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Numerical Investigations of a Class of Biological Models on Unbounded Domain

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Numerical Mathematics(Theory,Methods and Applications) 2019年第1期12卷 169-186页

作者： Qiumei Huang Dongfang Li jiwei zhang Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing 100124China School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratoryof Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China Beijing Computational Science Research Center Beijing1000193China

This paper is concerned with numerical computations of a class of biologi-cal models on unbounded spatial *** overcome the unboundedness of spatial domain,we first construct efficient local absorbing boundary conditions(LABCs)to re-formulate the Cauchy problem into an initial-boundary value(IBV)*** that,we construct a linearized finite difference scheme for the reduced IVB problem,and provide the corresponding error estimates and stability *** delay-dependent dynamical properties on the Nicholson’s blowflies equation and the Mackey-Glass equa-tion are numerically ***,numerical examples are given to demonstrate the efficiency of our LABCs and theoretical results of the numerical scheme.

关键词： Biological models artificial boundary method absorbing boundary conditions finite difference method stability,convergence

Numerical Computations of Nonlocal Schrodinger Equations on the Real Line

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Communications on Applied Mathematics and Computation 2020年第2期2卷 241-260页

作者： Yonggui Yan jiwei zhang Chunxiong Zheng Beijing Computational Science Research Center Beijing 100093China School of Mathematics and Statistics and Hubei Key Laboratory of Computational ScienceWuhan UniversityWuhan 430072China Department of Mathematical Sciences Tsinghua UniversityBeijing 100084China College of Mathematics and Systems Science Xinjiang UniversityUnimqi 830046China

The numerical computation of nonlocal Schrödinger equations (SEs) on the whole real axis is considered. Based on the artifcial boundary method, we frst derive the exact artifcial nonrefecting boundary conditions. For the numerical implementation, we employ the quadrature scheme proposed in Tian and Du (SIAM J Numer Anal 51:3458-3482, 2013) to discretize the nonlocal operator, and apply the z-transform to the discrete nonlocal system in an exterior domain, and derive an exact solution expression for the discrete system. This solution expression is referred to our exact nonrefecting boundary condition and leads us to reformulate the original infnite discrete system into an equivalent fnite discrete system. Meanwhile, the trapezoidal quadrature rule is introduced to discretize the contour integral involved in exact boundary conditions. Numerical examples are fnally provided to demonstrate the efectiveness of our approach.

关键词： Nonrefecting boundary conditions Artifcial boundary method Nonlocal Schrödinger equation z-transform Nonlocal models

冠心病患者PCI术后发生支架内再狭窄的影响因素分析

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临床医学工程 2024年第4期31卷 509-510页

作者：赵艳杨杰张继伟新乡市中心医院介入导管室河南新乡453000 新乡市中心医院介入特需病房河南新乡453000 新乡市中心医院介入急诊科河南新乡453000

目的分析冠心病患者经皮冠状动脉介入(PCI)术后发生支架内再狭窄(ISR)的相关影响因素。方法回顾性分析100例行PCI治疗的冠心病患者的临床资料,根据术后是否发生ISR分为发生组与未发生组,采用单因素分析和多因素Logistic回归分析探讨冠... 详细信息

目的分析冠心病患者经皮冠状动脉介入(PCI)术后发生支架内再狭窄(ISR)的相关影响因素。方法回顾性分析100例行PCI治疗的冠心病患者的临床资料,根据术后是否发生ISR分为发生组与未发生组,采用单因素分析和多因素Logistic回归分析探讨冠心病患者PCI术后发生ISR的危险因素。结果单因素和多因素Logistic回归分析显示,合并糖尿病、合并高血压、PCI术支架直径<3.5 mm、支架长度≥30 mm、支架数量≥2枚均为冠心病患者PCI术后发生ISR的危险因素(P<0.05)。结论合并糖尿病、合并高血压、PCI术支架直径过小、支架长度过长、多支架置入与冠心病患者PCI术后发生ISR密切相关。

关键词：冠心病经皮冠状动脉介入支架内再狭窄影响因素

Efficient Numerical Computation of Time-Fractional Nonlinear Schrodinger Equations in Unbounded Domain

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Communications in Computational Physics 2019年第1期25卷 218-243页

作者： jiwei zhang Dongfang Li Xavier Antoine Beijing Computational Science Research Center Beijing 100193P.R.China 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 Institut Elie Cartan de Lorraine UMR CNRS 7502Universit́e de LorraineInria Nancy-Grand EstSPHINX TeamF-54506 Vandoeuvre-l`es-Nancy CedexFrance

The aim of this paper is to derive a stable and efficient scheme for solving the one-dimensional time-fractional nonlinear Schrodinger equation set in an unbounded *** first derive absorbing boundary conditions for the fractional system by using the unified approach introduced in[47,48]and a linearization ***,the initial boundary-value problem for the fractional system with ABCs is discretized,a stability analysis is developed and the error estimate O(h^(2)+τ)is *** accel-erate the L1-scheme in time,a sum-of-exponentials approximation is introduced to speed-up the evaluation of the Caputo fractional *** resulting algorithm is highly efficient for long time ***,we end the paper by reporting some numerical simulations to validate the properties(accuracy and efficiency)of the derived scheme.

关键词： Time-fractional nonlinear Schrodinger equation absorbing boundary condition sta-bility analysis convergence analysis sum-of-exponentials approximation

Numerical Soliton Solutions for a Discrete Sine-Gordon System

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Communications in Computational Physics 2009年第9期6卷 903-918页

作者： Houde Han jiwei zhang Hermann Brunner Department of Mathematical Sciences Tsinghua UniversityBeijing 100084China Department of Mathematics Hong Kong Baptist UniversityKowloon TongHong KongChina Department of Mathematics and Statistics Memorial University of NewfoundlandSt.John’sNLCanada A1C 5S7

In this paper we use an analytical-numerical approach to find,in a systematic way,new 1-soliton solutions for a discrete sine-Gordon system in one spatial *** the spatial domain is unbounded,the numerical scheme employed to generate these soliton solutions is based on the artificial boundary method.A large selection of numerical examples provides much insight into the possible shapes of these new 1-solitons.

关键词： Sine-Gordon equation soliton solutions numerical single solitons artificial boundary method

Observation of small-scale processes over shelf break in the East China Sea

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Chinese Science Bulletin 2005年第24期50卷 2885-2890页

作者： ZHOU Lei TIAN jiwei zhang Xiaoqian Physical Oceanography Laboratory Ocean University of China Qingdao 266003 China

The turbulent dissipation along with tempera- ture and salinity was measured on board R/V Dong Fang Hong 2 over the shelf break of the East China Sea from March 7 to 9, 2004. Applying the Turner angle, it is found that the ‘diffusive’ double diffusion, salt-fingering, and stable stratification coexist in the upper water column of about 50 m. Below that depth, there exists weak salt-fingering. The turbulent dissipation rates are enhanced along the ray paths of M2 internal tides emanating from the shelf break with values ranging from 1.0×10?9 W·kg?1 to 1.2×10?6 W·kg?1. The corresponding diapycnal mixing rates are from 1×10?6 m2·s?1 to 1×10?2 m2·s?1. The spatially averaged mixing rate over the whole observation section is 2.3×10?3 m2·s?1, which is much larger than 1×10?5 m2·s?1 of the background diapy- cnal mixing rate in the open ocean.

关键词：中国东海陆架间断小规模突起两倍扩散率湍流耗散海水盐度温度

Observation of internal tides and near-inertial motions in the upper 450 m layer of the northern South China Sea

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Chinese Science Bulletin 2005年第24期50卷 2890-2895页

作者： LIANG Xinfeng zhang Xiaoqian TIAN jiwei Physical Oceanography Laboratory of Ocean University of China Qingdao 266003 China

Mooring ADCP current observations from Au- gust to November are used to study the barotropic tides, baroclinic tides and near-inertial motions in the upper 450 m layer of the northern South China Sea. The barotropic and baroclinic tides at the mooring station are all dominated by M2, K1, O1, P1, with the barotropic amplitudes being 7.8 cm·s?1, 7.0 cm·s?1, 5.4 cm·s?1 and 3.5 cm·s?1 respectively. The amplitudes of M2, K1, O1, P1 internal tides vary greatly, which are 12―15 cm·s?1 in the thermocline, and then decrease with increasing depth. The amplitude of the barotropic near-iner- tial motions is less than 1 cm·s?1, contributing little to the barotropic currents. However, that of the baroclinic near- inertial motions can be as large as 5 cm·s?1. The inclination of tidal ellipse tends to increase with increasing depth, implying upward propagation of energy, while that of the near-inertial ellipse tends to decrease with increasing depth, implying downward propagation of energy.

关键词：中国南海内潮惯性运动上层海水

STABILITY ANALYSIS FOR NONLINEAR SCHRODINGER EQUATIONS WITH NONLINEAR ABSORBING BOUNDARY CONDITIONS

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Journal of Computational Mathematics 2017年第1期35卷 1-18页

作者： jiwei zhang Zhenli Xu Xiaonan Wu Desheng Wang Applied and Computational Mathematics Division Beijing Computational Science Research Center China Department of Mathematics Institute of Natural Sciences and MOE Key Lab of Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai 200240 China Department of Mathematics Hong Kong Baptist University Kowloon Hong Kong China Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technological University Singapore 637371 Singapore

Local absorbing boundary conditions （LABCs） for nonlinear Schr6dinger equations have been constructed in papers [PRE 78（2008） 026709; and PRE 79 （2009） 046711] using the so-called unified approach. In this paper, we present stability analysis for the reduced problem with LABCs on the bounded computational domain by the energy estimate, and discuss a class of modified versions of LABCs. To prove the stability analysis of the re- duced problem, we turn to the technique of some auxiliary variables which reduces the higher-order derivatives in LABCs into a family of equations with lower-order derivatives. Furthermore, we extend the strategy to the stability analysis of two-dimensional problems by carefully dealing with the LABCs at corners. Numerical examples are given to demon- strate the effectiveness of our boundary conditions and validate the theoretical analysis.

关键词： Nonlinear SchrSdinger equations Energy estimates Absorbing boundaryconditions.

Artificial Boundary Conditions for Nonlocal Heat Equations on Unbounded Domain

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Communications in Computational Physics 2017年第1期21卷 16-39页

作者： Wei zhang Jiang Yang jiwei zhang Qiang Du Beijing Computational Science Research Centre BeijingP.R.China Department of Mathematics Columbia UniversityNew YorkNY 10027USA

This paper is concerned with numerical approximations of a nonlocal heat equation define on an infinite *** classes of artificial boundary conditions(ABCs)are designed,namely,nonlocal analog Dirichlet-to-Neumann-type ABCs(global in time)and high-order Pad´e approximate ABCs(local in time).These ABCs reformulate the original problem into an initial-boundary-value(IBV)problem on a bounded *** the global ABCs,we adopt a fast evolution to enhance computational efficiency and reduce memory *** order fully discrete schemes,both second-order in time and space,are given to discretize two reduced *** numerical experiments are carried out to show the accuracy and efficiency of the proposed methods.

关键词： Artificial boundary conditions nonlocal models Pad´e approximation nonlocal heat equations artificial boundary method