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Error analysis of SAV finite element method to phase field crystal model

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arXiv 2019年

作者： Wang, Liupeng Huang, Yunqing Jiang, Kai School of Mathematics and Computational Science Xiangtan University Xiangtan Hunan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan Hunan411105 China Key Laboratory of Ministry of Education for Intelligent Computing and Information Processing Xiangtan University Xiangtan Hunan411105 China

In this paper, we construct and analyze an energy stable scheme by combining the latest developed scalar auxiliary variable (SAV) approach and linear finite element method (FEM) for phase field crystal (PFC) model, and show rigorously that the scheme is first-order in time and second-order in space for the L2and H1 gradient ow equations. To reduce eficiently computational cost and capture accurately the phase interface, we give a simple adaptive strategy, equipped with a posteriori gradient estimator, i.e. L2norm of the recovered gradient. Extensive numerical experiments are presented to verify our theoretical results and to demonstrate the efiectiveness and accuracy of our proposed method. Copyright © 2019, The Authors. All rights reserved.

关键词： Finite element method

Error Estimates for the Iterative Discontinuous Galerkin Method to the Nonlinear Poisson-Boltzmann Equation

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Communications in computational Physics 2018年第1期23卷 168-197页

作者： Peimeng Yin Yunqing Huang Hailiang Liu Mathematics Department Iowa State UniversityAmesIA 50011USA Key Laboratory of Intelligent Computing&Information Processing of Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and EngineeringSchool of Mathematics and Computational ScienceXiangtan UniversityXiangtan411105P.R.China

This paper is devoted to the error estimate for the iterative discontinuous Galerkin(IDG)method introduced in[***,*** and ***.16:491-515,2014]to the nonlinear Poisson-Boltzmann *** total error includes both the iteration error and the discretization error of the direct DG method to linear elliptic *** the DDG method,the energy error is obtained by a constructive approach through an explicit global projection satisfying interface conditions dictated by the choice of numerical *** L^(2) error of order O(h^(m+1))for polynomials of degree m is further *** bounding constant is also shown to be independent of the iteration *** tests are given to validate the established convergence theory.

关键词： Poisson-Boltzmann equation DG methods global projection energy error estimates L^(2)error estimates

Jacobi Spectral Collocation Method Based on Lagrange Interpolation Polynomials for Solving Nonlinear Fractional Integro-Differential Equations

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Advances in Applied Mathematics and Mechanics 2018年第6期10卷 1440-1458页

作者： Xingfa Yang Yin Yang Yanping Chen Jie Liu State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body Hunan UniversityChangsha 410082HunanChina Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationSchool of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105HunanChina School of Mathematical Sciences South China Normal UniversityGuangzhou 510631GuangdongChina Center for Research on Leading Technology of Special Equipment School of Mechanical and Electric EngineeringGuangzhou UniversityGuangzhou 510006GuangdongChina

In this paper,we study a class of nonlinear fractional integro-differential equations,the fractional derivative is described in the Caputo *** the properties of the Caputo derivative,we convert the fractional integro-differential equations into equivalent integral-differential equations of Volterra type with singular kernel,then we propose and analyze a spectral Jacobi-collocation approximation for nonlinear integro-differential equations of Volterra *** provide a rigorous error analysis for the spectral methods,which shows that both the errors of approximate solutions and the errors of approximate fractional derivatives of the solutions decay exponentially in L^(∞)-norm and weighted L^(2)-norm.

关键词： Spectral method nonlinear fractional derivative Volterra integro-differential equations Caputo derivative

Mesh Quality and More Detailed Error Estimates of Finite Element Method

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高等学校计算数学学报（英文版） 2017年第2期10卷 420-436页

作者： Yunqing Huang Liupeng Wang Nianyu Yi Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan Hunan 411105 China

In this paper,we study the role of mesh quality on the accuracy of linear finite element *** derive a more detailed error estimate,which shows explicitly how the shape and size of elements,and symmetry structure of mesh effect on the error of numerical *** computable parameters Ge and Gv are given to depict the cell geometry property and symmetry structure of the *** compare with the standard a priori error estimates,which only yield information on the asymptotic error behaviour in a global sense,our proposed error estimate considers the effect of local element geometry properties,and is thus more *** certain conditions,the traditional error estimates and supercovergence results can be derived from the proposed error ***,the estimators Ge and Gv are computable and thus can be used for predicting the variation of *** tests are presented to illustrate the performance of the proposed parameters Ge and Gv.

关键词： Finite element methods error estimation cell geometry mesh quality

The ecotoxicological effects of thiamethoxam on photosynthesis and nitrogen fixation in cyanobacteria: From inhibition to recovery

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Journal of Environmental sciences 2025年

作者： Jiale Zhang Shiye Zhu Xiyan Xu Youzheng Chai Jihai Shao Gen Lu Jianhua Zeng Ma Bai Anwei Chen College of Environment and Ecology Hunan Agricultural University Changsha 410128 China School of Chemistry and Chemical Engineering Beijing Institute of Technology Beijing 100081 China Center for Water and Ecology State Key Joint Laboratory of Environment Simulation and Pollution Control School of Environment Tsinghua University Beijing 100084 China Institute of Resource Biology and Biotechnology Department of Biotechnology College of Life Science and Technology Huazhong University of Science and Technology Wuhan 430074 China School of Food Engineering Anhui Science and Technology University Fengyang AnHui 233100 China College of Chemistry & Pharmacy Northwest A&F University Yangling Shaanxi 712100 China

Thiamethoxam (THX) is a highly efficacious, broad-spectrum neonicotinoid insecticide that is prevalently detected in contemporary environmental settings. Although considerable research has been conducted on the adverse effects of THX on non-target organisms, there is a paucity of knowledge regarding its impact on nitrogen (N)-fixing cyanobacteria, which play a crucial role in the N-cycle. This study examined the impact of the neonicotinoid pesticide THX on N-fixing cyanobacteria Nostoc sp. PCC7120. It combined biochemical and molecular data to clarify the toxicity and recovery mechanism of Nostoc sp. PCC7120 exposed to THX. The results show that at low THX concentrations, cyanobacteria exhibited hormetic responses and then enter recovery phases, whereas at high concentrations, they showed toxicity phases before entering recovery phases. The main changes were in cell growth, antioxidant system, photosynthetic performance and N-fixation. The starch granules and vacuoles of Nostoc sp. PCC7120 became larger after THX treatment, indicating a shift in resources from growth to storage. Additionally, molecular stimulations indicated that THX could bind to molybdenum-iron cofactor sites of nitrogenase to destroy N-fixation, and also bind to Q A and Q B sites of photosynthetic proteins (D1 and D2) to affect photosynthesis. These findings provide a valuable reference for the ecological risks of THX and biogeochemical N-cycle.

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A multigrid-reduction-in-time solver with a new two-level convergence for unsteady fractional Laplacian problems

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arXiv 2019年

作者： Yue, Xiaoqiang Pan, Kejia Zhou, Jie Weng, Zhifeng Shu, Shi Tang, Juan Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China School of Mathematics and Statistics HNP-LAMA Central South University Changsha410083 China School of Mathematical Sciences Fujian Province University Key Laboratory of Computation Science Huaqiao University Quanzhou362021 China

The multigrid-reduction-in-time (MGRIT) technique has proven to be successful in achieving higher run-time speedup by exploiting parallelism in time. The goal of this article is to develop and analyze a MGRIT algorithm, using FCF-relaxation with time-dependent time-grid propagators, to seek the finite element approximations of unsteady fractional Laplacian problems. The multigrid with line smoother proposed in [L. Chen, R. H. Nochetto, et al., Math. Comp. 85 (2016) 2583–2607] is chosen to be the spatial solver. Motivated by [B. S. Southworth, SIAM J. Matrix Anal. Appl. 40 (2019) 564–608], we provide a new temporal eigenvalue approximation property and then deduce a generalized two-level convergence theory which removes the previous unitary diagonalization assumption on the fine and coarse time-grid propagators required in [X. Q. Yue, S. Shu, et al., Comput. Math. Appl. 78 (2019) 3471–3484]. Numerical computations are included to confirm the theoretical predictions and demonstrate the sharpness of the derived convergence upper bound. Copyright © 2019, The Authors. All rights reserved.

关键词： Finite element method

Adaptive-multilevel BDDC algorithm for three-dimensional plane wave Helmholtz systems

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arXiv 2019年

作者： Peng, Jie Shu, Shi Wang, Junxian Zhong, Liuqiang School of Mathematical Sciences South China Normal University Guangzhou510631 China School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China

In this paper we are concerned with the weighted plane wave least-squares (PWLS) method for three-dimensional Helmholtz equations, and develop the multi-level adaptive BDDC algorithms for solving the resulting discrete system. In order to form the adaptive coarse components, the local generalized eigenvalue problems for each common face and each common edge are carefully designed. The condition number of the two-level adaptive BDDC preconditioned system is proved to be bounded above by a user-defined tolerance and a constant that is only dependent on the maximum number of faces and edges per subdomain and the number of subdomains sharing a common edge. The effectiveness of these algorithms is illustrated on benchmark problem. The numerical results show the robustness of our two-level adaptive BDDC algorithms with respect to the wave number, the number of subdomains and the mesh size, and appear that our multi-level adaptive BDDC algorithm can reduce the number of dofs at the coarse problem and can be used to solving large wave number problems efficiently. Copyright © 2019, The Authors. All rights reserved.

关键词： Elastic waves

SATURATION AND RELIABLE HIERARCHICAL A POSTERIORI MORLEY FINITE ELEMENT ERROR CONTROL

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Journal of computational Mathematics 2018年第6期36卷 833-844页

作者： Carsten Carstensen Dietmar Gallistl Yunqing Huang Humboldt-Universitat zu Berlin Institut fiir Mathematik Unter den Linden 6 10099 Berlin Germany Department of Applied Mathematics University of Twente P.O. Box 217 7500 AE Enschede Institute for Computational and Applied Mathematics and Hunan Key Laboratory for Computation & Simulation in Science & Engineering Xiangtan University Xiangtan 411105 China

This paper proves the saturation assumption for the nonconforming Morley finite ele- ment discretization of the biharmonic equation. This asserts that the error of the Morley approximation under uniform refinement is strictly reduced by a contraction factor smaller than one up to explicit higher-order data approximation terms. The refinement has at least to bisect any edge such as red refinement or 3-bisections on any triangle. This justifies a hierarchical error estimator for the Morley finite element method, which simply compares the discrete solutions of one mesh and its red-refinement. The related adaptive mesh-refining strategy performs optimally in numerical experiments. A remark for Crouzeix-Raviart nonconforming finite element error control is included.

关键词： Saturation Hierarchical error estimation Finite element Nonconforming Biharmonie Morley Kirchhoff plate Crouzeix-Raviart

DeePMD-kit v2: A software package for Deep Potential models

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arXiv 2023年

作者： Zeng, Jinzhe Zhang, Duo Lu, Denghui Mo, Pinghui Li, Zeyu Chen, Yixiao Rynik, Marián Huang, Li'ang Li, Ziyao Shi, Shaochen Wang, Yingze Ye, Haotian Tuo, Ping Yang, Jiabin Ding, Ye Li, Yifan Tisi, Davide Zeng, Qiyu Bao, Han Xia, Yu Huang, Jiameng Muraoka, Koki Wang, Yibo Chang, Junhan Yuan, Fengbo Bore, Sigbjørn Løland Cai, Chun Lin, Yinnian Wang, Bo Xu, Jiayan Zhu, Jia-Xin Luo, Chenxing Zhang, Yuzhi Goodall, Rhys E.A. Liang, Wenshuo Singh, Anurag Kumar Yao, Sikai Zhang, Jingchao Wentzcovitch, Renata Han, Jiequn Liu, Jie Jia, Weile York, Darrin M. Weinan, E. Car, Roberto Zhang, Linfeng Wang, Han Laboratory for Biomolecular Simulation Research Institute for Quantitative Biomedicine Department of Chemistry and Chemical Biology Rutgers University PiscatawayNJ08854 United States AI for Science Institute Beijing100080 China DP Technology Beijing100080 China Academy for Advanced Interdisciplinary Studies Peking University Beijing100871 China HEDPS CAPT College of Engineering Peking University Beijing100871 China College of Electrical and Information Engineering Hunan University Changsha China Yuanpei College Peking University Beijing100871 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States Department of Experimental Physics Comenius University Mlynská Dolina F2 Bratislava842 48 Slovakia Center for Quantum Information Institute for Interdisciplinary Information Sciences Tsinghua University Beijing100084 China Center for Data Science Peking University Beijing100871 China ByteDance Research Zhonghang Plaza No. 43 North 3rd Ring West Road Haidian District Beijing China College of Chemistry and Molecular Engineering Peking University Beijing100871 China Baidu Inc. Beijing China Key Laboratory of Structural Biology of Zhejiang Province School of Life Sciences Westlake University Zhejiang Hangzhou China Westlake AI Therapeutics Lab Westlake Laboratory of Life Sciences and Biomedicine Zhejiang Hangzhou China Department of Chemistry Princeton University PrincetonNJ08544 United States SISSA Scuola Internazionale Superiore di Studi Avanzati Trieste34136 Italy Laboratory of Computational Science and Modeling Institute of Materials École Polytechnique Fédérale de Lausanne Lausanne1015 Switzerland Department of Physics National University of Defense Technology Hunan Changsha410073 China State Key Lab of Processors Institute of Computing Technology Chinese Academy of Sciences Beijing China University of Chinese Academy of Sciences Beijing China School of Electronics Engineerin

DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials (MLP) known as Deep Potential (DP) models. This package, which was released in 2017, has been widely used in the fields of physics, chemistry, biology, and material science for studying atomistic systems. The current version of DeePMD-kit offers numerous advanced features such as DeepPot-SE, attention-based and hybrid descriptors, the ability to fit tensile properties, type embedding, model deviation, Deep Potential - Range Correction (DPRc), Deep Potential Long Range (DPLR), GPU support for customized operators, model compression, non-von Neumann molecular dynamics (NVNMD), and improved usability, including documentation, compiled binary packages, graphical user interfaces (GUI), and application programming interfaces (API). This article presents an overview of the current major version of the DeePMD-kit package, highlighting its features and technical details. Additionally, the article benchmarks the accuracy and efficiency of different models and discusses ongoing developments. © 2023, CC BY-NC-ND.

关键词： Molecular dynamics