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

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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

Quantum Circuits for the heat equation with physical boundary conditions via Schrödingerisation

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arXiv 2024年

作者： Jin, Shi Liu, Nana Yu, Yue School of Mathematical Sciences Institute of Natural Sciences MOE-LSC Shanghai Jiao Tong University Shanghai200240 China University of Michigan Shanghai Jiao Tong University Joint Institute Shanghai200240 China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education National Center for Applied Mathematics in Hunan Xiangtan University Hunan Xiangtan411105 China

This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. These equations and/or their discretized forms usually do not evolve via unitary dynamics, thus are not suitable for quantum simulation. Boundary conditions (either time-dependent or independent) make the problem more difficult. To tackle this challenge, the Schrödingerisation method can be employed, which converts linear partial and ordinary differential equations with non-unitary dynamics into systems of Schrödinger-type equations, via the so-called warped phase transformation that maps the equation into one higher dimension. Despite advancements in Schrödingerisation techniques, the explicit implementation of quantum circuits for solving general PDEs, especially with physical boundary conditions, remains underdeveloped. We present two methods for handling the inhomogeneous terms arising from time-dependent physical boundary conditions. One approach utilizes Duhamel’s principle to express the solution in integral form and employs linear combination of unitaries (LCU) for coherent state preparation. Another method applies an augmentation to transform the inhomogeneous problem into a homogeneous one. We then apply the quantum simulation technique from [CJL23] to transform the resulting non-autonomous system to an autonomous system in one higher dimension. We provide detailed implementations of these two methods and conduct a comprehensive complexity analysis in terms of queries to the time evolution input oracle. © 2024, CC BY-NC-ND.

关键词： Ordinary differential equations

Design and Characterization of Low-Carbon Supersulfated Cement Prepared Using As-Received Electrolysis Manganese Dioxide Residue

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SSRN

SSRN 2023年

作者： Ma, Wenbo Bai, Tianwen Zhu, Wei Guo, Shuaicheng School of Mechanical Engineering and Mechanics Xiangtan University Xiangtan411105 China College of Civil Engineering Xiangtan University Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China Key Laboratory of Building Safety and Energy Efficiency of the Ministry of Education Hunan University Changsha410082 China International Science Innovation Collaboration Base for Green & Advanced Civil Engineering Materials of Hunan Province Hunan University Changsha410082 China Key Laboratory for Green & Advanced Civil Engineering Materials and Application Technology of Hunan Province College of Civil Engineering Hunan University Changsha410082 China

Utilizing electrolysis manganese dioxide residue (EMDR) to prepare the supersulfated cement can achieve effective waste recycling, and its application can reduce the carbon emission caused by Portland cement. This study aims to quantitatively build the correlation between the mechanical performance and cementitious matrix composition of EMDR-based supersulfated cement. The supersulfated cement containing clinker, slag and as received EMDR is designed and prepared based on the simplex centroid design method. The compressive strength, tensile strength and flexural strength of the EMDR based supersulfated cement paste were measured at 3-day, 7-day and 28-day ages. The compressive strength of the electrolysis manganese dioxide residue (EMDR) based supersulfated cement first increases and then decreases with the mass ratio between slag and EMDR. The added cement clinker can increase the compressive strength at 3-day and 7-day ages, but the 28-day age strength first decrease and then increase with the cement clinker content. Meanwhile, the flexural and tensile performances of the EMDR based supersulfated cement generally increase with the clinker content. The measured elastic modulus results indicated the added clinker could enhance the stiffness of the stiffness development. Then the strength development mechanisms of EMDR-based supersulfated cement are analyzed based on phase and microstructure characterization. It is found the clinker can accelerate the reaction rate between the slag and EMDR, and the consumption rate of the gypsum contained in EMDR. The calcium silicate hydrate (CSH) gel phase's contribution to tensile strength is more significant than that of ettringite phase. Based on the mechanism analysis, the index of [SO3]/[Al2O3] molar ratio is proposed for the matrix design of EMDR based SSC. This study can support the design and application of EMDR-based supersulfated cement. © 2023, The Authors. All rights reserved.

关键词： Aluminum oxide

Constrained Probabilistic Pareto Dominance for Expensive Constrained Multiobjective Optimization Problems

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IEEE Transactions on Evolutionary computation 2024年 1-1页

作者： Zhang, Zhiyao Wang, Yong Sun, Guangyong Pang, Tong Tang, Ke School of Automation Central South University Changsha China State Key Laboratory of Advanced Design and Manufacturing Technology for Vehicle Hunan University Changsha China Guangdong Key Laboratory of Brain-Inspired Intelligent Computation Department of Computer Science and Engineering and the Research Institute of Trustworthy Autonomous Systems Southern University of Science and Technology Shenzhen China

This paper proposes a new parameterless constraint-handling technique, named constrained probabilistic Pareto dominance (CPPD), for expensive constrained multiobjective optimization problems (CMOPs). In CPPD, when comparing two solutions, in terms of each original objective, we design a new objective for each solution, which is the negative product of two probabilities calculated based on the predicted fitness mean values and the uncertainty information provided by Kriging models: 1) the probability that this solution satisfies all constraints, denoted as PoF, and 2) the probability that this solution is better than the other on the original objective, denoted as PoB. It is evident that for each solution, PoF and PoB indicate its feasibility and its optimality on the corresponding original objective, respectively. Then, Pareto dominance based on new objectives is executed. As a result, both competitive feasible solutions and promising infeasible solutions with good diversity can be preserved by CPPD. These two kinds of solutions can help the population to exploit the located feasible parts and to explore new feasible parts, respectively. Further, based on CPPD, we develop a Pareto-based Kriging-assisted constrained multiobjective evolutionary algorithm (called PEA) to deal with expensive CMOPs with two or three objectives. Finally, PEA is generalized to solve expensive constrained many-objective optimization problems, named PEA+. The effectiveness of CPPD, PEA, and PEA+ is verified by comprehensive experiments. IEEE

关键词： Evolutionary algorithms

A Progressive Image Restoration Network for High-order Degradation Imaging in Remote Sensing

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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

A Novel Perturbation-Theory-Based Approach for Free Vibrations of Bi-Directional Functionally Graded Porous Beams with a New Bi-Directional Pore Distribution Pattern

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SSRN

SSRN 2024年

作者： Chen, Chen Zhou, Lilin Li, Daokui 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 Aviation Engineering Institute Civil Aviation Flight University of China Sichuan Guanghan618307 China

Porosity defects usually exist in the functionally graded material (FGM) due to the inherent deficiencies in the fabricating process. Omission and miscalculation of the defects possibly resulting in overpredicted load-carrying capacities. The current assumption of pore distribution ignores the influence of material gradient which is not accurate enough. A new hypothesis of a bi-directional (2D) FG porosity distribution pattern that closer to the observation is proposed to characterize the feature. Moreover, instead of the numerical method, this study pioneers a fresh thought of perturbation approach (PA) customized for solving the governing equations of the bi-directional functionally graded porous (2D FGP) beam for the first time. First, A new hypothesis of 2D porosity distribution pattern is proposed. Second, a free vibration model of the 2D FGP beam is established by the rule of mixture, Timoshenko beam theory, and Hamilton’s principle. Then, by applying the PA, the 2D FGP beam is equivalent to an even porous homogenous beam and a small material perturbation to facilitate the computation of natural frequencies. The results of high-precision show that the PA is adaptive and applicable. Finally, discussions and analyses are conducted. It is found that, the pore distribution pattern has a significant impact on the natural frequency. The frequency of the new 2D FGP beam decreases with the increase of the material gradient, the porosity coefficient, and the power-law indexes. The influence of pores can be ignored in a rough calculation once the pore distribution is observed to approach the proposed uneven pattern. © 2024, The Authors. All rights reserved.

关键词： Natural frequencies

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

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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

Gradient Recovery-Type a Posteriori Error Estimates for Steady-State Poisson-Nernst-Planck Equations

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Advances in Applied Mathematics and Mechanics 2020年第6期12卷 1353-1383页

作者： Ruigang Shen Shi Shu Ying Yang Mingjuan Fang School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtanHunan 411105China School of Mathematics and Computational Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationGuilin University of Electronic TechnologyGuilinGuangxi 541004China School of Mathematics and Computational Science Guilin University of Electronic TechnologyGuilinGuangxi 541004China

In this article,we derive the a posteriori error estimators for a class of steadystate Poisson-Nernst-Planck *** the gradient recovery operator,the upper and lower bounds of the a posteriori error estimators are established both for the electrostatic potential and *** is shown by theory and numerical experiments that the error estimators are reliable and the associated adaptive computation is efficient for the steady-state PNP systems.

关键词： Poisson-Nernst-Planck equations gradient recovery a posteriori error estimate

VIRTUAL ELEMENT METHODS WITHOUT EXTRINSIC STABILIZATION

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arXiv 2022年

作者： Chen, Chunyu Huang, Xuehai Wei, Huayi Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China School of Mathematics Shanghai University of Finance and Economics Shanghai200433 China

Virtual element methods (VEMs) without extrinsic stabilization in arbitrary degree of polynomial are developed for second order elliptic problems, including a nonconforming VEM and a conforming VEM in arbitrary dimension. The key is to construct local H(div)-conforming macro finite element spaces such that the associated L2 projection of the gradient of virtual element functions is computable, and the L2 projector has a uniform lower bound on the gradient of virtual element function spaces in L2 norm. Optimal error estimates are derived for these VEMs. Numerical experiments are provided to test the VEMs without extrinsic *** Codes 65N12, 65N22, 65N30 Copyright © 2022, The Authors. All rights reserved.

关键词： Stabilization