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arXiv 2020年

作者： Wei, Huayi Wang, Xin Chen, Chunyu Jiang, Kai School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan411105 China

In this paper, we develop a high-order adaptive virtual element method (VEM) to simulate the self-consistent field theory (SCFT) model in arbitrary domains. The VEM is very flexible in handling general polygon elements and can treat hanging nodes as polygon vertices without additional processing. Besides, to effectively simulate the phase separation behavior in strong segregation systems, an adaptive method on polygonal mesh equipped with a new marking strategy is developed. This new marking strategy will indicate the times of marked elements to be refined and coarsened, making full use of the information contained in the current numerical results. Using the halfedge data structure, we can apply the adaptive method to the arbitrary polygonal mesh. Numerical results demonstrate that the developed method is efficient in simulating polymers’ phase behavior in complex geometric domains. The accuracy is consistent with theoretical results. The adaptive method can greatly reduce computational costs to obtain prescribed numerical accuracy for strong segregation systems. Copyright © 2020, The Authors. All rights reserved.

关键词： Mean field theory

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High accuracy techniques based adaptive finite element methods for elliptic PDEs

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Journal of computational and Applied Mathematics 2026年 472卷

作者： Jingjing Xiao Ying Liu Nianyu Yi School of Mathematics and Computational Science Xiangtan University Xiangtan 411105 PR China School of Science Xi’an University of Technology Xi’an 710048 PR China Hunan National Center for Applied Mathematics； Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan 411105 PR China

This paper aims to develop an efficient adaptive finite element method for the second-order elliptic problem. Although the theory for adaptive finite element methods based on residual-type a posteriori error estimator and bisection refinement has been well established, in practical computations, the use of non-asymptotic exactness of error estimator and the excessive number of adaptive iteration steps often lead to inefficiency of the adaptive algorithm. We propose an efficient adaptive finite element method based on high-accuracy techniques including the superconvergence recovery technique and high-quality mesh optimization. The centroidal Voronoi Delaunay triangulation mesh optimization is embedded in the mesh adaptation to provide a high-quality mesh, and then ensure the superconvergence property of the recovered gradient and the asymptotic exactness of the error estimator. A tailored adaptive strategy, which can generate high-quality meshes with a target number of vertices, is developed to ensure the adaptive computation process terminates within 7 steps. The effectiveness and robustness of the adaptive algorithm are numerically demonstrated.

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Hybridization of evolutionary algorithm and deep reinforcement learning for multi-objective orienteering optimization

arXiv

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arXiv 2022年

作者： Liu, Wei Wang, Rui Zhang, Tao Li, Kaiwen Li, Wenhua Ishibuchi, Hisao The College of System Engineering National University of Defense Technology Changsha410073 China The Hunan Key Laboratory of Multi-Energy System Intelligent Interconnection Technology HKLMSI2T Changsha410073 China Guangdong Provincial Key Laboratory of Braininspired Intelligent Computation Department of Computer Science and Engineering Southern University of Science and Technology Shenzhen518055 China

Multi-objective orienteering problems (MO-OPs) are classical multi-objective routing problems and have received a lot of attention in the past decades. This study seeks to solve MO-OPs through a problem-decomposition framework, that is, a MO-OP is decomposed into a multi-objective knapsack problem (MOKP) and a travelling salesman problem (TSP). The MOKP and TSP are then solved by a multi-objective evolutionary algorithm (MOEA) and a deep reinforcement learning (DRL) method, respectively. While the MOEA module is for selecting cities, the DRL module is for planning a Hamiltonian path for these cities. An iterative use of these two modules drives the population towards the Pareto front of MO-OPs. The effectiveness of the proposed method is compared against NSGA-II and NSGA-III on various types of MO-OP instances. Experimental results show that our method exhibits the best performance on almost all the test instances, and has shown strong generalization ability. Copyright © 2022, The Authors. All rights reserved.

关键词： Multiobjective optimization

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An Interpretable MRI Reconstruction Network with Two-grid-cycle Correction and Geometric Prior Distillation

arXiv

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arXiv 2022年

作者： Fan, Xiaohong Yang, Yin Chen, Ke Zhang, Jianping Dong, Ke The School of Mathematics and Computational Science Xiangtan University Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education Xiangtan411105 China The School of Mathematics and Computational Science Xiangtan University Hunan National Applied Mathematics Center Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan411105 China Centre for Mathematical Imaging Techniques Department of Mathematical Sciences The University of Liverpool Merseyside LiverpoolL6972L United Kingdom The School of Mathematics and Computational Science Xiangtan University Hunan National Applied Mathematics Center Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education Xiangtan411105 China Department of Radiation Oncology Xiangtan Central Hospital Xiangtan411101 China

Although existing deep learning compressed-sensing-based Magnetic Resonance Imaging (CS-MRI) methods have achieved considerably impressive performance, explainability and generalizability continue to be challenging for such methods since the transition from mathematical analysis to network design not always natural enough, often most of them are not flexible enough to handle multi-sampling-ratio reconstruction assignments. In this work, to tackle explainability and generalizability, we propose a unifying deep unfolding multi-sampling-ratio interpretable CS-MRI framework. The combined approach offers more generalizability than previous works whereas deep learning gains explainability through a geometric prior module. Inspired by the multigrid algorithm, we first embed the CSMRI-based optimization algorithm into correction-distillation scheme that consists of three ingredients: pre-relaxation module, correction module and geometric prior distillation module. Furthermore, we employ a condition module to learn adaptively step-length and noise level, which enables the proposed framework to jointly train multi-ratio tasks through a single model. The proposed model not only compensates for the lost contextual information of reconstructed image which is refined from low frequency error in geometric characteristic k-space, but also integrates the theoretical guarantee of model-based methods and the superior reconstruction performances of deep learning-based methods. Therefore, it can give us a novel perspective to design biomedical imaging networks. Numerical experiments show that our framework outperforms state-of-the-art methods in terms of qualitative and quantitative evaluations. Our method achieves 3.18 dB improvement at low CS ratio 10% and average 1.42 dB improvement over other comparison methods on brain dataset using Cartesian sampling mask. Copyright © 2022, The Authors. All rights reserved.

关键词： Distillation

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Are Electric Vehicles Greener than Hybrid Electric Vehicles in Carsharing? Insights from Large-Scale Multi-Objective simulation-Optimization

SSRN

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SSRN 2024年

作者： Li, Yan Hu, Lu Li, Haobin Chew, Ek Peng Li, Hao Zhu, Juanxiu Department of Industrial Systems Engineering and Management National University of Singapore Singapore Centre of Excellence in Modelling and Simulation for Next Generation Ports National University of Singapore Singapore School of Transportation and Logistics Southwest Jiaotong University Chengdu China School of Traffic and Transportation Engineering Changsha University of Science and Technology Changsha China Hunan Key Laboratory of Smart Roadway and Cooperative Vehicle Infrastructure Systems Changsha University of Science and Technology Changsha China School of Management Xihua University Chengdu China

Hybrid electric vehicles (HEVs) are perceived as transitional products bridging the gap between fueled vehicles and electric vehicles (EVs) because people intuitively believe that EVs are more environmentally friendly than HEVs. But is this perception true in the context of carsharing services (CSSs)? This paper pioneers a general large-scale multi-objective simulation-optimization (MOSO) method to explore the values of deploying HEVs in CSSs. We firstly develop a physically logical simulation model, emulating operations of CSSs and capturing mesoscopic dynamics of shared vehicles in a link-based traffic network. This model adopts an event-driven discrete-event mechanism, enhancing efficiency while maintaining high fidelity. Subsequently, we design a simulation-optimization framework aimed at achieving Pareto optimality by jointly optimizing station capacity, fleet size, and trip pricing. The goal is twofold: to maximize operational profits and to minimize carbon emissions, thereby quantitatively analysing the potential of shared HEVs (SHEVs). To tackle the high-dimensional MOSO problem, we propose a general algorithm that incorporates the multiple gradient descent algorithm with the simultaneous perturbation stochastic approximation algorithm. Furthermore, we derive its analytical expression for bi-objective optimization problems. We theoretically prove and practically demonstrate its strong global convergence. The efficiency of this method was validated through large-scale computational experiments conducted in Chengdu, Sichuan Province, involving 66,710 decision variables. These experiments showcased the method's superiority over existing MOSO algorithms. Several groups of sensitivity experiments focusing on vehicle types and traffic scenarios reveal some interesting findings. (1) Regardless of the increase in travel distances, SHEVs, which can be viewed as shared EVs (SEVs) without range anxiety (RA), continue to primarily rely on electricity rather than fuel fo

关键词： Stochastic systems

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The Control Design of Space Flying Net Robot System Based on RBF Network

The Control Design of Space Flying Net Robot System Based on...

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Chinese Automation Congress (CAC)

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

ISBN: (纸本)9781665426480

Space Flying Net Robot System (SFNRS) is a new capture method of space debris. In this paper, the SFNRS dynamic equations are established by using the lumped mass method. The previous studies about controller design assumed that the mass of the maneuvering unit in SFNRS is known and a constant while it is unknown in fact. In addition, the upper boundary of tension in the space net is often assumed as a known constant, but it is difficult to get the value. In this paper, the radial basis function (RBF) network is used to design a controller in order to overcome the shortcomings above. Finally, the simulation is carried out to verify the effectiveness and the robustness of the proposed method.

关键词： Upper bound Control design Space debris simulation Radial basis function networks Aerospace electronics Robustness

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An Improved Third-order CWENO-Z Scheme at critical points 2

An Improved Third-order CWENO-Z Scheme at critical points

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2019 2nd International Conference on Advanced Materials, Intelligent Manufacturing and Automation, AMIMA 2019

作者： Tang, Shujiang Li, Mingjun Han, Shuang School of Mathematics and Computational Science Xiangtan University Xiangtan Hunan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan Hunan411105 China

In this paper, by modifying the smoothness factor of the third-order CWENO scheme, we present the two-parameter CWENO-NZ3 scheme to improve accuracy at critical points. We selected some classical examples for numerical simulation, such as one-dimensional Sod shock tube, Shock-entropy wave interaction, Riemann problem with strong discontinuity and Rayleigh-Taylor instability problem. Numerically comparing with the classical third-order CWENO schemes, it is found that the improved schemes not only improve accuracy and resolution at the extreme points, but also reduce dissipation. © Published under licence by IOP Publishing Ltd.

关键词： Shock tubes

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A Two-level Overlapping Schwarz Method Using Energy Minimizing Multiscale Finite Element Functions 25th

A Two-level Overlapping Schwarz Method Using Energy Minimizi...

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25th International Conference on Domain Decomposition Methods in science and engineering, DD 2018

作者： Kim, Hyea Hyun Chung, Eric T. Wang, Junxian Department of Applied Mathematics and Institute of Natural Sciences Kyung Hee University Region Korea Republic of Department of Mathematics The Chinese University of Hong Kong SAR Hong Kong Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan China

ISBN: (纸本)9783030567491

关键词： Finite element method

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AN ADAPTIVE FINITE ELEMENT METHOD FOR TWO-DIMENSIONAL ELLIPTIC EQUATIONS WITH LINE DIRAC SOURCES

arXiv

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arXiv 2021年

作者： Cao, Huihui Li, Hengguang Yi, Nianyu Yin, Peimeng Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China Wayne State University Department of Mathematics DetroitMI48202 United States Multiscale Methods and Dynamics Group Computer Science and Mathematics Division Oak Ridge National Laboratory Oak RidgeTN37831 United States

In this paper, we propose a novel adaptive finite element method for an elliptic equation with line Dirac delta functions as a source term. We first study the well-posedness and global regularity of the solution in the whole domain. Instead of regularizing the singular source term and using the classical residual-based a posteriori error estimator, we propose a novel a posteriori estimator based on an equivalent transmission problem with zero source term and nonzero flux jumps on line fractures. The transmission problem is defined in the same domain as the original problem excluding on line fractures, and the solution is therefore shown to be more regular. The estimator relies on meshes conforming to the line fractures and its edge jump residual essentially uses the flux jumps of the transmission problem on line fractures. The error estimator is proven to be both reliable and efficient, an adaptive finite element algorithm is proposed based on the error estimator and the bisection refinement method. Numerical tests show that quasi-optimal convergence rates are achieved even for high order approximations and the adaptive meshes are only locally refined at singular points. © 2021, CC BY-NC-ND.

关键词： Fracture

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An improved functional dependency network model for information systems effectiveness analysis 2020

An improved functional dependency network model for informat...

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2020 International Conference on Wireless Communication and Sensor Networks, icWCSN 2020

作者： Luo, Aimin Yi, Shuanghui Liu, Junxian Kou, Yuxiao Gao, Lanlan Zhang, Mengmeng Science and Technology on Information Systems Engineering Laboratory National University of Defense Technology Changsha Hunan410073 China National Key Laboratory for Complex System Simulation Beijing China Academy of Military Science of the PLA Beijing100000 China

ISBN: (纸本)9781450377638

To address the limitations of the FDNA approach, in this paper, we analyze the dependency of the receiver node on the feeder nodes as well as the impact of the node's operability level on the system effectiveness, and improve the FDNA approach. We also propose a computing method for system effectiveness based on an improved FDNA model, and conduct relevant case verification. © 2020 ACM.

关键词： Information systems

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