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AN EFFICIENT THRESHOLD DYNAMICS METHOD FOR TOPOLOGY OPTIMIZATION FOR FLUIDS

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arXiv 2018年

作者： Chen, Huangxin Leng, Haitao Wang, Dong Wang, Xiao-Ping School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing Xiamen University Fujian361005 China Department of Mathematics Hong Kong University of Science and Technology Clear Water Bay Kowloon Hong Kong Department of Mathematics University of Utah Salt Lake CityUT United States

We propose an efficient threshold dynamics method for topology optimization for fluids modeled with the Stokes equation. The proposed algorithm is based on minimization of an objective energy function that consists of the dissipation power in the fluid and the perimeter approximated by nonlocal energy, subject to a fluid volume constraint and the incompressibility condition. We show that the minimization problem can be solved with an iterative scheme in which the Stokes equation is approximated by a Brinkman equation. The indicator functions of the fluid-solid regions are then updated according to simple convolutions followed by a thresholding step. We demonstrate mathematically that the iterative algorithm has the total energy decaying property. The proposed algorithm is simple and easy to implement. A simple adaptive time strategy is also used to accelerate the convergence of the iteration. Extensive numerical experiments in both two and three dimensions show that the proposed iteration algorithm converges in much fewer iterations and is more efficient than many existing methods. In addition, the numerical results show that the algorithm is very robust and insensitive to the initial guess and the parameters in the model. Copyright © 2018, The Authors. All rights reserved.

关键词： Convolution

A note on the run length function for intermittent maps

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arXiv 2018年

作者： Cui, Hongfei Fang, Lulu Zhang, Yiwei Wuhan Institute of Physics and Mathematics Chinese Academy of Sciences Wuhan430071 China Sun Yat-sen university Guangzhou510275 China School of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Sciences and Technology Wuhan430074 China

We study the run length function for intermittent maps. In particular, we show that the longest consecutive zero digits (resp. one digits) having a time window of polynomial (resp. logarithmic) length. Our proof is relatively elementary in the sense that it only relies on the classical Borel-Cantelli lemma and the polynomial decay of intermittent maps. Our results are compensational to the Erd?os-Rényi law obtained by Denker and Nicol in [8]. Copyright © 2018, The Authors. All rights reserved.

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A rigorous computer aided estimation for gelfond exponent of weighted thue-morse sequences

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arXiv 2018年

作者： ZHANG, YIWEI YIN, KE WU, WANQUAN School of Mathematics and Statistics Center for Mathematical Science Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology 1037 Luoyu Road Wuhan430074 China School of Computer Science and Technology Huazhong University of Science and Technology 1037 Luoyu Road Wuhan430074 China

In this paper, we will provide a mathematically rigorous computer aided estimation for the exact values and robustness for Gelfond exponent of weighted Thue-Morse sequences. This result improves previous discussions on Gelfond exponent by Gelfond, Devenport, Mauduit, Rivat, Sarközy and Fan et. al.37C40, 90C27 Copyright © 2018, The Authors. All rights reserved.

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A preconditioned riemannian gauss-Newton method for least squares inverse eigenvalue problems

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arXiv 2018年

作者： Yao, Teng-Teng Bai, Zheng-Jian Jin, Xiao-Qing Zhao, Zhi Department of Mathematics School of Sciences Zhejiang University of Science and Technology Hangzhou310023 China School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling & High Performance Scientific Computing Xiamen University Xiamen361005 China Department of Mathematics University of Macau China Department of Mathematics School of Sciences Hangzhou Dianzi University Hangzhou310018 China

This paper is concerned with the least squares inverse eigenvalue problem of reconstructing a linear parameterized real symmetric matrix from the prescribed partial eigenvalues in the sense of least squares, which was originally proposed by Chen and Chu [SIAM J. Numer. Anal., 33 (1996), pp. 2417-2430]. We provide a Riemannian inexact Gausss-Newton method for solving the least squares inverse eigenvalue problem. The global and local convergence analysis of the proposed method is discussed. Also, a preconditioned conjugate gradient method with an efficient preconditioner is proposed for solving the Riemannian Gauss-Newton equation. Finally, some numerical tests, including an application in the inverse Sturm-Liouville problem, are reported to illustrate the efficiency of the proposed method.65F18, 65F15 Copyright © 2018, The Authors. All rights reserved.

关键词： Newton-Raphson method

Electrospun nanofibrous membrane for electrodialysis

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Journal of Physics: Conference Series 2019年第1期1209卷

作者： J X Jiang G F Zheng X Wang G Fu J Liu W W Li M F Zhuang SH M Guo Department of Instrumental and Electrical Engineering Xiamen University Xiamen 361102 China School of Mechanical and Manufacturing Engineering Xiamen Institute of Technology Xiamen 361024 China School of Mathematical Sciences Xiamen University Xiamen 361021 China Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing School of Mathematical Sciences Xiamen University Xiamen 361005 China

The direct fabrication of homogenous membrane for electrodialysis has become the research hotspots in the field of water purification. A novel multi-jet electrospinning method with sheath gas was presented to study the fabrication of homogenous electrodialysis membrane. By soaking into sulfuric acid, the reactive exchange groups can be introduced into the electrospun nanofibrous membrane that has been hot pressed. Thanks to the pores among nanofibers, electrospun electrodialysis membrane had advantages of higher porosity, higher water uptake and lower membrane resistance, which promoted the ion transmission through the membrane. The porosity, water uptake and ion exchange capacity (IEC) reduced with the increase of membrane thickness. An electrodialysis separation system was set up to test its separation performance. The results showed that the desalinization ratio of NaCl solution could be reached to 58.15% within 30 minutes. The electrospun nanofibrous membrane for electrodialysis provides a simple and effective way to expand its industrial application.

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LOCAL SUPERCONVERGENCE OF CONTINUOUS GALERKIN SOLUTIONS FOR DELAY DIFFERENTIAL EQUATIONS OF PANTOGRAPH TYPE

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Journal of Computational Mathematics 2016年第2期34卷 186-199页

作者： Xiuxiu Xu Qiumei Huang Hongtao Chen Beijing Institute for Scientific and Engineering Computing Beijing University of Technology Beijing 100124 China School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing Xiamen University Xiamen 361005 China

This paper is concerned with the superconvergent points of the continuous Galerkin solutions for delay differential equations of pantograph type. We prove the local nodal superconvergence of continuous Galerkin solutions under uniform meshes and locate all the superconvergent points based on the supercloseness between the continuous Galerkin solution U and the interpolation Hhu of the exact solution u. The theoretical results are illustrated by numerical examples.

关键词： Pantograph delay differential equations Uniform mesh Continuous Galerkinmethods Supercloseness Superconvergence.

Energy Stable Finite Element/Spectral Method for Modified Higher-Order Generalized Cahn-Hilliard Equations

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数学研究 2018年第3期51卷 253-293页

作者： Hongyi Zhu Laurence Cherfils Alain Miranville Shuiran Peng Wen Zhang School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling&High Performance Scientific Computing Xiamen UniversityXiamen 361005P.R.China Laboratoire des Sciences de l'Ingénieur pour l'Environnement Université de La RochelleUMR CNRS 7356F-17042 La Rochelle CedexFrance School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling&High Performance Scientific Computing Xiamen UniversityXiamen 361005P.R.China Laboratoire de Mathématiques et Applications Université de PoitiersUMR CNRS 7348Boulevard Marie et Pierre CurieTéléport 2F-86962 Chasseneuil Futuroscope CedexFrance Laboratoire de Mathématiques et Applications Université de PoitiersUMR CNRS 7348Boulevard Marie et Pierre CurieTéléport 2F-86962 Chasseneuil Futuroscope CedexFrance School of Sciences East China University of TechnologyNanchang 330013P.R.China

Our aim in this paper is to study a fully discrete scheme for modified higher-order(in space)anisotropic generalized Cahn-Hilliard models which have extensive applications in biology,image processing,*** particular,the scheme is a combina-tion of finite element or spectral method in space and a second-order stable scheme in *** obtain energy stability results,as well as the existence and uniqueness of the numerical solution,both for the space semi-discrete and fully discrete *** also give several numerical simulations which illustrate the theoretical results and,espe-cially,the effects of the higher-order terms on the anisotropy.

关键词： Modified Cahn-Hilliard equation higher-order models energy stability anisotropy

A role of random slow manifolds in detecting stochastic bifurcation

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arXiv 2018年

作者： He, Ziying Cai, Rui Duan, Jinqiao Liu, Xianming Center for Mathematical Sciences Huazhong University of Sciences and Technology Wuhan430074 China School of Mathematics and Statistics Huazhong University of Sciences and Technology Wuhan430074 China Hubei Key Laboratory for Engineering Modeling and Scientific Computing Huazhong University of Sciences and Technology Wuhan430074 China Department of Applied Mathematics Illinois Institute of Technology ChicagoIL60616 United States

We consider the relation for the stochastic equilibrium states between the reduced system on a random slow manifold and the original system. This provides a theoretical basis for the reduction about sophisticated detailed models by the random slow manifold without significant damage to the overall qualitative properties. Based on this result, we reveal a role of random slow manifolds in detecting stochastic bifurcation by an example. The example exhibits a stochastic bifurcation phenomenon and possesses a random slow manifold that carries the stochastic bifurcation information of the system. Specifically, the lower dimensional reduced system on the random slow manifold retains the stochastic bifurcation phenomenon from the original *** Codes 60H10, 58J65 Copyright © 2018, The Authors. All rights reserved.

关键词： Perturbation techniques

A wong-zakai approximation for random slow manifolds with application to parameter estimation

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arXiv 2018年

作者： He, Ziying Zhang, Xinyong Jiang, Tao Liu, Xianming Center for Mathematical Sciences Huazhong University of Sciences and Technology Wuhan430074 China School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Sciences and Technology Wuhan430074 China Department of Mathematical Sciences Tsinghua University Beijing100084 China Collaborative Innovation Center of China Pilot Reform Exploration and Assessment Hubei Sub-Center Hubei University of Economics Wuhan430205 China

We study a Wong-Zakai approximation for the random slow manifold of a slow-fast stochastic dynamical system. We first deduce the existence of the random slow manifold about an approximation system driven by an integrated Ornstein-Uhlenbeck (O-U) process. Then we compute the slow manifold of the approximation system, in order to gain insights of the long time dynamics of the original stochastic system. By restricting this approximation system to its slow manifold, we thus get a reduced slow random system. This reduced slow random system is used to accurately estimate a system parameter of the original system. An example is presented to illustrate this *** Codes Primary: 37L55, 35R60, Secondary: 60H15, 58J65 Copyright © 2018, The Authors. All rights reserved.

关键词： Parameter estimation