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A PRIMAL FINITE ELEMENT SCHEME OF THE HODGE LAPLACE PROBLEM

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arXiv 2022年

作者： Zhang, Shuo LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China

In this paper, a unified family, for any n ≽ 2 and 1 ≼ k ≼ n − 1, of nonconforming finite element schemes are presented for the primal weak formulation of the n-dimensional Hodge-Laplace equation on (Equation presented) and on the simplicial subdivisions of the domain. The finite element scheme possesses an O(h)-order convergence rate for sufficiently regular data, and an O(hs)order rate on any s-regular domain, 0 Copyright © 2022, The Authors. All rights reserved.

关键词： Finite element method

A PRIMAL FINITE ELEMENT SCHEME OF THE H(d) ∩ H(δ) ELLIPTIC PROBLEM

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arXiv 2022年

In this paper, a unified family, for n > 2 and 1 6 k 6 n − 1, of finite element schemes are presented for the primal weak formulation of the n-dimensional (Equation presented) elliptic problem. Copyright © 202... 详细信息

关键词： Finite element method

Local meshless methods for elliptic PDEs with multipoint boundary conditions: investigating efficiency and accuracy of various RBFs

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The European Physical Journal Special Topics 2024年 1-18页

作者： Ahmad, Masood Khan, Muhammad Nawaz Ahmad, Imtiaz Department of Basic Sciences University of Engineering and Technology Peshawar Peshawar Pakistan Mathematics in Applied Sciences and Engineering Research Group Scientific Research Center Al-Ayen University Nasiriyah Iraq Institute of Informatics and Computing in Energy (IICE) Universiti Tenaga Nasional Kajang Malaysia

The present study addresses the numerical solution of two-dimensional steady-state heat conduction problems with nonlocal multi-point boundary conditions across three distinct domains: a unit rectangle with a quarter-circle cutout of radius 0.5, an irregular domain, and a Cassini curve. Dirichlet boundary conditions are imposed on specific segments, while nonlocal boundary conditions are applied to the remaining portions. The Kansa method is employed to solve the steady-state heat conduction equation, utilizing three types of radial basis functions (RBFs) to explore the influence of the shape parameter on accuracy and matrix conditioning. These include the inverse multiquadric RBF, a modified inverse multiquadric RBF proposed here for the first time, and a hybrid RBF [1]. As a meshless method, the Kansa approach eliminates the need for mesh generation or node connectivity within local subdomains. To evaluate accuracy and performance, the $$L_{\infty }$$ error norm is employed. The results demonstrate the effectiveness of the proposed techniques in solving the 2D steady-state heat conduction problem. A comparative analysis is conducted to assess the accuracy and computational efficiency of the methods.

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POINTWISE ESTIMATES FOR THE FUNDAMENTAL SOLUTIONS OF HIGHER ORDER SCHRÖDINGER EQUATIONS IN ODD DIMENSIONS I: LOW DIMENSIONAL CASE

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arXiv 2024年

作者： Cheng, Han Huang, Shanlin Huang, Tianxiao Zheng, Quan Institute of Applied Physics and Computational Mathematics Beijing100088 China School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China Sun Yat-sen University Guangdong Zhuhai519082 China School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Wuhan430074 China

In this paper, for any odd n and any integer m ≥ 1 with n tu(x, t) = ((−∆)m + V(x))u(x, t), t ∈ , x ∈ n, where V is a real-valued potential with certain decay. Let Pac(H) denote the projection onto the absolutely continuous spectrum space of H = (−∆)m + V, and assume that H has no positive embedded eigenvalue. Our main result says that e−itHPac(H) has integral kernel K(t, x, y) satisfying (Equation presented), where the constants C, h > 0, and h can be specified by m, n and the zero energy resonances of H. A similar result for smoothing operators like (Equation presented) is also given. One of the main novelties lies in a new and unified approach to obtain the asymptotic expansions of perturbed resolvents under various types of zero energy resonances. © 2024, CC0.

关键词： Schrodinger equation

An Augmented Subspace Based Adaptive Proper Orthogonal Decomposition Method for Time Dependent Partial Differential Equations

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arXiv 2023年

作者： Dai, Xiaoying Hu, Miao Xin, Jack Zhou, Aihui LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Department of Mathematics University of California at Irvine IrvineCA92697 United States

In this paper, we propose an augmented subspace based adaptive proper orthogonal decomposition (POD) method for solving the time dependent partial differential equations. By augmenting the POD subspace with some auxiliary modes, we obtain an augmented subspace. We use the difference between the approximation obtained in this augmented subspace and that obtained in the original POD subspace to construct an error indicator, by which we obtain a general framework for augmented subspace based adaptive POD method. We then provide two strategies to obtain some specific augmented subspaces, the random vector based augmented subspace and the coarse-grid approximations based augmented subspace. We apply our new method to two typical 3D advection-diffusion equations with the advection being the Kolmogorov flow and the ABC flow. Numerical results show that our method is more efficient than the existing adaptive POD methods, especially for the advection dominated models. Copyright © 2023, The Authors. All rights reserved.

关键词： Advection

Using Data Mining Techniques to Analyze Facial Expression Motion Vectors 6th

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Using Data Mining Techniques to Analyze Facial Expression Mo...

6th International Conference on Dynamics of Information Systems, DIS 2023

作者： Roshanzamir, Mohamad Alizadehsani, Roohallah Roshanzamir, Mahdi Shoeibi, Afshin Gorriz, Juan M. Khosravi, Abbas Nahavandi, Saeid Acharya, U. Rajendra Department of Computer Engineering Faculty of Engineering Fasa University Fasa74617-81189 Iran Deakin University GeelongVIC Australia Department of Electrical and Computer Engineering University of Tabriz Tabriz Iran Data Science and Computational Intelligence Institute University of Granada Granada Spain Department of Signal Theory Networking and Communications Universidad de Granada Granada Spain Swinburne University of Technology HawthornVIC3122 Australia School of Mathematics Physics and Computing University of Southern Queensland Springfield Australia

ISBN: (纸本)9783031503191

Automatic recognition of facial expressions is a common problem in human-computer interaction. While humans can recognize facial expressions very easily, machines cannot do it as easily as humans. Analyzing facial changes during facial expressions is one of the methods used for this purpose by the machines. In this research, facial deformation caused by facial expressions is considered for automatic facial expression recognition by machines. To achieve this goal, the motion vectors of facial deformations are captured during facial expression using an optical flow algorithm. These motion vectors are then used to analyze facial expressions using some data mining algorithms. This analysis not only determined how changes in the face occur during facial expressions but can also be used for facial expression recognition. The facial expressions investigated in this research are happiness, sadness, surprise, fear, anger, and disgust. According to our research, these facial expressions were classified into 12 classes of facial motion vectors. We applied our proposed analysis mechanism to the extended Cohen-Kanade facial expression dataset. Our developed automatic facial expression system achieved 95.3%, 92.8%, and 90.2% accuracy using Deep Learning (DL), Support Vector Machine (SVM), and C5.0 classifiers, respectively. In addition, based on this research, it was determined which parts of the face have a greater impact on facial expression recognition. © 2024, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Data mining

Elastic Full Waveform Inversion Based on the Trust Region Strategy

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American Journal of computational mathematics 2021年第4期11卷 241-266页

作者： Wensheng Zhang Yijun Li 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 Beijing China School of Mathematical Sciences University of Chinese Academy Sciences Beijing China

In this paper, we investigate the elastic wave full-waveform inversion (FWI) based on the trust region method. The FWI is an optimization problem of minimizing the misfit between the observed data and simulated data. Usually, the line search method is used to update the model parameters iteratively. The line search method generates a search direction first and then finds a suitable step length along the direction. In the trust region method, it defines a trial step length within a certain neighborhood of the current iterate point and then solves a trust region subproblem. The theoretical methods for the trust region FWI with the Newton type method are described. The algorithms for the truncated Newton method with the line search strategy and for the Gauss-Newton method with the trust region strategy are presented. Numerical computations of FWI for the Marmousi model by the L-BFGS method, the Gauss-Newton method and the truncated Newton method are completed. The comparisons between the line search strategy and the trust region strategy are given and show that the trust region method is more efficient than the line search method and both the Gauss-Newton and truncated Newton methods are more accurate than the L-BFGS method.

关键词： Elastic Wave Equations Full-Waveform Inversion Trust Region Strate-gy Line Search Strategy Newton-Type Method Time Domain

An Optimization Method for Renewable Energy and Energy Storage Capacity Allocation Based on Temporal Production Simulation

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An Optimization Method for Renewable Energy and Energy Stora...

IEEE Conference on Energy Internet and Energy System Integration (EI2)

作者： Hongbo Du Chi Li Liang Chen Jinping Zhang Caixia Kou College of Sciences Beijing University of Posts and Telecommunications Beijing China National Key Laboratory of Renewable Energy Grid-Integration China Electric Power Research Institute Beijing China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

With the rapid expansion of large-scale renewable energy bases in China, optimizing the allocation of renewable energy and energy storage capacity is crucial for improving system efficiency. In this paper, a joint optimal configuration method of wind-photovoltaic-energy storage capacity based on time series production simulation is proposed for renewable energy transmission base. Its aim is to minimize the total investment cost of the system under certain constraints about the proportion of renewable energy power generation, renewable energy utilization rate, conventional thermal power operation, energy storage power station operation, ultra-high voltage direct current (UHVDC) regulation and power transmission. To handle the nonlinear constraints, linearization is achieved by introducing integer variables. For the complex operation constraints of conventional thermal power and UHVDC channel, a simplified modeling method of start-stop cycle and adjustment cycle is proposed, which can effectively reduce the number of integer variables and improve the solving efficiency. The effectiveness of the proposed method is tested on the data of a renewable energy base in Northwest China.

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A Diffuse-Interface Lattice Boltzmann Method for the Dendritic Growth with Thermosolutal Convection

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Communications in computational Physics 2023年第4期33卷 1164-1188页

作者： Chengjie Zhan Zhenhua Chai Baochang Shi Ping Jiang Shaoning Geng Dongke Sun School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan430074P.R.China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and TechnologyWuhan 430074P.R.China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan430074P.R.China The State Key Laboratory of Digital Manufacturing Equipment and Technology School of Mechanical Science and EngineeringHuazhong University of Science and TechnologyWuhan 430074P.R.China School of Mechanical Engineering Southeast UniversityNanjing 211189P.R.China

In this work,we proposed a diffuse-interface model for the dendritic growth with thermosolutal *** this model,the sharp boundary between the fluid and solid dendrite is firstly replaced by a thin but nonzero thickness diffuse interface,which is described by the order parameter,and the diffuse-interface based governing equations for the dendritic growth are *** solve the model for the dendritic growth with thermosolutal convection,we also developed a diffuse-interface multirelaxation-time lattice Boltzmann(LB)*** this method,the order parameter in the phase-field equation is combined into the force caused by the fluid-solid interaction,and the treatment on the complex fluid-solid interface can be *** addition,four LB models are designed for the phase-field equation,concentration equation,temperature equation and the Navier-Stokes equations in a unified ***,we performed some simulations of the dendritic growth to test the present diffuse-interface LB method,and found that the numerical results are in good agreements with some previous works.

关键词： Dendritic growth diffuse interface lattice Boltzmann method phase-field method.