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A LINEAR, UNCONDITIONALLY STABLE, SECOND ORDER DECOUPLED METHOD FOR THE NEMATIC LIQUID CRYSTAL FLOWS WITH SAV APPROACH

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arXiv 2025年

作者： Cao, Ruonan Yi, Nianyu School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China

In this paper, we present a second order, linear, fully decoupled, and unconditionally energy stable scheme for solving the Erickson-Leslie model. This approach integrates the pressure correction method with a scalar auxiliary variable technique. We rigorously demonstrate the unconditional energy stability of the proposed scheme. Furthermore, we present several numerical experiments to validate its convergence order, stability, and computational efficiency. © 2025, CC BY.

关键词： computational efficiency

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

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

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

AN EFFICIENT NULLSPACE-PRESERVING SADDLE SEARCH METHOD FOR PHASE TRANSITIONS INVOLVING TRANSLATIONAL INVARIANCE

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arXiv 2023年

作者： Cui, Gang Jiang, Kai Zhou, Tiejun 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

In this work, we propose an efficient nullspace-preserving saddle search (NPSS) method for a class of phase transitions involving translational invariance, where the critical states are often degenerate. The NPSS method includes two stages, escaping from the basin and searching for the index-1 generalized saddle point. The NPSS method climbs upward from the generalized local minimum in segments to overcome the challenges of degeneracy. In each segment, an effective ascent direction is ensured by keeping this direction orthogonal to the nullspace of the initial state in this segment. This method can escape the basin quickly and converge to the transition states. We apply the NPSS method to the phase transitions between crystals, and between crystal and quasicrystal, based on the Landau-Brazovskii and Lifshitz-Petrich free energy functionals. Numerical results show a good performance of the NPSS *** Codes 37M05, 49K35, 37N30 © 2023, CC BY-NC-ND.

关键词： Free energy

FETD Study of theWave Propagation in Chiral Metamaterials

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Advances in Applied Mathematics and Mechanics 2021年第1期13卷 191-202页

作者： Lei Yang Fuhao Liu Wei Yang Faculty of Information Technology Macao University of Science and TechnologyMacaoChina School of Mathematics and Computational Science Xiangtan UniversityXiangtanHunan 411105China Hunan Key Laboratory for Computation and Simulation in Science and Engineering and School of Mathematics and Computational Science Xiangtan UniversityXiangtanHunan 411105China

In this paper,we propose a finite element time-domain(FETD)method for the Maxwell’s equations in chiral metamaterials(CMMs).The time-domain model equations are constructed by the auxiliary differential equations(ADEs)*** source excitation method entitled total-field and scattered-field(TF/SF)decomposition technique is applied to FETD method for the first time in simulating the propagation of electromagnetic wave in CMMs,based on which a unified ADE-FETD-UPMLTF/SF scheme is proposed to simulate the wave in *** following properties of CMMs can be observed successfully from the numerical experiments based on our method,i.e.,the ability of the polarization rotation,and the negative phase *** amplitude of reflected wave can effectively be controlled by the physical parameters of CMMs.

关键词： Maxwell’s equations finite element time-domain(FETD) chiral metamaterials(CMMs).

On the stability and exponential decay of the 3D MHD system with mixed partial dissipation near a equilibrium state

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arXiv 2024年

作者： Deng, Xuemin Xiao, Yuelong Zang, Aibin Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411100 China The Center of Applied Mathematics Yichun University Jiangxi Yichun336000 China

A main result of this paper establishes the global stability of the 3D MHD equations with mixed partial dissipation near a background magnetic field in the domain Ω = T2 × R with T2 = [0, 1]2. More precisely, each velocity equation lacks its own directional dissipation, and the magnetic equation lacks vertical dissipation in the MHD system. The key point to obtain the stability result is that we decompose the solution (u, b) into the zeroth horizontal mode and the non-zeroth modes and complete the desired bound with the strong Poincaré type inequalities in the treatment of several nonlinear terms. Then we focus on the large-time behavior of the solution, where the non-zeroth modes decay exponentially in H2, and the solution converges to its zeroth horizontal mode. Copyright © 2024, The Authors. All rights reserved.

关键词： Magnetohydrodynamics

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

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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

Hamiltonian Boundary Value Methods (HBVMs) for functional differential equations with piecewise continuous arguments

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arXiv 2024年

作者： Gurioli, Gianmarco Wang, Weijie Yan, Xiaoqiang Università degli Studi di Firenze Florence Italy School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan411105 China Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Hunan411105 China

In this paper, a class of high-order methods to numerically solve Functional Differential Equations with Piecewise Continuous Arguments (FDEPCAs) is discussed. The framework stems from the expansion of the vector field associated with the reference differential equation along the shifted and scaled Legendre polynomial orthonormal basis, working on a suitable extension of Hamiltonian Boundary Value Methods. Within the design of the methods, a proper generalization of the perturbation results coming from the field of ordinary differential equations is considered, with the aim of handling the case of FDEPCAs. The error analysis of the devised family of methods is performed, while a few numerical tests on Hamiltonian FDEPCAs are provided, to give evidence to the theoretical findings and show the effectiveness of the obtained resolution *** Codes 65L05, 65L03, 65L06, 65P10 Copyright © 2024, The Authors. All rights reserved.

关键词： Ordinary differential equations

IMPLICIT-EXPLICIT RUNGE-KUTTA-ROSENBROCK METHODS WITH ERROR ANALYSIS FOR NONLINEAR STIFF DIFFERENTIAL EQUATIONS

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Journal of computational Mathematics 2021年第4期39卷 599-620页

作者： Bin Huang Aiguo Xiao Gengen Zhang School of Mathematics and Computational Science&Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtan 411105China South China Research Center for Applied Mathematics and Interdisciplinary Studies South China Normal UniversityGuangzhou 510631China

Implicit-explicit Runge-Kutta-Rosenbrock methods are proposed to solve nonlinear sti ordinary di erential equations by combining linearly implicit Rosenbrock methods with explicit Runge-Kutta ***,the general order conditions up to order 3 are ***,for the nonlinear sti initial-value problems satisfying the one-sided Lipschitz condition and a class of singularly perturbed initial-value problems,the corresponding errors of the implicit-explicit methods are *** last,some numerical examples are given to verify the validity of the obtained theoretical results and the e ectiveness of the methods.

关键词： Sti di erential equations Implicit-explicit Runge-Kutta-Rosenbrock method Order conditions Convergence

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

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

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