检索结果-内蒙古大学图书馆

arXiv 2025年

作者： Ding, Renjie Wang, Dongling Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan Hunan411105 China

Newton-type solvers have been extensively employed for solving a variety of nonlinear system of algebraic equations. However, for some complex nonlinear system of algebraic equations, efficiently solving these systems remains a challenging task. The primary reason for this challenge arises from the unbalanced nonlinearities within the nonlinear system. Therefore, accurately identifying and balancing the unbalanced nonlinearities in the system is essential. In this work, we propose a residual-driven adaptive strategy to identify and balance the nonlinearities in the system. The fundamental idea behind this strategy is to assign an adaptive weight multiplier to each component of the nonlinear system, with these weight multipliers increasing according to a specific update rule as the residual components increase, thereby enabling the Newton-type solver to select a more appropriate step length, ensuring that each component in the nonlinear system experiences sufficient reduction rather than competing against each other. More importantly, our strategy yields negligible additional computational overhead and can be seamlessly integrated with other Newton-type solvers, contributing to the improvement of their efficiency and robustness. We test our algorithm on a variety of benchmark problems, including a chemical equilibrium system, a convective diffusion problem, and a series of challenging nonlinear systems. The experimental results demonstrate that our algorithm not only outperforms existing Newton-type solvers in terms of computational efficiency but also exhibits superior robustness, particularly in handling systems with highly imbalanced nonlinearities. © 2025, CC BY.

关键词： Nonlinear equations

来源：评论

学校读者我要写书评

暂无评论

Guidance Law Design for Varying-Speed Missile Based on Classic Differential Geometric Principle

Guidance Law Design for Varying-Speed Missile Based on Class...

引用

International Conference on Guidance, Navigation and Control, ICGNC 2022

作者： Liu, Yuanhe Li, Kebo Qin, Xuesheng Liang, Yan’gang College of Aerospace Science and Engineering National University of Defense Technology Changsha410072 China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Changsha410072 China

ISBN: (纸本)9789811966125

For the guidance law design problem of the varying-speed missile against the stationary target, a differential geometric guidance law (DGGL) design approach is proposed in this paper. The missile kinematic model and guidance model in the arc-length domain are first derived through the differential geometric curve theory (DGCT). The concept of guidance curvature is introduced. Then, considering the nonlinearity of the guidance model, the error dynamic approach is extended to the arc-length domain, and several typical desired error dynamic equations are introduced. On this basis, taking the optimal error dynamics approach as an example, the corresponding DGGLs are derived. The optimality of the designed guidance law is extended to the scenarios of nonlinearity and varying speed. Finally, the corresponding DGGLs are simulated and compared in varying-speed missile scenarios to demonstrate the effectiveness of the proposed approach. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

关键词： Geometry

来源：评论

学校读者我要写书评

暂无评论

GTO Maneuver Trajectory Optimization Based on Analytical Model Iteration

GTO Maneuver Trajectory Optimization Based on Analytical Mod...

引用

International Conference on Guidance, Navigation and Control, ICGNC 2022

作者： Zhang, Hanyu Zhang, Jin Huang, Xuan College of Aerospace Science and Engineering National University of Defense Technology Changsha410073 China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Changsha410073 China

ISBN: (纸本)9789811966125

This paper proposes a fast, efficient, and applicable optimization method for geosynchronous transfer orbit (GTO) maneuvers. The strategy with combined maneuvers executed at apogees is adopted, and the maneuver parameters are calculated using the geometric relationship of velocity vectors and orbital parameters. The initial guess is calculated based on the J2 analytical dynamics model, and then the targeting iterative method based on analytical impulse calculation and numerical orbital integration is used for local optimization to obtain the high-precision solution. Finally, the trajectory optimization problems for GTO maneuvers launched from four different launch sites are simulated to verify the applicability and efficiency of the method. The results show that the proposed method has good convergence ability, the calculating time is less than 60 s, and the required number of numerical integration is less than 100. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

关键词： Analytical models

来源：评论

学校读者我要写书评

暂无评论

Design approach of contingency point return trajectory for manned lunar missions based on homotopy continuation 3

Design approach of contingency point return trajectory for m...

引用

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

作者： Lu, Lin Li, Haiyang Dong, Tianshan Zhu, Binyu College of Aerospace Science and Engineering National University of Defense Technology Changsha410073 China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Changsha410073 China Beijing Institute of Spacecraft System Engineering Beijing100094 China

In terms of the requirement of contingency return during the circumlunar flight phase in manned lunar missions, this article presents a contingency point return trajectory design approach. In consideration of the point return constraint, an initial value estimate model is proposed. A nonlinear programming problem is constructed and solved by adopting an improved differential evolution algorithm with good global search ability. On the basis of the initial value estimate, homotopy continuation is used to gradually approximate and obtain the high-fidelity solution. The simulation results indicate that the design approach can effectively calculate a contingency point return trajectory with good convergence. © Published under licence by IOP Publishing Ltd.

关键词： Lunar missions

来源：评论

学校读者我要写书评

暂无评论

Local convergence analysis of L1/finite element scheme for a constant delay reaction-subdiffusion equation with uniform time mesh

arXiv

引用

arXiv 2024年

作者： Bu, Weiping Zheng, Xin School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan411105 China

The aim of this paper is to develop a refined error estimate of L1/finite element scheme for a reaction-subdiffusion equation with constant delay τ and uniform time mesh. Under the non-uniform multi-singularity assumption of exact solution in time, the local truncation errors of the L1 scheme with uniform mesh is investigated. Then we introduce a fully discrete finite element scheme of the considered problem. Next, a novel discrete fractional Grönwall inequality with constant delay term is proposed, which does not include the increasing Mittag-Leffler function comparing with some popular other cases. By applying this Grönwall inequality, we obtain the pointwisein-time and piecewise-in-time error estimates of the finite element scheme without the Mittag-Leffler function. In particular, the latter shows that, for the considered interval ((i-1)τ, iτ], although the convergence in time is low for i = 1, it will be improved as the increasing i, which is consistent with the factual assumption that the smoothness of the solution will be improved as the increasing i. Finally, we present some numerical tests to verify the developed theory. Copyright © 2024, The Authors. All rights reserved.

关键词： Finite element method

来源：评论

学校读者我要写书评

暂无评论

Mixed-integer Planning of Spacecraft Accompanying Flying Trajectory with Full-duration Illumination Angle Constraints

引用

Yuhang Xuebao/Journal of Astronautics 2025年第2期46卷 334-345页

作者： Fang, Xuankun Wang, Hua Lu, Lin Huo, Chengyi He, Junhua College of Aerospace Science and Engineering National University of Defense Technology Changsha410073 China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Changsha410073 China

To address the unique requirements of close-range high-definition optical observation missions for space targets，an impulsive maneuver planning method is developed，which accounts for sunlight angle constraints throughout the entire accompanying flight process. Initially，the variation patterns of the angle β are analyzed，and a simplified model for the motion of the sun vector is established within the target orbital coordinate system. Subsequently，the relative orbit of the accompanying spacecraft is designed using impulsive control. The nominal sunlight angle constraint is incorporated，considering the impact of orbital perturbations，and a mixed-integer planning model for the relative orbit of the accompanying spacecraft is formulated based on the CW equations. Next，the differential evolution algorithm is employed to determine the impulsive control strategy for the accompanying flight that minimizes fuel consumption，providing a reference maneuver scheme for mission execution. Numerical simulation results demonstrate that the adopted maneuver planning method can derive a maneuver control scheme that meets the required sunlight angle for the entire process with optimal fuel consumption，confirming the method’s effectiveness and accuracy. Lastly，through extensive simulation calculations，the relationship between the total velocity increment and its related influence parameters during the entire accompanying flight process is analyzed. © 2025 Chinese Society of Astronautics. All rights reserved.

关键词： Integer programming

来源：评论

学校读者我要写书评

暂无评论

Asymptotic stability of many numerical schemes for phase-field modeling

arXiv

引用

arXiv 2024年

作者： Li, Pansheng Wang, Dongling Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

The numerical stability of nonlinear equations has been a long-standing concern and there is no standard framework for analyzing long-term qualitative behavior. In the recent breakthrough work [XX23], a rigorous numerical analysis was conducted on the numerical solution of a scalar ODE containing a cubic polynomial derived from the Allen-Cahn equation. It was found that only the implicit Euler method converge to the correct steady state for any given initial value u0 under the unique solvability and energy stability. But all the other commonly used second-order numerical schemes exhibit sensitivity to initial conditions and may converge to an incorrect equilibrium state as tn → ∞. This indicates that energy stability may not be decisive for the long-term qualitative correctness of numerical solutions. We found that using another fundamental property of the solution, namely monotonicity instead of energy stability, is sufficient to ensure that many common numerical schemes converge to the correct equilibrium state. This leads us to introduce the critical step size constant h∗ = h∗(u0, ϵ) that ensures the monotonicity and unique solvability of the numerical solutions, where the scaling parameter ϵ ∈ (0, 1). For a given numerical method, if the initial value u0 is given, no matter how large it is, we prove that h∗ > 0. As long as the actual simulation step 0 ∗, the numerical solution preserves monotonicity and converges to the correct equilibrium state. On the other hand, we prove that the implicit Euler scheme h∗ = h∗(ϵ), which is independent of u0 and only depends on ϵ. Hence regardless of the initial value taken, the simulation can be guaranteed to be correct when h ∗. But for various other numerical methods, no mater how small the step size h is in advance, there will always be initial values that cause simulation errors. In fact, for these numerical methods, we prove that infu0∈R h∗(u0, ϵ) = 0. Various numerical experiments are used to confirm the theoretical anal

关键词： Nonlinear equations

来源：评论

学校读者我要写书评

暂无评论

A Convergence Analysis of a Structure-Preserving Gradient Flow Method for the All-Electron Kohn-Sham Model

引用

Numerical Mathematics(Theory,Methods and Applications) 2023年第3期16卷 597-621页

作者： Yedan Shen Ting Wang Jie Zhou Guanghui Hu School of Mathematics and Information Science Guangzhou UniversityGuangzhouChina Faculty of Science and Technology University of MacaoMacao SARChina Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtanChina School of Mathematical Computational Sciences Xiangtan UniversityXiangtanChina Zhuhai UM Science&Technology Research Institute ZhuhaiChina Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications University of MacaoMacao SARChina

In[Dai et al.,***.18(4)(2020)],a structure-preserving gradient flow method was proposed for the ground state calculation in Kohn-Sham density functional theory,based on which a linearized method was developed in[Hu et al.,EAJAM.13(2)(2023)]for further improving the numerical *** this paper,a complete convergence analysis is delivered for such a linearized method for the all-electron Kohn-Sham ***,the convergence,the asymptotic stability,as well as the structure-preserving property of the linearized numerical scheme in the method is discussed following previous works,while spatially,the convergence of the h-adaptive mesh method is demonstrated following[Chen et al.,***.12(2014)],with a key study on the boundedness of the Kohn-Sham potential for the all-electron Kohn-Sham *** examples confirm the theoretical results very well.

关键词： Kohn-Sham density functional theory gradient flow model structure-preserving linear scheme convergence analysis

来源：评论

学校读者我要写书评

暂无评论

Kernel-learning parameter prediction and evaluation in algebraic multigrid method for several PDEs

arXiv

引用

arXiv 2025年

作者： Zhang, Juan Luo, Junyue Zhang, Fangfang Yue, Xiaoqiang Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

This paper explores the application of kernel learning methods for parameter prediction and evaluation in the Algebraic Multigrid Method (AMG), focusing on several Partial Differential Equation (PDE) problems. AMG is an efficient iterative solver for large-scale sparse linear systems, particularly those derived from elliptic and parabolic PDE discretizations. However, its performance heavily relies on numerous parameters, which are often set empirically and are highly sensitive to AMG’s effectiveness. Traditional parameter optimization methods are either computationally expensive or lack theoretical support. To address this, we propose a Gaussian Process Regression (GPR)-based strategy to optimize AMG parameters and introduce evaluation metrics to assess their effectiveness. Trained on small-scale datasets, GPR predicts nearly optimal parameters, bypassing the time-consuming parameter sweeping process. We also use kernel learning techniques to build a kernel function library and determine the optimal kernel function through linear combination, enhancing prediction accuracy. In numerical experiments, we tested typical PDEs such as the constant-coefficient Poisson equation, variable-coefficient Poisson equation, diffusion equation, and Helmholtz equation. Results show that GPR-predicted parameters match grid search results in iteration counts while significantly reducing computational time. A comprehensive analysis using metrics like mean squared error, prediction interval coverage, and Bayesian information criterion confirms GPR’s efficiency and reliability. These findings validate GPR’s effectiveness in AMG parameter optimization and provide theoretical support for AMG’s practical application. © 2025, CC BY.

关键词： Poisson equation

来源：评论

学校读者我要写书评

暂无评论

Influences of Element Types on Nonlinear Finite Element Analysis of a Concrete Column Under Near-Field Blast Loading

Influences of Element Types on Nonlinear Finite Element Anal...

引用

Recent Advances in Applied Mechanics and Mechanical engineering - Select Proceedings of ICAMME 2022

作者： Xu, Jie Hendriks, Max A. N. Rots, Jan G. Tsouvalas, Apostolos 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 Faculty of Civil Engineering and Geosciences Delft University of Technology Zuid Holland Delft2628 CN Netherlands

ISBN: (纸本)9789819923748

Due to the accompanying severe consequences of explosions, the blast puts a great threat to public security. Nonlinear finite element analysis is a possible method for civil engineers to check the integrity of the structures under blast loading without underestimating the limit of the structures. However, different choices of element types would generally put a great influence on the analytical results and the corresponding computational expenses. Therefore, how should civil engineers simplify their physical model into finite element models to gain relatively accurate numerical results with acceptable computational expenses is of great interest. In this article, 6 different types of elements are discussed with different orders and shapes for a certain physical situation, and the corresponding experimental results and the numerical results for a very detailed finite element model are used as the baseline for judgement, which could be helpful for civil engineers to make proper simplifications in the set-up of finite element models. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

关键词： Engineers

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：