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High-order finite volume methods for solving compressible multicomponent flows

Science China Mathematics 2025年第3期68卷 729-760页

作者： Feng Zheng Jianxian Qiu School of Mathematics and Statistics Fujian Key Laboratory of Mathematical Analysis and ApplicationFujian Normal UniversityFuzhou 350117China School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling&High-Performance Scientific Computing Xiamen UniversityXiamen 361005China

In this paper, we propose a high-order finite volume method for solving multicomponent fluid problems. Our method couples the quasi-conservative form with the reconstruction of conservative variables in a characteristic manner. The source term and numerical fluxes are carefully designed to maintain the pressure and velocity equilibrium for the interface-only problem and preserve the equilibrium of physical parameters in a single-component fluid. These ingredients enable our scheme to achieve both high-order accuracy in the smooth region and the high resolution in the discontinuity region of the solution. Extensive numerical tests are performed to verify the high resolution and accuracy of the scheme.

关键词： finite volume high-order multicomponent flows

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CENTRAL LIMIT THEOREM FOR TEMPORAL AVERAGE OF BACKWARD EULER-MARUYAMA METHOD

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Journal of Computational Mathematics 2025年第3期43卷 588-614页

作者： Diancong Jin School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific ComputingHuazhong University of Science and TechnologyWuhan 430074China

This work focuses on the temporal average of the backward Euler-Maruyama(BEM)method,which is used to approximate the ergodic limit of stochastic ordinary differential equations(SODEs).We give the central limit theorem(CLT)of the temporal average of the BEM method,which characterizes its asymptotics in *** the deviation order is smaller than the optimal strong order,we directly derive the CLT of the temporal average through that of original equations and the uniform strong order of the BEM *** the case that the deviation order equals to the optimal strong order,the CLT is established via the Poisson equation associated with the generator of original *** experiments are performed to illustrate the theoretical *** main contribution of this work is to generalize the existing CLT of the temporal average of numerical methods to that for SODEs with super-linearly growing drift coefficients.

关键词： Central limit theorem Temporal average Ergodicity Backward Euler-Maruyama method

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Adaptive cyclic gradient methods with interpolation

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Computational Optimization and Applications 2025年 1-25页

作者： Xie, Yixin Sun, Cong Yuan, Ya-Xiang Beijing100876 China Ministry of Education Beijing100876 China State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China

Gradient method is an important method for solving large scale problems. In this paper, a new gradient method framework for unconstrained optimization problem is proposed, where the stepsize is updated in a cyclic way. The Cauchy step is approximated by the quadratic interpolation. And the cycle for stepsize update is adjusted adaptively. Combining with the adaptive nonmonotone line search technique, we prove the global convergence of the proposed method. Furthermore, its sublinear convergence rate for convex problems and R-linear convergence rate for problems with quadratic functional growth property are analyzed. Numerical results show that our proposed algorithm enjoys good performances in terms of both computational cost and obtained function values. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

关键词： Interpolation

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A HIGH ORDER SCHEME FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH THE CAPUTO-HADAMARD DERIVATIVE

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Journal of Computational Mathematics 2025年第3期43卷 615-640页

作者： Xingyang Ye Junying Cao Chuanju Xu School of Science Jimei UniversityXiamen 361021China School of Data Science and Information Engineering Guizhou Minzu UniversityGuiyang 550025China School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing Xiamen UniversityXiamen 361005China

In this paper,we consider numerical solutions of the fractional diffusion equation with theαorder time fractional derivative defined in the Caputo-Hadamard sense.A high order time-stepping scheme is constructed,analyzed,and numerically *** contribution of the paper is twofold:1)regularity of the solution to the underlying equation is investigated,2)a rigorous stability and convergence analysis for the proposed scheme is performed,which shows that the proposed scheme is 3+αorder *** numerical examples are provided to verify the theoretical statement.

关键词： Caputo-Hadamard derivative Fractional differential equations High order scheme Stability and convergence analysis

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Adapted Runge-Kutta Methods for Nonlinear First-Order Delay BVPs with Time-variable Delay

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Acta Mathematicae Applicatae Sinica 2025年第2期41卷 400-413页

作者： Cheng-jian ZHANG Yang WANG Hao HAN School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China

This paper deals with numerical solutions for nonlinear first-order boundary value problems(BVPs) with time-variable delay. For solving this kind of delay BVPs, by combining Runge-Kutta methods with Lagrange interpolation, a class of adapted Runge-Kutta(ARK) methods are developed. Under the suitable conditions, it is proved that ARK methods are convergent of order min{p, μ+ν +1}, where p is the consistency order of ARK methods and μ, ν are two given parameters in Lagrange interpolation. Moreover, a global stability criterion is derived for ARK methods. With some numerical experiments, the computational accuracy and global stability of ARK methods are further testified.

关键词： delay boundary value problems adapted Runge-Kutta method Lagrange interpolation error analysis global stability

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A numerical magnitude aware multi-channel hierarchical encoding network for math word problem solving

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Neural computing and Applications 2025年第3期37卷 1651-1672页

作者： Xu, Junjie Chen, Yuzhong Xiao, Lingsheng Liao, Hongmiao Zhong, Jiayuan Dong, Chen College of Computer and Data Science Fuzhou University Fujian Province Fuzhou350108 China Engineering Research Center of Big Data Intelligence Ministry of Education Fuzhou China Fujian Provincial Key Laboratory of Network Computing and Intelligent Information Processing Fujian Province Fuzhou350108 China

Math word problem (MWP) represents a critical research area within reading comprehension, where accurate comprehension of math problem text is crucial for generating math expressions. However, current approaches still grapple with unresolved challenges in grasping the sensitivity of math problem text and delineating distinct roles across various clause types, and enhancing numerical representation. To address these challenges, this paper proposes a Numerical Magnitude Aware Multi-Channel Hierarchical Encoding Network (NMA-MHEA) for math expression generation. Firstly, NMA-MHEA implements a multi-channel hierarchical context encoding module to learn context representations at three different channels: intra-clause channel, inter-clause channel, and context-question interaction channel. NMA-MHEA constructs hierarchical constituent-dependency graphs for different levels of sentences and employs a Hierarchical Graph Attention Neural Network (HGAT) to learn syntactic and semantic information within these graphs at the intra-clause and inter-clause channels. NMA-MHEA then refines context clauses using question information at the context-question interaction channel. Secondly, NMA-MHEA designs a number encoding module to enhance the relative magnitude information among numerical values and type information of numerical values. Experimental results on two public benchmark datasets demonstrate that NMA-MHEA outperforms other state-of-the-art models. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2024.

关键词： Semantics

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On greedy randomized coordinate updating iteration methods for solving symmetric eigenvalue problems

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Applied Numerical Mathematics 2025年 216卷 76-97页

作者： Bai, Zhong-Zhi State Key Laboratory of Mathematical Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences P.O. Box 2719 Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In order to compute the smallest eigenvalue and its corresponding eigenvector of a large-scale, real, and symmetric matrix, we propose a class of greedy randomized coordinate updating iteration methods based on the principle that the indices of larger entries in absolute value of the current residual are selected with a higher probability and, with respect to this index set, the next iterate is updated from the current iterate along with the selected coordinate such that the corresponding entry of the residual is annihilated, resulting in fast convergence rates of the proposed iteration methods. Under appropriate conditions, we prove the convergence of both sequences of the Rayleigh-quotients and the acute angles between the iterates and the eigenvector in terms of the expectation. By numerical experiments, we show that this class of greedy randomized coordinate updating iteration methods are advantageous over the parameterized power method and the coordinate descent method in both iteration counts and computing times. Moreover, with theoretical analysis and computational performance, we confirm that the convergence property of this class of iteration methods can be improved significantly by suitably choosing the arbitrary nonnegative parameter involved in the greedy probability criterion. © 2025 IMACS

关键词： Eigenvalues and eigenfunctions

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A DECOUPLED,LINEARLY IMPLICIT AND UNCONDITIONALLY ENERGY STABLE SCHEME FOR THE COUPLED CAHN-HILLIARD SYSTEMS

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Journal of Computational Mathematics 2025年第3期43卷 708-730页

作者： Dan Zhao Dongfang Li Yanbin Tang Jinming Wen School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China College of Information Science and Technology Jinan UniversityGuangzhou 510632China

We present a decoupled,linearly implicit numerical scheme with energy stability and mass conservation for solving the coupled Cahn-Hilliard *** time-discretization is done by leap-frog method with the scalar auxiliary variable(SAV)*** only needs to solve three linear equations at each time step,where each unknown variable can be solved *** is shown that the semi-discrete scheme has second-order accuracy in the temporal *** convergence results are proved by a rigorous analysis of the boundedness of the numerical solution and the error estimates at different *** examples are presented to further confirm the validity of the methods.

关键词： Coupled Cahn-Hilliard system Leap-frog method Scalar auxiliary variable Error estimate

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Al-F co-doping towards enhanced electrolyte-electrodes interface properties for halide and sulfide solid electrolytes

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Chinese Chemical Letters 2025年第1期36卷 610-617页

作者： Han Yan Jingming Yao Zhangran Ye Qiaoquan Lin Ziqi Zhang Shulin Li Dawei Song Zhenyu Wang Chuang Yu Long Zhang College of Physics and Energy Fujian Normal UniversityFuzhou 350117China Clean Nano Energy Center State Key Laboratory of Metastable Materials Science and TechnologyYanshan UniversityQinhuangdao 066004China Tianjin Key Laboratory for Photoelectric Materials and Devices School of Materials Science and EngineeringTianjin University of TechnologyTianjin 300384China Guilin Electrical Equipment Scientific Research Institute Co. Ltd.Guilin 541004China State Key Laboratory of Advanced Electromagnetic Engineering and Technology School of Electrical and Electronic EngineeringHuazhong University of Science and TechnologyWuhan 430000China

All-solid-state Li batteries(ASSLBs)using solid electrolytes(SEs)have gained significant attention in recent years considering the safety issue and their high energy *** these advantages,the commercialization of ASSLBs still faces challenges regarding the electrolyte/electrodes interfaces and growth of Li *** doping is an effective and direct method to enhance the performance of ***,we report an Al-F co-doping strategy to improve the overall properties including ion conductivity,high voltage stability,and cathode and anode ***,the Al-F co-doping enables the formation of a thin Li-Al alloy layer and fluoride interphases,thereby constructing a relatively stable interface and promoting uniform Li *** similar merits of Al-F co-doping are also revealed in the Li-argyrodite *** assembled with these optimized electrolytes gain good electrochemical performance,demonstrating the universality of Al-F co-doping towards advanced SEs.

关键词： Solid electrolytes Li halides Li_(2)ZrCl_(6) Li argyrodites Fluorine doping

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Byzantine-robust distributed support vector machine

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Science China Mathematics 2025年第3期68卷 707-728页

作者： Xiaozhou Wang Weidong Liu Xiaojun Mao School of Statistics East China Normal UniversityShanghai 200062China Key Laboratory of Advanced Theory and Application in Statistics and Data Science(Ministry of Education) East China Normal UniversityShanghai 200062China School of Mathematical Sciences Shanghai Jiao Tong UniversityShanghai 200240China Key Laboratory of Artificial Intelligence(Ministry of Education) Shanghai Jiao Tong UniversityShanghai 200240China Key Laboratory of Scientific and Engineering Computing(Ministry of Education) Shanghai Jiao Tong UniversityShanghai 200240China

The development of information technology brings diversification of data sources and large-scale data sets and calls for the exploration of distributed learning algorithms. In distributed systems, some local machines may behave abnormally and send arbitrary information to the central machine(known as Byzantine failures), which can invalidate the distributed algorithms based on the assumption of faultless systems. This paper studies Byzantine-robust distributed algorithms for support vector machines(SVMs) in the context of binary classification. Despite a vast literature on Byzantine problems, much less is known about the theoretical properties of Byzantine-robust SVMs due to their unique challenges. In this paper, we propose two distributed gradient descent algorithms for SVMs. The median and trimmed mean operations in aggregation can effectively defend against Byzantine failures. Theoretically, we show the convergence of the proposed estimators and provide the statistical error rates. After a certain number of iterations, our estimators achieve near-optimal rates. Simulation studies and real data analysis are conducted to demonstrate the performance of the proposed Byzantine-robust distributed algorithms.

关键词： Byzantine robustness convergence distributed learning support vector machine

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