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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

The Schur complements for SDD1 matrices and their application to linear complementarity problems

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arXiv 2025年

作者： Hu, Yang Liu, Jianzhou Zeng, Wenlong School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan China Department of Mathematics Shanghai University Shanghai200444 China

In this paper we propose a new scaling method to study the Schur complements of SDD1 matrices. Its core is related to the non-negative property of the inverse M-matrix, while numerically improving the Quotient formula. Based on the Schur complement and a novel norm splitting manner, we establish an upper bound for the infinity norm of the inverse of SDD1 matrices, which depends solely on the original matrix entries. We apply the new bound to derive an error bound for linear complementarity problems of B1-matrices. Additionally, new lower and upper bounds for the determinant of SDD1 matrices are presented. Numerical experiments validate the effectiveness and superiority of our results. © 2025, CC BY.

关键词： Matrix algebra

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

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

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).

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

High-accurate and efficient numerical algorithms for the self-consistent field theory of liquid-crystalline polymers

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arXiv 2024年

作者： He, Zhijuan Jiang, Kai Tan, Liwei Wang, Xin 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 School of Mathematical Sciences Shanghai Jiao Tong University Shanghai200240 China

Self-consistent field theory (SCFT) is one of the most widely-used framework in studying the equilibrium phase behaviors of inhomogenous polymers. For liquid crystalline polymeric systems, the main numerical challenges of solving SCFT encompass efficiently solving plenty of six dimensional partial differential equations (PDEs), precisely determining the subtle energy difference among self-assembled structures, and developing effective iterative methods for nonlinear SCF iteration. To address these challenges, this work introduces a suite of high-order and efficient numerical methods tailored for SCFT of liquid-crystalline polymers. These methods include various advaced PDE solvers, an improved Anderson iteration algorithm to accelerate SCFT calculations, and an optimization technique of adjusting the computational domain during the SCF iterations. Extensive numerical tests demonstrate the efficiency of the proposed methods. Based on these algorithms, we further explore the self-assembly behavior of liquid crystalline polymers through simulations in four, five, and six dimensions, uncovering intricate three-dimensional spatial structures. Copyright © 2024, The Authors. All rights reserved.

关键词： Crystalline materials