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arXiv 2024年

作者： Feng, Yujie Yang, Yin Fan, Xiaohong Zhang, Zhengpeng Bu, Lijing Zhang, Jianping School of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory for Intelligent Computing and Information Processing of the Ministry of Education Xiangtan411105 China School of Mathematics and Computational Science Xiangtan University National Center for Applied Mathematics in Hunan Hunan International Scientific and Technological Innovation Cooperation Base of Computational Science Xiangtan411105 China College of Mathematical Medicine Zhejiang Normal University Jinhua321004 China School of Automation and Electronic Information Xiangtan University Xiangtan411105 China

Recently, deep learning methods have gained remarkable achievements in the field of image restoration for remote sensing (RS). However, most existing RS image restoration methods focus mainly on conventional first-order degradation models, which may not effectively capture the imaging mechanisms of remote sensing images. Furthermore, many RS image restoration approaches that use deep learning are often criticized for their lacks of architecture transparency and model interpretability. To address these problems, we propose a novel progressive restoration network for high-order degradation imaging (HDI-PRNet), to progressively restore different image degradation. HDI-PRNet is developed based on the theoretical framework of degradation imaging, offering the benefit of mathematical interpretability within the unfolding network. The framework is composed of three main components: a module for image denoising that relies on proximal mapping prior learning, a module for image deblurring that integrates Neumann series expansion with dual-domain degradation learning, and a module for super-resolution. Extensive experiments demonstrate that our method achieves superior performance on both synthetic and real remote sensing images. Copyright © 2024, The Authors. All rights reserved.

关键词： Image reconstruction

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A fast finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction-diffusion equation

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International Journal of Modeling, simulation, and Scientific Computing 2020年第2期11卷 115-132页

作者： Yaping Zhang Jiliang Cao Weiping Bu Aiguo Xiao School of Mathematics and Computational Science and Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University 411105 HunanP.R.China College of Science Shaoyang University 422000 ShaoyangP.R.China

In this work,we develop a finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction-diffusion equation(2D-DOTSFRDE)with low regularity solution at the initial time.A fast evaluation of the distributedorder time fractional derivative based on graded time mesh is obtained by substituting the weak singular kernel for the *** stability and convergence of the developed semi-discrete scheme to 2D-DOTSFRDE are *** the spatial approximation,the finite element method is *** convergence of the corresponding fully discrete scheme is ***,some numerical tests are given to verify the obtained theoretical results and to demonstrate the effectiveness of the method.

关键词： Distributed-order fractional derivative fractional reaction-diffusion equation fast evaluation graded mesh finite element method error estimate

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A CONSERVATIVE RELAXATION CRANK-NICOLSON FINITE ELEMENT METHOD FOR THE SCHRÖDINGER-POISSON EQUATION

arXiv

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arXiv 2024年

作者： Liu, Huini Yi, Nianyu Yin, Peimeng 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 Department of Mathematical Sciences The University of Texas at El Paso El PasoTX79968 United States

In this paper, we propose a novel mass and energy conservative relaxation Crank-Nicolson finite element method for the Schrödinger-Poisson equation. Utilizing only a single auxiliary variable, we simultaneously reformulate the distinct nonlinear terms present in both the Schrödinger equation and the Poisson equation into their equivalent expressions, constructing an equivalent system to the original Schrödinger-Poisson equation. Our proposed scheme, derived from this new system, operates linearly and bypasses the need to solve the nonlinear coupled equation, thus eliminating the requirement for iterative techniques. We in turn rigorously derive error estimates for the proposed scheme, demonstrating second-order accuracy in time and (k+1)th order accuracy in space when employing polynomials of degree up to k. Numerical experiments validate the accuracy and effectiveness of our method and emphasize its conservation properties over long-time *** Codes 35Q55, 65M15, 65M60 © 2024, CC BY-NC-ND.

关键词： Poisson equation

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MVMS-RCN: A Dual-Domain Unified CT Reconstruction with Multi-sparse-view and Multi-scale Refinement-correction

arXiv

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arXiv 2024年

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

X-ray Computed Tomography (CT) is one of the most important diagnostic imaging techniques in clinical applications. Sparse-view CT imaging reduces the number of projection views to a lower radiation dose and alleviates the potential risk of radiation exposure. Most existing deep learning (DL) and deep unfolding sparse-view CT reconstruction methods: 1) do not fully use the projection data;2) do not always link their architecture designs to a mathematical theory;3) do not flexibly deal with multi-sparse-view reconstruction assignments. This paper aims to use mathematical ideas and design optimal DL imaging algorithms for sparse-view CT reconstructions. We propose a novel dual-domain unified framework that offers a great deal of flexibility for multi-sparse-view CT reconstruction through a single model. This framework combines the theoretical advantages of model-based methods with the superior reconstruction performance of DL-based methods, resulting in the expected generalizability of DL. We propose a refinement module that utilizes unfolding projection domain to refine full-sparse-view projection errors, as well as an image domain correction module that distills multi-scale geometric error corrections to reconstruct sparse-view CT. This provides us with a new way to explore the potential of projection information and a new perspective on designing network architectures. The multi-scale geometric correction module is end-to-end learnable, and our method could function as a plug-and-play reconstruction technique, adaptable to various applications. Extensive experiments demonstrate that our framework is superior to other existing state-of-the-art methods. Our source codes are available at https://***/fanxiaohong/MVMS-RCN. Copyright © 2024, The Authors. All rights reserved.

关键词： Geometry

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A Multi-scale Generalized Shrinkage Threshold Network for Image Blind Deblurring in Remote Sensing

arXiv

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arXiv 2023年

作者： Feng, Yujie Yang, Yin Fan, Xiaohong Zhang, Zhengpeng Zhang, Jianping School of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory for Intelligent Computing and Information Processing The Ministry of Education Xiangtan411105 China School of Mathematics and Computational Science Xiangtan University National Center for Applied Mathematics in Hunan Hunan International Scientific and Technological Innovation Cooperation Base of Computational Science Xiangtan411105 China School of Automation and Electronic Information Xiangtan University Xiangtan411105 China

MSC Codes 54H30, 68U10, 94A08Remote sensing images are essential for many applications of the earth’s sciences, but their quality can usually be degraded due to limitations in sensor technology and complex imaging environments. To address this, various remote sensing image deblurring methods have been developed to restore sharp and high-quality images from degraded observational data. However, most traditional model-based deblurring methods usually require predefined hand-crafted prior assumptions, which are difficult to handle in complex applications. On the other hand, deep learning-based deblurring methods are often considered as black boxes, lacking transparency and interpretability. In this work, we propose a new blind deblurring learning framework that utilizes alternating iterations of shrinkage thresholds. This framework involves updating blurring kernels and images, with a theoretical foundation in network design. Additionally, we propose a learnable blur kernel proximal mapping module to improve the accuracy of the blur kernel reconstruction. Furthermore, we propose a deep proximal mapping module in the image domain, which combines a generalized shrinkage threshold with a multi-scale prior feature extraction block. This module also incorporates an attention mechanism to learn adaptively the importance of prior information, improving the flexibility and robustness of prior terms, and avoiding limitations similar to hand-crafted image prior terms. Consequently, we design a novel multi-scale generalized shrinkage threshold network (MGSTNet) that focuses specifically on learning deep geometric prior features to enhance image restoration. Experimental results on real and synthetic remote sensing image datasets demonstrate the superiority of our MGSTNet framework compared to existing deblurring methods. Copyright © 2023, The Authors. All rights reserved.

关键词： Shrinkage

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RECOVERY TYPE A POSTERIORI ERROR ESTIMATION OF AN ADAPTIVE FINITE ELEMENT METHOD FOR CAHN-HILLIARD EQUATION

arXiv

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arXiv 2023年

作者： Chen, Yaoyao Huang, Yunqing Yi, Nianyu Yin, Peimeng School of Mathematics and Statistics Anhui Normal University Wuhu241000 China Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China Multiscale Methods and Dynamics Group Computer Science and Mathematics Division Oak Ridge National Laboratory Oak RidgeTN37831 United States

In this paper, we derive a novel recovery type a posteriori error estimation of the Crank-Nicolson finite element method for the Cahn-Hilliard equation. To achieve this, we employ both the elliptic reconstruction technique and a time reconstruction technique based on three time-level approximations, resulting in an optimal a posteriori error estimator. We propose a time-space adaptive algorithm that utilizes the derived a posteriori error estimator as error indicators. Numerical experiments are presented to validate the theoretical findings, including comparing with an adaptive finite element method based on a residual type a posteriori error estimator. © 2023, CC BY-NC-ND.

关键词： Recovery

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A BDDC method for three-dimensional advection-diffusion problems with an adaptive coarse space

arXiv

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arXiv 2025年

作者： Peng, Jie Shu, Shi Wang, Junxian Zhong, Liuqiang College of Mathematics and Statistics Hengyang Normal University Hengyang421010 China School of Mathematical Sciences South China Normal University Guangzhou510631 China School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China

The solution of nonsymmetric positive definite (NSPD) systems for advection-diffusion problems is an important research topic in science and engineering. The adaptive BDDC method is a significant class of non-overlapping domain decomposition methods, which is often used for solving symmetric positive definite problems. In this paper, we apply the adaptive BDDC method to solve the NSPD systems of te advection-diffusion problems. Moreover, by designing a class of edge generalized eigenvalue problems based on prior selected primal constraints, the number of primal unknowns is further reduced. Numerical experiments have verified the effectiveness of the proposed methods. Copyright © 2025, The Authors. All rights reserved.

关键词： Domain decomposition methods

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Lattice Boltzmann simulation reveals supercritical bifurcation in flow mode transitions of power-law fluids in the four-roll mill

arXiv

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arXiv 2025年

作者： Yu, Yuan Jiang, Xiao Gu, Qingqing Lin, Chuandong Zhu, Qingyong Yuan, Hai-Zhuan School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China National Center for Applied Mathematics in Hunan Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China School of Energy and Power Engineering University of Shanghai for Science and Technology Shanghai200093 China Sino-French Institute of Nuclear Engineering and Technology Sun Yat-sen University Zhuhai519082 China School of Aeronautics and Astronautics Sun Yat-sen University Shenzhen518107 China

The four-roll mill has been traditionally viewed as a device generating simple extensional flow with a central stagnation point. Our systematic investigation using a two-relaxation-time regularized lattice Boltzmann (TRT-RLB) model reveals unexpected richness in the flow physics, identifying two previously unreported supercritical bifurcation modes: a quadrifoliate vortex mode featuring four symmetrical counter-rotating vortices, and a dumbbell-shaped quad-vortex mode where vortices detach from but remain symmetric about the stagnation point. The numerical framework, representing the first successful extension of TRT-RLB method to power-law fluid dynamics, enables comprehensive mapping of flow characteristics across Reynolds numbers (1 ≤ Re ≤ 50), power-law indices (0.7 ≤ n ≤ 1.3), and geometric configurations. The transition from quadrifoliate vortex mode exhibits distinct pathways depending on the power-law index: at relatively small n, the flow undergoes a direct supercritical bifurcation to simple extensional flow, while at relatively large n, it evolves through an intermediate dumbbell-shaped state. Among geometric parameters, the roller radius r emerges as the dominant factor controlling bifurcation points and vortex dimensions, whereas the roller-container gap δ exerts minimal influence on flow regimes. The transitions between flow modes can be precisely characterized through the evolution of vortex dimensions and velocity gradients at the stagnation point, providing quantitative criteria for flow regime identification. These findings enrich our fundamental understanding of bifurcation phenomena in extensional devices and provide quantitative guidelines for achieving desired flow patterns in four-roll mill applications. Copyright © 2025, The Authors. All rights reserved.

关键词： Vortex flow

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Phase behavior of symmetric diblock copolymers under 3D soft confinement

arXiv

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arXiv 2024年

作者： He, Zhijuan Huang, Jin Jiang, Kai Shi, An-Chang School of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing Ministry of Education 411105 China Laboratory of Mathematics and Complex Systems Ministry of Education School of Mathematical Sciences Beijing Normal University Beijing100875 China Department of Physics and Astronomy McMaster University HamiltonONL8S 4M1 Canada

The phase behavior of symmetric diblock copolymers under three-dimensional (3D) soft confinement is investigated using the self-consistent field theory. The soft confinement is realized in binary blends composed AB diblock copolymers and C homopolymers, where the copolymers self-assemble to form a droplet embedded in the homopolymer matrix. The phase behavior of the confined block copolymers is regulated by the degree of confinement and the selectivity of the homopolymers, resulting in a rich variety of novel structures. When the C homopolymers are neutral to the A- and B-blocks, stacked lamellae (SL) are formed where the number of layers increases with the droplet volume, resulting in a morphological transition sequence from Janus particle to square SL. When the C homopolymers are strongly selective to the B-blocks, a series of non-lamellar morphologies, including onion-, hamburger-, cross-, ring-, and cookie-like structures, are observed. A detailed free energy analysis reveals a first-order reversible transformation between SL and onion-like (OL) structures when the selectivity of the homopolymers is changed. Our results provide a comprehensive understanding of how various factors, such as the copolymer concentration, homopolymer chain length, degree of confinement, homopolymer selectivity, affect the self-assembled structures of diblock copolymers under soft 3D confinement. Copyright © 2024, The Authors. All rights reserved.

关键词： Free energy

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A fast calculation method for three-impulse contingency return trajectory during the near-moon phase based on differential algebra

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Chinese Journal of Aeronautics 2025年第4期 290-308页

作者： Lin LU Haiyang LI Tianshan DONG Wanmeng ZHOU College of Aerospace Science and Technology National University of Defense Technology Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Beijing Institute of Spacecraft System Engineering China Astronaut Research and Training Center

Aimed at the demand of contingency return at any time during the near-moon phase in the manned lunar landing missions,a fast calculation method for three-impulse contingency return trajectories is ***,a three-impulse contingency return trajectory scheme is presented by combining the Lambert transfer and maneuver at the special ***,a calculation model of three-impulse contingency return trajectories is ***,fast calculation methods are proposed by adopting the high-order Taylor expansion of differential algebra in the twobody trajectory dynamics model and perturbed trajectory dynamics ***,the performance of the proposed methods is verified by numerical *** results indicate that the fast calculation method of two-body trajectory has higher calculation efficiency compared to the semi-analytical calculation method under a certain accuracy *** to its high efficiency,the characteristics of the three-impulse contingency return trajectories under different contingency scenarios are further analyzed *** findings can be used for the design of contingency return trajectories in future manned lunar landing missions.

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