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Hexahedral constraint-free finite element method on meshes with hanging nodes

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Science China Mathematics 2019年第12期62卷 2591-2616页

作者： Xuying Zhao Zhong-Ci Shi LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingNCMISAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences Capital Normal UniversityBeijing 100048China

Nonconforming grids with hanging nodes are frequently used in adaptive finite element comput at *** all earlier works on such methods,proper cons train ts should be enforced on degrees of freedom on edges/faces with hanging nodes to keep continuity,which yield numerical computations much *** 2014,Zhao et al.(2014)presented quadrilateral constraint-free finite element methods on quadrilateral grids with hanging *** paper further develops a hexahedral constraint-free finite element method on hexahedral grids with hanging nodes,which is of greater challenge than the two-dimensional ***-based a posteriori error reliability and efficiency are also established in this paper.

关键词： adaptive finite element a posteriori error estimate hexahedral nonconforming element hangingnode

MONOLITHIC MULTIGRID FOR REDUCED MAGNETOHYDRODYNAMIC EQUATIONS

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Journal of Computational Mathematics 2021年第3期39卷 453-470页

作者： Xiaodi Zhang Weiying Zheng LSEC NCMISInstitute of Computational Mathermatics and Scientific ComputingAcademy of Mathematics and Systerns ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Science University of Chinese Academy of SciencesBeijing 100049China

In this paper,the monolithic multigrid method is investigated for reduced magnetohydrodynamic *** propose a diagonal Braess-Sarazin smoother for the finite element discrete system and prove the uniform convergence of the MMG method with respect to mesh sizes.A multigrid-preconditioned FGMRES method is proposed to solve the magnetohydrodynamic *** turns out to be robust for relatively large physical *** extensive numerical experiments,we demonstrate the optimality of the monolithic multigrid method with respect to the number of degrees of freedom.

关键词： Monolithic multigrid Magnetohydrodynamic equations Diagonal Braess-Sarazin smoother Finite element method

Distributed Lagrange Multiplier/Fictitious Domain Finite Element Method for a Transient Stokes Interface Problem with Jump Coefficients

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Computer Modeling in Engineering & Sciences 2019年第4期119卷 35-62页

作者： Andrew Lundberg Pengtao Sun Cheng Wang Chen-song Zhang Department of Mathematical Sciences University of NevadaLas Vegas4505 Maryland ParkwayLas VegasNV 89154USA School of Mathematical Sciences Tongji UniversityShanghaiChina LSEC&ncmis Academy of Mathematics and System ScienceBeijingChina

The distributed Lagrange multiplier/fictitious domain(DLM/FD)-mixed finite element method is developed and analyzed in this paper for a transient Stokes interface problem with jump *** semi-and fully discrete DLM/FD-mixed finite element scheme are developed for the first time for this problem with a moving interface,where the arbitrary Lagrangian-Eulerian(ALE)technique is employed to deal with the moving and immersed *** and optimal convergence properties are obtained for both *** experiments are carried out for different scenarios of jump coefficients,and all theoretical results are validated.

关键词： Transient Stokes interface problem jump coefficients distributed Lagrange multiplier fictitious domain method mixed finite element an optimal error estimate stability

Nested Group Testing Procedure

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Communications in Mathematics and Statistics 2023年第4期11卷 663-693页

作者： Wenjun Xiong Juan Ding Wei Zhang Aiyi Liu Qizhai Li School of Mathematics and Statistics Guangxi Normal UniversityGuilin 541004People’s Republic of China Department of Information and Computing Science College of SciencesHohai UniversityNanjing 210098People’s Republic of China LSC NCMISAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190People’s Republic of China Biostatisics and Bioinformatics Branch Eunice Kennedy Shriver National Institute of Child HealthBethesda 20817USA University of Chinese Academy of Sciences Beijing 100049People’s Republic of China

We investigated the false-negative,true-negative,false-positive,and true-positive predictive values from a general group testing procedure for a heterogeneous *** show that its false(true)-negative predictive value of a specimen is larger(smaller),and the false(true)-positive predictive value is smaller(larger)than that from individual testing procedure,where the former is in *** we propose a nested group testing procedure,and show that it can keep the sterling characteristics and also improve the false-negative predictive values for a specimen,not larger than that from individual *** characteristics are studied from both theoretical and numerical points of *** nested group testing procedure is better than individual testing on both false-positive and false-negative predictive values,while retains the efficiency as a basic characteristic of a group testing *** to Dorfman’s,Halving and Sterrett procedures are *** from extensive simulation studies and an application to malaria infection in microscopy-negative Malawian women exemplify the findings.

关键词： Group testing Negative predictive value Positive predictive value Retest

OPTIMAL QUADRATIC NITSCHE EXTENDED FINITE ELEMENT METHOD FOR INTERFACE PROBLEM OF DIFFUSION EQUATION

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Journal of Computational Mathematics 2018年第5期36卷 693-717页

作者： Fei Wang Shuo Zhang School of Mathematics and Statistics Xi'an Jiaotong University Xi'an 710049 China Department of Mathematics Pennsylvania State University University Park PA 16802 USA. LSEC ICMSEC NCMIS Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100190 China.

In this paper, we study Nitsche extended finite element method （XFEM） for the inter- face problem of a two dimensional diffusion equation. Specifically, we study the quadratic XFEM scheme on some shape-regular family of grids and prove the optimal convergence rate of the scheme with respect to the mesh size. Main efforts are devoted onto classifying the cases of intersection between the elements and the interface and prove a weighted trace inequality for the extended finite element functions needed, and the general framework of analysing XFEM c^n be implemented then.

关键词： Interface problems Extended finite element methods Error estimates Nitsche's scheme Quadratic element.

AN ADAPTIVE FAST INTERFACE TRACKING METHOD

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Journal of Computational Mathematics 2015年第6期33卷 576-586页

作者： Yana Di Jelena Popovic Olof Runborg LSEC NCMIS Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Department of Numerical Analysis CSC KTH 100 44 Stockholm Sweden Department of Mathematics and Swedish e-Science Research Center (SeRC) KTH 100 44 Stockholm Sweden

An adaptive numerical scheme is developed for the propagation of an interface in a velocity field based on the fast interface tracking method proposed in [2]. A multiresolution stategy to represent the interface instead of point values, allows local grid refinement while controlling the approximation error on the interface. For time integration, we use an explicit Runge-Kutta scheme of second-order with a multiseale time step, which takes longer time steps for finer spatial scales. The implementation of the algorithm uses a dynamic tree data structure to represent data in the computer memory. We briefly review first the main algorithm, describe the essential data structures, highlight the adaptive scheme, and illustrate the computational efficiency by some numerical examples.

关键词： Interface tracking Multiresolution adaptivity Fast algorithms.

A single-nucleus transcriptomic atlas of the dog hippocampus reveals the potential relationship between specific cell types and domestication

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National Science Review 2022年第11期9卷 108-120页

作者： Qi-Jun Zhou Xingyan Liu Longlong Zhang Rong Wang Tingting Yin Xiaolu Li Guimei Li Yuqi He Zhaoli Ding Pengcheng Ma Shi-Zhi Wang Bingyu Mao Shihua Zhang Guo-Dong Wang State Key Laboratory of Genetic Resources and Evolution Kunming Institute of ZoologyChinese Academy of Sciences ncmis CEMS RCSDSAcademy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences Kunming College of Life Science University of Chinese Academy of Sciences College of Life Science University of Chinese Academy of Sciences Genomic Center of Biodiversity Kunming Institute of ZoologyChinese Academy of Sciences Center for Excellence in Animal Evolution and Genetics Chinese Academy of Sciences Key Laboratory of Systems Health Science of Zhejiang Province School of Life ScienceHangzhou Institute for Advanced StudyUniversity of Chinese Academy of Sciences

The process of domestication has led to dramatic differences in behavioral traits between domestic dogs and gray wolves. Whole-genome research found that a class of putative positively selected genes were related to various aspects of learning and memory, such as long-term potentiation and long-term depression. In this study, we constructed a single-nucleus transcriptomic atlas of the dog hippocampus to illustrate its cell types, cell lineage and molecular features. Using the transcriptomes of 105 057 nuclei from the hippocampus of a Beagle dog, we identified 26 cell clusters and a putative trajectory of oligodendrocyte *** analysis revealed a significant convergence between dog differentially expressed genes(DEGs) and putative positively selected genes(PSGs). Forty putative PSGs were DEGs in glutamatergic neurons, especially in Cluster 14, which is related to the regulation of nervous system development. In summary, this study provides a blueprint to understand the cellular mechanism of dog domestication.

关键词： dog single-nucleus RNA sequencing hippocampus domestication

A CASCADIC MULTIGRID METHOD FOR EIGENVALUE PROBLEM

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Journal of Computational Mathematics 2017年第1期35卷 74-90页

作者： Xiaole Han Hehu Xie Fei Xu IAPCM Institute of Applied Physics and Computational Mathematics Beijing 100093 China LSEC NCMIS Institute of Computational Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China Beijing Institute for Scientific and Engineering Computing Beijing University of Technology Beijing 100124 China

A cascadic multigrid method is proposed for eigenvalue problems based on the multilevel correction scheme. With this new scheme, an eigenvalue problem on the finest space can be solved by linear smoothing steps on a series of multilevel finite element spaces and nonlinear correcting steps on special coarsest spaces. Once the sequence of finite element spaces and the number of smoothing steps are appropriately chosen, the optimal convergence rate with the optimal computational work can be obtained. Some numerical experiments are presented to validate our theoretical analysis.

关键词： Eigenvalue problem Cascadic multigrid Multilevel correction scheme Finiteelement method.

Frontiers in biomolecular mesh generation and molecular visualization systems

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Visual Computing for Industry,Biomedicine,and Art 2018年第1期1卷 69-81页

作者： Sheng Gui Dawar Khan Qin Wang Dong-Ming Yan Ben-Zhuo Lu LSEC NCMISAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China National Laboratory of Pattern Recognition Institute of AutomationChinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100049China

With the development of biomolecular modeling and simulation,especially implicit solvent modeling,higher requirements are set for the stability,efficiency and mesh quality of molecular mesh generation *** this review,we summarize the recent works in biomolecular mesh generation and molecular ***,we introduce various definitions of molecular surface and corresponding meshing ***,as the mesh quality significantly influences biomolecular simulation,we investigate some remeshing methods in the fields of computer graphics and molecular ***,we show the application of biomolecular mesh in the boundary element method(BEM)and the finite element method(FEM).Finally,to conveniently visualize the numerical results based on the mesh,we present two types of molecular visualization systems.

关键词： Biomolecular mesh generation Remeshing BEM FEM Molecular visualization