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ONE-PARAMETER FINITE DIFFERENCE METHODS AND THEIR ACCELERATED SCHEMES FOR SPACE-FRACTIONAL SINE-GORDON EQUATIONS WITH DISTRIBUTED DELAY

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Journal of Computational Mathematics 2024年第3期42卷 705-734页

作者： Tao Sun Chengjian Zhang Haiwei Sun 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 Department of Mathematics University of MacaoMacaoChina

This paper deals with numerical methods for solving one-dimensional(1D)and twodimensional(2D)initial-boundary value problems(IBVPs)of space-fractional sine-Gordon equations(SGEs)with distributed *** 1D problems,we construct a kind of oneparameter finite difference(OPFD)*** is shown that,under a suitable condition,the proposed method is convergent with second order accuracy both in time and *** implementation,the preconditioned conjugate gradient(PCG)method with the Strang circulant preconditioner is carried out to improve the computational efficiency of the OPFD *** 2D problems,we develop another kind of OPFD *** such a method,two classes of accelerated schemes are suggested,one is alternative direction implicit(ADI)scheme and the other is ADI-PCG *** particular,we prove that ADI scheme can arrive at second-order accuracy in time and *** some numerical experiments,the computational effectiveness and accuracy of the methods are further ***,for the suggested methods,a numerical comparison in computational efficiency is presented.

关键词： Fractional sine-Gordon equation with distributed delay One-parameter finite difference methods Convergence analysis ADI scheme PCG method

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A VARIATIONAL ANALYSIS FOR THE MOVING FINITE ELEMENT METHOD FOR GRADIENTFLOWS

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Journal of Computational Mathematics 2023年第2期41卷 191-210页

作者： Xianmin Xu LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingNCMISAMSSChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

By using the Onsager principle as an approximation tool,we give a novel derivation for the moving finite element method for gradient flow *** show that the discretized problem has the same energy dissipation structure as the continuous *** enables us to do numerical analysis for the stationary solution of a nonlinear reaction diffusion equation using the approximation theory of free-knot piecewise *** show that under certain conditions the solution obtained by the moving finite element method converges to a local minimizer of the total energy when time goes to *** global minimizer,once it is detected by the discrete scheme,approximates the continuous stationary solution in optimal *** examples for a linear diffusion equation and a nonlinear Allen-Cahn equation are given to verify the analytical results.

关键词： Moving finite element method Convergence analysis Onsager principle

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Investigation of transonic aerodynamics on a triple-delta wing in side slip conditions

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CEAS Aeronautical Journal 2022年第2期13卷 453-470页

作者： Di Fabbio, Tony Tangermann, Eike Klein, Markus Numerical Methods in Aerospace Engineering Institute of Applied Mathematics and Scientific Computing Bundeswehr University Munich Neubiberg85577 Germany

The vortex-dominated flow around the triple-delta wing ADS-NA2-W1 aircraft is investigated in order to achieve a better understanding of the flow physics phenomena that occur over the aircraft particularly at the transonic speed condition. Both URANS and scale-resolving DDES have been employed in order to explore the range of suitability of current CFD methods. The Spalart–Allmaras One-Equation Model with corrections for negative turbulent viscosity and Rotation/Curvature (SA-negRC) is employed to close the RANS equations, whereas the SAneg-based DDES model is applied in the scale-resolving computations. The DLR TAU-Code is used to perform the numerical simulations. The deficiencies of the URANS results are illustrated and promising improvements are reached employing the SAneg-DDES numerical method. The hybrid method results show great advancement in the prediction of the multiple-delta wing flow by revealing physical aspects which have not been seen from URANS with sufficient accuracy like vortex–vortex interaction and shock-vortex interaction. These phenomena furthermore explain in a clear way the improved prediction of the surface pressure coefficient over the aircraft and consequently of the aerodynamic force and moment coefficients. © 2022, The Author(s).

关键词： Vortex flow

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A deep learning approach for recognizing and solving handwritten mathematical equations

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Neural computing and Applications 2025年第14期37卷 8759-8772页

作者： Yadav, Pavinder Shantilal, Sankhala Bhavik Kumar, Vipin Sihag, Parveen Sharma, Pawan Kumar Rana, Pankaj Department of Mathematics and Scientific Computing National Institute of Technology HP Hamirpur India Department of Civil Engineering Chandigarh University Punjab Mohali India Department of Physical Sciences Baba Mastnath University Asthal Bohar Haryana Rohtak India

Recognizing handwritten equations is considerably more challenging than identifying printed ones, primarily due to variations in writing styles. Even though there have been recent improvements in handwriting recognition for things like equation solvers and automation, it is still hard for machines to understand a handwritten mathematical expression (HME). This paper presents a deep learning model for recognizing and solving handwritten equations, as well as its graphical user interface (GUI). A manually constructed large dataset comprising approximately 66k images of digits, mathematical symbols, and characters is utilized, with a fine-tuned InceptionV3 model employed for image classification and segmentation. The system is designed to extract handwritten equations from an image, perform character recognition, and generate the roots of the polynomial equation up to degree four. According to the findings, the trained model achieves remarkable accuracy in recognizing and solving handwritten equations, with over 94% accuracy on the training set. By eliminating the possibility of human error, automatic handwritten equation solvers provide more accurate results than manual methods. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2025.

关键词： Convolutional neural networks

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Maximizing Submodular+Supermodular Functions Subject to a Fairness Constraint

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Tsinghua Science and Technology 2024年第1期29卷 46-55页

作者： Zhenning Zhang Kaiqiao Meng Donglei Du Yang Zhou Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing 100124China Faculty of Management University of New BrunswickFredericton E3B 5A3Canada School of Mathematics and Statistics Shandong Normal UniversityJinan 250014China

We investigate the problem of maximizing the sum of submodular and supermodular functions under a fairness *** sum function is non-submodular in *** an offline model,we introduce two approximation algorithms:A greedy algorithm and a threshold greedy *** a streaming model,we propose a one-pass streaming *** also analyze the approximation ratios of these algorithms,which all depend on the total curvature of the supermodular *** total curvature is computable in polynomial time and widely utilized in the literature.

关键词： submodular function supermodular function fairness constraint greedy algorithm threshold greedy algorithm streaming algorithm

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Nonlinear Extrapolation Estimates of π

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 91-108页

作者： Wen-qing Xu Sha-sha Wang Da-chuan Xu Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing100124China Department of Mathematics and Statistics California State UniversityLong BeachCalifornia90840USA Department of Mathematics and Physics Shijiazhuang Tiedao UniversityShijiazhuang050043China

The classical Archimedean approximation of π uses the semiperimeter or area of regular polygons inscribed in or circumscribed about a unit circle in R~2 and it is well-known that by using linear combinations of these basic estimates,modern extrapolation techniques can greatly speed up the approximation ***,when n vertices are randomly selected on the circle,the semiperimeter and area of the corresponding random inscribed and circumscribing polygons are known to converge to π almost surely as n→∞,and by further applying extrapolation processes,faster convergence rates can also be achieved through similar linear combinations of the semiperimeter and area of these random *** this paper,we further develop nonlinear extrapolation methods for approximating π through certain nonlinear functions of the semiperimeter and area of such *** focus on two types of extrapolation estimates of the forms χ_n=S_n~αA_n~β and Y_n(p)=(αS_n~p+βA_n~p)~(1/p) where α+β=1,p≠0,and Sn and An respectively represents the semiperimeter and area of a random n-gon inscribed in the unit circle in R~2,and Xn may be viewed as the limit of Y_n(p) when p→*** deriving probabilistic asymptotic expansions with carefully controlled error estimates for Xn and Y_n(p),we show that the choice α=4/3,β=-1/3 minimizes the approximation error in both cases,and their distributions are also asymptotically normal.

关键词： Archimedean polygons random polygons approximations ofπ extrapolation processes asymptotic convergence

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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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Bicriteria Algorithms for Approximately Submodular Cover Under Streaming Model

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Tsinghua Science and Technology 2023年第6期28卷 1030-1040页

作者： Yijing Wang Xiaoguang Yang Hongyang Zhang Yapu Zhang Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China School of Mathematics and Statistics Ningbo UniversityNingbo 315211China Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing 100124China

In this paper,we mainly investigate the optimization model that minimizes the cost function such that the cover function exceeds a required threshold in the set cover problem,where the cost function is additive linear,and the cover function is non-monotone approximately *** study the problem under streaming model and propose three bicriteria approximation ***,we provide an intuitive streaming algorithm under the assumption of known optimal objective *** intuitive streaming algorithm returns a solution such that its cover function value is no less thanα(1−ϵ)times threshold,and the cost function is no more than(2+ϵ)^(2)/(ϵ^(2)ω^(2))⋅κ,whereκis a value that we suppose for the optimal solution andαis the approximation ratio of an algorithm for unconstrained maximization problem that we can call *** we present a bicriteria streaming algorithm scanning the ground set multi-pass to weak the assumption that we guess the optimal objective value in advance,and maintain the same bicriteria approximation *** we modify the multi-pass streaming algorithm to a single-pass one without compromising the performance ***,we also propose some numerical experiments to test our algorithm’s performance comparing with some existing methods.

关键词： approximately submodular linear additive streaming model bicriteria algorithm

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The convergence properties of infeasible inexact proximal alternating linearized minimization

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Science China Mathematics 2023年第10期66卷 2385-2410页

作者： Yukuan Hu Xin Liu State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

The proximal alternating linearized minimization(PALM)method suits well for solving blockstructured optimization problems,which are ubiquitous in real *** the cases where subproblems do not have closed-form solutions,e.g.,due to complex constraints,infeasible subsolvers are indispensable,giving rise to an infeasible inexact PALM(PALM-I).Numerous efforts have been devoted to analyzing the feasible PALM,while little attention has been paid to the *** usage of the PALM-I thus lacks a theoretical *** essential difficulty of analysis consists in the objective value nonmonotonicity induced by the *** study in the present work the convergence properties of the *** particular,we construct a surrogate sequence to surmount the nonmonotonicity issue and devise an implementable inexact *** upon these,we manage to establish the stationarity of any accumulation point,and moreover,show the iterate convergence and the asymptotic convergence rates under the assumption of the Lojasiewicz *** prominent advantages of the PALM-I on CPU time are illustrated via numerical experiments on problems arising from quantum physics and 3-dimensional anisotropic frictional contact.

关键词： proximal alternating linearized minimization infeasibility nonmonotonicity surrogate sequence inexact criterion iterate convergence asymptotic convergence rate

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A System to Detect Oilwell Anomalies Using Deep Learning and Decision Diagram Dual Approach

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SPE Journal 2023年第3期29卷 1540-1553页

作者： Aranha, P.E. Lopes, L.G.O. Sobrinho, E.S. Paranhos Oliveira, I.M.N. de Araújo, J.P.N. Santos, B.B. Lima, E.T. da Silva, T.B. Vieira, T.M.A. Lira, W.W.M. Policarpo, N.A. Sampaio, M.A. Well Construction Department Petrobras Brazil Department of Mining and Petroleum Engineering Universidade de São Paulo Brazil Laboratory of Scientific Computing and Visualization Federal University of Alagoas Brazil

Detecting unexpected events is a field of interest in oil and gas companies to improve operational safety and reduce costs associated with nonproductive time (NPT) and failure repair. This work presents a system for real-time monitoring of unwanted events using the production sensor data from oil wells. It uses a combination of long short-term memory (LSTM) autoencoder and a rule-based analytic approach to perform the detection of anomalies from sensor data. Initial studies are conducted to determine the behavior and correlations of pressure and temperature values for the most common combinations of well valve states. The proposed methodology uses pressure and temperature sensor data, from which a decision diagram (DD) classifies the well status, and this response is applied to the training of neural networks devoted to anomaly detection. Data sets related to several operations in wells located at different oil fields are used to train and validate the dual approach presented. The combination of the two techniques enables the deep neural network to evolve constantly through the normal data collected by the analytical method. The developed system exhibits high accuracy, with true positive detection rates exceeding 90% in the early stages of anomalies identified in both simulated and actual well production scenarios. It was implemented in more than 20 floating production, storage, and offloading (FPSO) vessels, monitoring more than 250 production/injection subsea wells, and can be applied both in real-time operation and in testing scenarios. Copyright © 2023 Society of Petroleum Engineers.

关键词： Anomaly detection

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