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A Stochastic Gradient Descent Method for computational Design of Random Rough Surfaces in Solar Cells

Communications in computational Physics 2023年第10期34卷 1361-1390页

作者： Qiang Li Gang Bao Yanzhao Cao Junshan Lin Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Department of Mathematics Zhejiang UniversityChina Department of Mathematics and Statistics Auburn UniversityAuburnAL 36849USA

In this work,we develop a stochastic gradient descent method for the computational optimal design of random rough surfaces in thin-film solar *** formulate the design problems as random PDE-constrained optimization problems and seek the optimal statistical parameters for the random *** optimizations at fixed frequency as well as at multiple frequencies and multiple incident angles are *** evaluate the gradient of the objective function,we derive the shape derivatives for the interfaces and apply the adjoint state method to perform the *** stochastic gradient descent method evaluates the gradient of the objective function only at a few samples for each iteration,which reduces the computational cost *** numerical experiments are conducted to illustrate the efficiency of the method and significant increases of the absorptance for the optimal random *** also examine the convergence of the stochastic gradient descent algorithm theoretically and prove that the numerical method is convergent under certain assumptions for the random interfaces.

关键词： Optimal design random rough surface solar cell Helmholtz equation stochastic gradient descent method

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A New Sixth-Order WENO Scheme for Solving Hyperbolic Conservation Laws

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Communications on Applied mathematics and Computation 2023年第1期5卷 3-30页

作者： Kunlei Zhao Yulong Du Li Yuan State Key Laboratory of Scientific and Engineering Computing(LSEC)and Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100190China School of Mathematical Sciences Beihang UniversityBeijing 100191China

In this paper,we develop a new sixth-order WENO scheme by adopting a convex combina-tion of a sixth-order global reconstruction and four low-order local *** the classical WENO schemes,the associated linear weights of the new scheme can be any positive numbers with the only requirement that their sum equals ***,a very simple smoothness indicator for the global stencil is *** new scheme can achieve sixth-order accuracy in smooth *** tests in some one-and two-dimensional bench-mark problems show that the new scheme has a little bit higher resolution compared with the recently developed sixth-order WENO-Z6 scheme,and it is more efficient than the classical fifth-order WENO-JS5 scheme and the recently developed sixth-order WENO6-S scheme.

关键词： Global smoothness indicator Linear weights Sixth-order accuracy WENO

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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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Attention-Enhanced and Knowledge-Fused Dual Item Representations Network for Recommendation

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Tsinghua Science and Technology 2025年第2期30卷 585-599页

作者： Qiang Hua Jiachao Zhou Feng Zhang Chunru Dong Dachuan Xu College of Mathematics and Information Science Hebei UniversityBaoding 071002China Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing 100124China

Integrating Knowledge Graphs(KGs)into recommendation systems as supplementary information has become a prevalent *** leveraging the semantic relationships between entities in KGs,recommendation systems can better comprehend user *** to the unique structure of KGs,methods based on Graph Neural Networks(GNNs)have emerged as the current technical ***,existing GNN-based methods struggle to(1)filter out noisy information in real-world KGs,and(2)differentiate the item representations obtained from the knowledge graph and bipartite *** this paper,we introduce a novel model called Attention-enhanced and Knowledge-fused Dual item representations Network for recommendation(namely AKDN)that employs attention and gated mechanisms to guide aggregation on both knowledge graphs and bipartite *** particular,we firstly design an attention mechanism to determine the weight of each edge in the information aggregation on KGs,which reduces the influence of noisy information on the items and enables us to obtain more accurate and robust representations of the ***,we exploit a gated aggregation mechanism to differentiate collaborative signals and knowledge information,and leverage dual item representations to fuse them together for better capturing user behavior *** conduct extensive experiments on two public datasets which demonstrate the superior performance of our AKDN over state-of-the-art methods,like Knowledge Graph Attention Network(KGAT)and Knowledge Graph-based Intent Network(KGIN).

关键词： Recommender System(RS) Knowledge Graph(KG) Graph Neural Networks(GNN) attention mechanism

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METRICALLY REGULAR MAPPING AND ITS UTILIZATION TO CONVERGENCE ANALYSIS OF A RESTRICTED INEXACT NEWTON-TYPE METHOD

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Journal of computational mathematics 2022年第1期40卷 44-69页

作者： Mohammed Harunor Rashid Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Department of Mathematics Faculty of ScienceUniversity of RajshahiRajshahi-6205Bangladesh

In the present paper,we study the restricted inexact Newton-type method for solving the generalized equation 0∈f(x)+F(x),where X and Y are Banach spaces,f:X→Y is a Frechet differentiable function and F:X■Y is a set-valued mapping with closed *** establish the convergence criteria of the restricted inexact Newton-type method,which guarantees the existence of any sequence generated by this method and show this generated sequence is convergent linearly and quadratically according to the particular assumptions on the Frechet derivative of ***,we obtain semilocal and local convergence results of restricted inexact Newton-type method for solving the above generalized equation when the Frechet derivative of f is continuous and Lipschitz continuous as well as f+F is metrically *** application of this method to variational inequality is *** addition,a numerical experiment is given which illustrates the theoretical result.

关键词： Generalized equation Restricted inexact Newton-type method Metrically regular mapping Partial Lipschitz-like mapping Semilocal convergence.

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A POSITIVITY-PRESERVING FINITE ELEMENT METHOD FOR QUANTUM DRIFT-DIFFUSION MODEL

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Journal of computational mathematics 2023年第5期41卷 909-932页

作者： Pengcong Mu Weiying Zheng School of Mathematical Science University of Chinese Academy of SciencesBeijing 100049China LSEC NCMISInstitute of Computational Mathematics and Scientific ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

In this paper,we propose a positivity-preserving finite element method for solving the three-dimensional quantum drift-diffusion *** model consists of five nonlinear elliptic equations,and two of them describe quantum corrections for quasi-Fermi *** propose an interpolated-exponential finite element(IEFE)method for solving the two quantum-correction *** IEFE method always yields positive carrier densities and preserves the positivity of second-order differential operators in the Newton linearization of quantum-correction ***,we solve the two continuity equations with the edge-averaged finite element(EAFE)method to reduce numerical oscillations of quasi-Fermi *** Poisson equation of electrical potential is solved with standard Lagrangian finite *** prove the existence of solution to the nonlinear discrete problem by using a fixed-point iteration and solving the minimum problem of a new discrete functional.A Newton method is proposed to solve the nonlinear discrete *** experiments for a three-dimensional nano-scale FinFET device show that the Newton method is robust for source-to-gate bias voltages up to 9V and source-to-drain bias voltages up to 10V.

关键词： Quantum drift-diffusion model Positivity-preserving finite element method Newton method FinFET device High bias voltage

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Positive definiteness of real quadratic forms resulting from the variable-step L1-type approximations of convolution operators

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Science China mathematics 2024年第2期67卷 237-252页

作者： Hong-Lin Liao Tao Tang Tao Zhou School of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211106China Division of Science and Technology BNU-HKBU United International CollegeZhuhai 519087China SUSTech International Center for Mathematics Shenzhen 518055China NCMIS&LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

The positive definiteness of real quadratic forms with convolution structures plays an important rolein stability analysis for time-stepping schemes for nonlocal operators. In this work, we present a novel analysistool to handle discrete convolution kernels resulting from variable-step approximations for convolution *** precisely, for a class of discrete convolution kernels relevant to variable-step L1-type time discretizations, weshow that the associated quadratic form is positive definite under some easy-to-check algebraic conditions. Ourproof is based on an elementary constructing strategy by using the properties of discrete orthogonal convolutionkernels and discrete complementary convolution kernels. To our knowledge, this is the first general result onsimple algebraic conditions for the positive definiteness of variable-step discrete convolution kernels. Using theunified theory, we obtain the stability for some simple nonuniform time-stepping schemes straightforwardly.

关键词： discrete convolution kernels positive definiteness variable time-stepping orthogonal convolution kernels complementary convolution kernels

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A Derivative-free Trust-region Method for Optimization on the Ellipsoid

A Derivative-free Trust-region Method for Optimization on th...

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2023 International Conference on Advances in Computer Science and engineering Technology, ACSE 2023

作者： Xie, Pengcheng State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences ZhongGuanCun East Road No. 55 Beijing China

Optimization methods play a crucial role in various fields and applications. In some optimization problems, the derivative information of the objective function is unavailable. Such black-box optimization problems need to be solved by derivative-free optimization methods. At the same time, optimization problems with ellipsoidal constraints are important and have widespread applications in various fields as well. Following the development of the late professor M. J. D. Powell's efficient derivative-free trust-region optimization methods, this paper considers solving derivative-free optimization problems on the ellipsoid. Our new optimization solver EC-NEWUOA for problems on the ellipsoid in ., n is designed based on Powell's derivative-free software NEWUOA for unconstrained optimization problems. The proposed techniques for our new method mainly include using the Courant penalty function, the augmented Lagrangian method, and the projection technique. Details about the method and theoretical analysis are included in this paper. We also compare our new method with other algorithms by solving test problems and then show the numerical advantages of our new method. © Published under licence by IOP Publishing Ltd.

关键词： Lagrange multipliers

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CONVERGENCE ANALYSIS OF SOME FINITE ELEMENT PARALLEL ALGORITHMS FOR THE STATIONARY INCOMPRESSIBLE MHD EQUATIONS

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Journal of computational mathematics 2024年第1期42卷 49-70页

作者： Xiaojing Dong Yinnian He Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationSchool of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China Institute of Applied Physics and Computational Mathematics Beijing 100088China School of Mathematics and Statistics Xi'an Jiaotong UniversityXi'an 710049China

By combination of iteration methods with the partition of unity method(PUM),some finite element parallel algorithms for the stationary incompressible magnetohydrodynamics(MHD)with different physical parameters are presented and *** algorithms are highly *** first,a global solution is obtained on a coarse grid for all approaches by one of the iteration *** parallelized residual schemes,local corrected solutions are calculated on finer meshes with overlapping *** subdomains can be achieved flexibly by a class of *** proposed algorithm is proved to be uniformly stable and ***,one numerical example is presented to confirm the theoretical findings.

关键词： Partition of unity method Local and parallel algorithm Finite element method Iteration methods Magnetohydrodynamics

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NVERSE CONDUCTIVITY PROBLEM WITH INTERNAL DATA

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Journal of computational mathematics 2023年第3期41卷 482-500页

作者： Faouzi Triki Tao Yin Laboratoire Jean Kuntzmann UMR CNRS 5224Université Grenoble-Alpes700 Avenue Centrale38401 Saint-Martin-d’HèresFrance Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of ScienceBeijing 100190China

This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal *** problem finds applications in multi-wave imaging,greedy methods to approximate parameter-dependent elliptic problems,and image treatment with partial differential *** first show that the inverse problem for smooth coefficients can be rewritten as a linear transport *** that the coefficient is known near the boundary,we study the well-posedness of associated transport equation as well as its numerical resolution using discontinuous Galerkin *** propose a regularized transport equation that allow us to derive rigorous convergence rates of the numerical method in terms of the order of the polynomial approximation as well as the regularization *** finally provide numerical examples for the inversion assuming a lower regularity of the coefficient,and using synthetic data.

关键词： Inverse problems Multi-wave imaging Static transport equation Internal data Diffusion coeffcient Stability estimates Regularization

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