device is governed by a system of quasi-linear partial differential *** electric potential equation is approximated by a mixed finite element method,and the concentration equations are approximated by a standard Galerkin *** estimate the error of the numerical solutions in the sense of the *** linearize the full discrete scheme of the problem,we present an efficient two-grid method based on the idea of Newton *** main procedures are to solve the small scaled nonlinear equations on the coarse grid and then deal with the linear equations on the fine *** estimation for the two-grid solutions is analyzed in *** is shown that this method still achieves asymptotically optimal approximations as long as a mesh size satisfies H=O(h^1/2).Numerical experiments are given to illustrate the efficiency of the two-grid method.

关键词： two-grid method semiconductor device mixed finite element method Galerkin method L^q error estimate

Free vibration exploration of axially functionally graded carbon nanotube-reinforced beams through an innovative perturbative methodology 3

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Free vibration exploration of axially functionally graded ca...

2024 3rd International Conference on Aerospace, Aerodynamics and Mechatronics engineering, AAME 2024

作者： Chen, Chen Zhou, Lilin Ye, Tianyu Li, Daokui College of Aerospace Science and Engineering National University of Defense Technology Hunan Changsha410073 China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Hunan Changsha410073 China Aviation Engineering Institute Civil Aviation Flight University of China Sichuan Guanghan618307 China

Axially functionally graded (AFG) carbon nanotube-reinforced composite (CNTRC) emerges as a promising solution for tailoring the stiffness and strength of various beam-like structures. Applications range from optimizing the weight-to-strength ratio of airplane wings to fine-tuning the frequency of micro-beam sensors, and even alleviating stresses induced by centrifugal forces or temperature gradients in turbine blades. However, the challenge of solving variable coefficient partial differential equations (VCPDEs) arising from the axial material gradient limits conventional methods to numerical and simulation techniques. In this study, a novel perturbation approach (PA) customized for AFG-CNTRC is highlighted for solving the problem analytically, simply, and precisely. First, the vibration model of an AFG-CNTRC beam is established according to the Euler-Bernoulli theory (EBT). Second, the vibration governing equations are solved by the PA and the state space method (SSM) analytically. Finally, the adaptivity and accuracy of the PA are validated and the effects of carbon nanotubes (CNTs) distribution patterns are analyzed. It is found that increasing CNT content at either end will increase the natural frequency for symmetric boundary conditions (BCs). The frequency decreases with the degree of nonlinearity distribution of CNTs. The frequency under the C-F BC exhibits low sensitivity to parameter effects. © Published under licence by IOP Publishing Ltd.

关键词： State space methods

Two Physics-Based Schwarz Preconditioners for Three-Temperature Radiation Diffusion Equations in High Dimensions

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Communications in computational Physics 2022年第8期32卷 829-849页

作者： Xiaoqiang Yue Jianmeng He Xiaowen Xu Shi Shu Libo Wang National Center for Applied Mathematics in Hunan Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationHunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtan 411105P.R.China Laboratory of Computational Physics Institute of Applied Physics and ComputationalMathematicsBeijing 100094P.R.China College of Information Science and Technology JinanUniversityGuangzhou 510632P.R.China

We concentrate on the parallel,fully coupled and fully implicit solution of the sequence of 3-by-3 block-structured linear systems arising from the symmetrypreserving finite volume element discretization of the unsteady three-temperature radiation diffusion equations in high *** this article,motivated by[***,***,***,SIAM *** ***.33(2012)653–680]and[***,***,***,***.442(2021)110513],we aim to develop the additive and multiplicative Schwarz preconditioners subdividing the physical quantities rather than the underlying domain,and consider their sequential and parallel implementations using a simplified explicit decoupling factor approximation and algebraic multigrid subsolves to address such linear ***,computational efficiencies and parallel scalabilities of the proposed approaches are numerically tested in a number of representative real-world capsule implosion benchmarks.

关键词： Radiation diffusion equations Schwarz methods algebraic multigrid parallel and distributed computing

Investigation on a quantum algorithm for linear differential equations

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arXiv 2024年

作者： Dong, Xiaojing Peng, Yizhe Tang, Qili Yang, Yin Yu, Yue Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education National Center for Applied Mathematics in Hunan School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

Ref. [BCOW17] introduced a pioneering quantum approach (coined BCOW algorithm) for solving linear differential equations with optimal error tolerance. Originally designed for a specific class of diagonalizable linear differential equations, the algorithm was extended by Krovi in [Kro23] to encompass broader classes, including non-diagonalizable and even singular matrices. Despite the common misconception, the original algorithm is indeed applicable to non-diagonalizable matrices, with diagonalisation primarily serving for theoretical analyses to establish bounds on condition number and solution error. By leveraging basic estimates from [Kro23], we derive bounds comparable to those outlined in the Krovi algorithm, thereby reinstating the advantages of the BCOW approach. Furthermore, we extend the BCOW algorithm to address time-dependent linear differential equations by transforming non-autonomous systems into higher-dimensional autonomous ones, a technique also applicable for the Krovi algorithm. © 2024, CC BY-NC-ND.

关键词： Consensus algorithm

Quorum sensing regulation methods and their effects on biofilm in biological waste treatment systems: A review

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Frontiers of Environmental science & engineering 2022年第7期16卷 47-59页

作者： Zhuqiu Sun Jinying Xi Chunping Yang Wenjie Cong Environmental Simulation and Pollution Control State Key Joint Laboratory School of EnvironmentTsinghua UniversityBeijing100084China State Environmental Protection Key Laboratory of Microorganism Application and Risk Control(SMARC) Beijing100084China Guangdong Provincial Key Laboratory of Petrochemical Pollution Processes and Control School of Environmental Science and EngineeringGuangdong University of Petrochemical TechnologyMaoming525099China College of Environmental Science and Engineering Hunan University and Key Laboratory of Environmental Biology and Pollution Control(Hunan University)Ministry of EducationChangsha410082China

Quorum sensing (QS) plays an important role in microbial aggregation control. Recently, the optimization of biological waste treatment systems by QS regulation gained an increasing attention. The effects of QS regulation on treatment performances and biofilm were frequently investigated. To understand the state of art of QS regulation, this review summarizes the methods of QS enhancement and QS inhibition in biological waste treatment systems. Typical QS enhancement methods include adding exogenous QS molecules, adding QS accelerants and cultivating QS bacteria, while typical QS inhibition methods include additions of quorum quenching (QQ) bacteria, QS-degrading enzymes, QS-degrading oxidants, and QS inhibitors. The specific improvements after applying these QS regulation methods in different treatment systems are concluded. In addition, the effects of QS regulation methods on biofilm in biological waste treatment systems are reviewed in terms of biofilm formation, extracellular polymeric substances production, microbial viability, and microbial community. In the end, the knowledge gaps in current researches are analyzed, and the requirements for future study are suggested.

关键词： Quorum sensing Biological waste treatment Biofilm formation

The grad-div conforming virtual element method for the quad-div problem in three dimensions

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arXiv 2024年

作者： Dong, Xiaojing Han, Yibing Huang, Yunqing Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Er huan Road Hunan Xiangtan411105 China

We propose a new stable variational formulation for the quad-div problem in three dimensions and prove its well-posedness. Using this weak form, we develop and analyze the H(grad-div)-conforming virtual element method of arbitrary approximation orders on polyhedral meshes. Three families of H(grad-div)conforming virtual elements are constructed based on the structure of a de Rham sub-complex with enhanced smoothness, resulting in an exact discrete virtual element complex. In the lowest-order case, the simplest element has only one degree of freedom at each vertex and face, respectively. We rigorously prove the interpolation error estimates, the stability of discrete bilinear forms, the well-posedness of discrete formulation and the optimal error estimates. Some numerical examples are shown to verify the theoretical results. © 2024, CC BY-NC-ND.

关键词： Mesh generation

Low-rank generalized alternating direction implicit iteration method for solving matrix equations

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arXiv 2024年

作者： Zhang, Juan Xun, Wenlu Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan China School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan China

This paper presents an effective low-rank generalized alternating direction implicit iteration (R-GADI) method for solving large-scale sparse and stable Lyapunov matrix equations and continuous-time algebraic Riccati matrix equations. The method is based on generalized alternating direction implicit iteration (GADI), which exploits the low-rank property of matrices and utilizes the Cholesky factorization approach for solving. The advantage of the new algorithm lies in its direct and efficient low-rank formulation, which is a variant of the Cholesky decomposition in the Lyapunov GADI method, saving storage space and making it computationally effective. When solving the continuous-time algebraic Riccati matrix equation, the Riccati equation is first simplified to a Lyapunov equation using the Newton method, and then the R-GADI method is employed for computation. Additionally, we analyze the convergence of the R-GADI method and prove its consistency with the convergence of the GADI method. Finally, the effectiveness of the new algorithm is demonstrated through corresponding numerical experiments. Copyright © 2024, The Authors. All rights reserved.

关键词： Riccati equations