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C1-Conforming Quadrilateral Spectral Element Method for Fourth-Order Equations

Communications on Applied Mathematics and Computation 2019年第3期1卷 403-434页

作者： Huiyuan Li Weikun Shan Zhimin Zhang State Key Laboratory of Computer Science/Laboratory of parallel Computing Institute of SoftwareChinese Academy of SciencesBeijing 100190China School of Science Henan University of TechnologyZhengzhou 450001HenanChina Beijing computational Science research center Beijing 100193China Department of Mathematics Wayne State UniversityDetroitMI 48202USA

This paper is devoted to Professor Benyu Guo's open question on the C1-conforming quadrilateral spectral element method for fourth-order equations which has been endeavored for years. Starting with generalized Jacobi polynomials on the reference square, we construct the C1-conforming basis functions using the bilinear mapping from the reference square onto each quadrilateral element which fall into three categories-interior modes, edge modes, and vertex modes. In contrast to the triangular element, compulsively compensatory requirements on the global C1-continuity should be imposed for edge and vertex mode basis functions such that their normal derivatives on each common edge are reduced from rational functions to polynomials, which depend on only parameters of the common edge. It is amazing that the C1-conforming basis functions on each quadrilateral element contain polynomials in primitive variables, the completeness is then guaranteed and further confirmed by the numerical results on the Petrov-Galerkin spectral method for the non-homogeneous boundary value problem of fourth-order equations on an arbitrary quadrilateral. Finally, a C1-conforming quadrilateral spectral element method is proposed for the biharmonic eigenvalue problem, and numerical experiments demonstrate the effectiveness and efficiency of our spectral element method.

关键词： Quadrilateral spectral element method Fourth-order equations Mapped polynomials C1-conforming basis Polynomial inclusion Completeness

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Feedback control for manipulating magnetization in spin-exchange optical pumping system

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Science China(Physics,Mechanics & Astronomy) 2018年第8期61卷 27-32页

作者： Ke Zhang Jun Li Min Jiang Nan Zhao XinHua Peng Beijing computational Science research center Bejing 100193Chin Hefei National Laboratory for Physical Sciences at Microscale Department of Modern PhysicsUniversity of Science and Technology of ChinaHefei 230026China Synergetic Innovation center of Quantum Information&Quantum Physics University of Science and Technology of ChinaHefei 230026China

Control of magnetization plays an important role in the scientific and technological field of manipulating spin systems. In this work, we study the problem of manipulating nuclear magnetization in the spin-exchange optical pumping system, including accelerating the recovery of nuclear polarization and fixing it on a specific desired state. A real-time feedback control strategy is exploited here. We have also done some numerical simulations, with the results clearly demonstrating the effectiveness of our method, that the nuclear magnetization is able to be driven towards the equilibrium state at a much faster speed and also can be stabilized to a target state. We expect that our feedback control method can find applications in gyro experiments.

关键词： optical pumping feedback control nuclear magnetic resonance state stabilization

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Hazard-evaluation-oriented Moving Horizon parallel Steering Control for Driver-Automation Collaboration During Automated Driving

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IEEE/CAA Journal of Automatica Sinica 2018年第6期5卷 1062-1073页

作者： Hongyan Guo Linhuan Song Jun Liu Fei-Yue Wang Dongpu Cao Hong Chen Chen Lv Partick Chi-Kwong Luk State Key Laboratory of Automotive Simulation and Control and the Department of Con-trol Science and Engineering Jilin University(Campus Nanling)Changchun130025China State Key Laboratory of Management and Control for Complex systems Institute of AutomationChinese Academy of SciencesBeijing 100190China research center for Military computational experiments and parallel systems technology National University of Defense TechnologyChangsha 410073China Mechanical and Mechatronics Engineering Department at the University ot Waterloo 200 University Avenue West WaterlooONNZL3G1Canada Department of Automotive Engineering Cranfield UniversityBedfordshire MK43 0ALUK School of Water Energy and EnvironmentCranfield UniversityBedfordshire MK43 0ALUK

Prompted by emerging developments in connected and automated vehicles, parallel steering control, one aspect of parallel driving, has become highly important for intelligent vehicles for easing the burden and ensuring the safety of human drivers. This paper presents a parallel steering control framework for an intelligent vehicle using moving horizon *** framework considers lateral stability, collision avoidance and actuator saturation and describes them as constraints, which can blend the operation of a human driver and a parallel steering controller effectively. Moreover, the road hazard and the steering operation error are employed to evaluate the operational hazardous of an intelligent vehicle. Under the hazard evaluation,the intelligent vehicle will be mainly operated by the human driver when the vehicle operates in a safe and stable *** automated steering driving objective will play an active role and regulate the steering operations of the intelligent vehicle based on the hazard evaluation. To verify the effectiveness of the proposed hazard-evaluation-oriented moving horizon parallel steering control approach, various validations are conducted, and the results are compared with a parallel steering scheme that does not consider automated driving situations. The results illustrate that the proposed parallel steering controller achieves acceptable performance under both conventional conditions and hazardous conditions.

关键词： Hazard evaluation intelligent vehicle atera stability moving horizon optimization paralle steering control

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A study on coupling technique and implementation of the wave-circulation coupled model

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High technology Letters 2014年第1期20卷 82-87页

作者：张志远 Liu Li Zhou Yufeng Zhang Cheng Li Ruizhe Chen Yushu Song Guojie Yang Guangwen Department of Computer Science and technology Tsinghua University Ministry of Education Key Laboratory for Earth system Modeling Center for Earth System ScienceTsinghua University Hydro-Meteorological center of Navy

The coupler is fundamental for a coupled model to realize complex interactions among component *** paper focuses on the coupling process of Wave-Circulation(W-C) coupled model which consists of MASNUM(key laboratory of marine science and numerical modeling wave model)and POM(Princeton Ocean Model).The current coupling module of this coupled model is based on the inefficient I/O file,which has already become a performance bottleneck especially when the coupled model utilizes a large number of *** improve the performance of the W-C model,a flexible coupling module based on the model coupling toolkit(MCT) is designed and implemented to replace the current I/O file coupling module in the coupled *** studies that we have carried out demonstrate that our online coupling module can dramatically improve the parallel performance of the coupled *** online coupling module outperforms the I/O file coupling *** processes increase to 96,the whole process of EXP-C takes only 695.8 seconds,which is only 58.8%of the execution time of *** on our experiments under 2D parallel Decomposition(2DPD),we suggest setting parallel decomposition strategies automatically to component models in order to achieve high parallel efficiency.

关键词： coupling technique model coupling toolkit (MCT) W-C coupled online cou-pling module 2D parallel Decomposition (2DPD) parallel performance

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Experimental investigation on rainfall infiltration and solute transport in layered porous and fractured media

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Journal of Coal Science & Engineering(China) 2012年第1期18卷 29-34页

作者： Wang, Hui-fang Wang, Ming-yu center for Water system Security & Key Laboratory of computational Geodynamics Graduate University of Chinese Academy of Sciences Beijing China

Layered structures with upper porous and lower fractured media are widely distributed in the world. An experimen- tal investigation on rainfall infiltration and solute transport in such layered structures can provide the necessary foundation for effectively preventing and forecasting water bursting in mines, controlling contamination of mine water, and accomplishing ecological restoration of mining areas. A typical physical model of the layered structures with porous and fractured media was created in this study. Then rainfall infiltration experiments were conducted after salt solution was sprayed on the surface of the layered structure. The volumetric water content and concentration of chlorine ions at different specified positions along the profile of the experiment system were measured in real-time. The experimental results showed that the lower fractured media, with a considerably higher permeability than that of the upper porous media, had significant effects on preventing water infil- tration. Moreover, although the porous media were homogeneous statistically in the whole domain, spatial variations in the features of effluent concentrations with regards to time, or so called breakthrough curves, at various sampling points located at the horizontal plane in the porous media near the porous-fractured interface were observed, indicating the diversity of solute transport at small scales. Furthermore, the breakthrough curves of the outflow at the bottom, located beneath the underlying fractured rock, were able to capture and integrate features of the breakthrough curves of both the upper porous and fractured media, which exhibited multiple peaks, while the peak values were reduced one by one with time.

关键词： rainfall infiltration solute transport layered porous and fractured media lab experiment breakthrough curves

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Updating preconditioner for iterative method in time domain simulation of power systems

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Science China(Technological Sciences) 2011年第4期54卷 1024-1034页

作者： WANG Ke XUE Wei LIN HaiXiang XU ShiMing ZHENG WeiMin Laboratory of parallel Software and computational Science Institute of SoftwareChinese Academy of SciencesBeijing 000China Department of Computer Science and technology Tsinghua UniversityBeijing 000China Tsinghua National Laboratory for Information Science and technology(TNList) Beijing 100084China Delft Institute of Applied Mathematics Delft University of TechnologyDelft 2628 CDThe Netherlands

The numerical solution of the differential-algebraic equations(DAEs) involved in time domain simulation(TDS) of power systems requires the solution of a sequence of large scale and sparse linear *** use of iterative methods such as the Krylov subspace method is imperative for the solution of these large and sparse linear *** motivation of the present work is to develop a new algorithm to efficiently precondition the whole sequence of linear systems involved in *** an improvement of dishonest preconditioner(DP) strategy,updating preconditioner strategy(UP) is introduced to the field of TDS for the first *** idea of updating preconditioner strategy is based on the fact that the matrices in sequence of the linearized systems are continuous and there is only a slight difference between two consecutive *** order to make the linear system sequence in TDS suitable for UP strategy,a matrix transformation is applied to form a new linear sequence with a good shape for preconditioner *** algorithm proposed in this paper has been tested with 4 cases from real-life power systems in *** show that the proposed UP algorithm efficiently preconditions the sequence of linear systems and reduces 9%-61% the iteration count of the GMRES when compared with the DP method in all test *** experiments also show the effectiveness of UP when combined with simple preconditioner reconstruction strategies.

关键词： differential-algebraic equations GMRES updating preconditioner power system simulation

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EFFICIENT SPECTRAL METHODS FOR EIGENVALUE PROBLEMS OF THE INTEGRAL FRACTIONAL LAPLACIAN ONABALLOFANYDIMENSION

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Journal of computational Mathematics 2024年第4期42卷 1032-1062页

作者： Suna Ma Huiyuan Li Zhimin Zhang Hu Chen Lizhen Chen College of Science Nanjing University of Posts and TelecommunicationsNanjingChina State Key Laboratory of Computer Science/Laboratory of parallel Computing Institute of SoftwareChinese Academy of SciencesBeijingChina Department of Mathematics Wayne State UniversityDetroitUSA School of Mathematical Sciences Ocean University of ChinaQingdaoChina Beijing computational Science research center BeijingChina

An efficient spectral-Galerkin method for eigenvalue problems of the integral fractional Laplacian on a unit ball of any dimension is proposed in this *** symmetric positive definite linear system is retained explicitly which plays an important role in the numerical *** a sharp estimate on the algebraic system's condition number is established which behaves as N4s with respect to the polynomial degree N,where 2s is the fractional derivative *** regularity estimate of solutions to source problems of the fractional Laplacian in arbitrary dimensions is firstly investigated in weighted Sobolev *** the regularity of eigenfunctions of the fractional Laplacian eigenvalue problem is readily ***,rigorous error estimates of the eigenvalues and eigenvectors are *** experiments are presented to demonstrate the accuracy and efficiency and to validate the theoretical results.

关键词： Integral fractional Laplacian Spectral method Eigenvalue problem Regularity analysis Error estimate

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Fuel efficient model predictive control strategies for a group of connected vehicles incorporating vertical vibration

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Science China(Technological Sciences) 2017年第11期60卷 1732-1746页

作者： QIAN LiJun QIU LiHong CHEN Peng ABDOLLAHI Zoleikha PISU Pierluigi Department of Vehicle Engineering Hefei University of Technology International center for Automotive research Clemson University

This paper presents a decentralized fuel efficient model predictive control(MPC) strategy for a group of connected vehicles incorporating vertical vibration. To capture the vehicle vibration dynamics, the dynamics of the suspension system is integrated with the longitudinal dynamics of the vehicle. Furthermore, a MPC framework with finite time horizon is formulated to calculate the optimal velocity profile that compromises fuel economy, mobility and ride comfort for every individual vehicle with the safety and physical constraints considered. In the MPC framework, the target velocity is calculated using signal phase and timing(SPAT)information to reduce the number of stoppage at red lights, and the vertical acceleration is calculated parallel to the calculation of the fuel consumption. The MPC optimal problem is solved with fast-MPC approach which enhances the computational efficiency via exploiting the structure of the control system and approximate methods. Simulation studies are conducted over different SPATs and connectivity penetration rates and the results validate the advantages of the proposed control architecture.

关键词： model predictive control connected vehicles fuel economy vertical vibration intelligent transportation system

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Fast parallel algorithm for three-dimensional distance-driven model in iterative computed tomography reconstruction

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Chinese Physics B 2015年第2期24卷 513-520页

作者：陈建林李磊王林元蔡爱龙席晓琦张瀚铭李建新闫镔 National Digital Switching system Engineering & Technological R&D center

The projection matrix model is used to describe the physical relationship between reconstructed object and *** a model has a strong influence on projection and backprojection,two vital operations in iterative computed tomographic *** distance-driven model（DDM） is a state-of-the-art technology that simulates forward and back *** model has a low computational complexity and a relatively high spatial resolution;however,it includes only a few methods in a parallel operation with a matched model *** study introduces a fast and parallelizable algorithm to improve the traditional DDM for computing the parallel projection and backprojection *** proposed model has been implemented on a GPU（graphic processing unit） platform and has achieved satisfactory computational efficiency with no *** runtime for the projection and backprojection operations with our model is approximately 4.5 s and 10.5 s per loop,respectively,with an image size of 256×256×256 and 360 projections with a size of 512×*** compare several general algorithms that have been proposed for maximizing GPU efficiency by using the unmatched projection/backprojection models in a parallel *** imaging resolution is not sacrificed and remains accurate during computed tomographic reconstruction.

关键词： computed tomography iterative reconstruction parallelizable algorithm distance-driven model

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Majorana tunneling in a one-dimensional wire with non-Hermitian double quantum dots

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Chinese Physics B 2024年第1期33卷 686-691页

作者：牛鹏斌罗洪刚 Institute of Solid State Physics Shanxi Datong Universityand Shanxi Provincial Key Laboratory of Microstructural Electromagnetic Functional MaterialsDatong 037009China School of Physical Science and technology Lanzhou UniversityLanzhou 730000China Beijing computational Science research center Beijing 100084China

The combination of non-Hermitian physics and Majorana fermions can give rise to new effects in quantum transport systems. In this work, we investigate the interplay of PT-symmetric complex potentials, Majorana tunneling and interdot tunneling in a non-Hermitian double quantum dots system. It is found that in the weak-coupling regime the Majorana tunneling has pronounced effects on the transport properties of such a system, manifested as splitting of the single peak into three and a reduced 1/4 peak in the transmission function. In the presence of the PT-symmetric complex potentials and interdot tunneling, the 1/4 central peak is robust against them, while the two side peaks are tuned by them. The interdot tunneling only induces asymmetry, instead of moving the conductance peak, due to the robustness of the Majorana modes. There is an exceptional point induced by the union of Majorana tunneling and interdot tunneling. With increased PT-symmetric complex potentials, the two side peaks will move towards each other. When the exceptional point is passed through, these two side peaks will disappear. In the strong-coupling regime, the Majorana fermion induces a 1/4 conductance dip instead of the three-peak structure. PT-symmetric complex potentials induce two conductance dips pinned at the exceptional point. These effects should be accessible in experiments.

关键词： Majorana fermion non-Hermitian quantum dot parity–time symmetry exceptional point

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