检索结果-内蒙古大学图书馆

SSRN 2023年

作者： Huang, Qian-Min Ren, Yu-Xin Wang, Qian Department of Engineering Mechanics Tsinghua University Beijing100084 China CAEP Software Center for High Performance Numerical Simulation Beijing100088 China Institute of Applied Physics and Computational Mathematics Beijing100088 China Beijing Computational Science Research Center Beijing100193 China

This paper presents a general positivity-preserving algorithm for implicit high-order finite volume schemes solving Euler and Navier-Stokes equations. Previous positivity-preserving algorithms are mainly based on mathematical analyses, being highly dependent on the existence of low-order positivity-preserving numerical schemes for specific governing equations. This dependency poses serious restrictions on extending these algorithms to temporally implicit schemes, since it is difficult to know if a low-order implicit scheme is positivity-preserving. The present positivity-preserving algorithm is based on an asymptotic analysis of the solutions near local vacuum minimum points. The asymptotic analysis shows that the solutions decay exponentially with time to maintain non-negative density and pressure at a local vacuum minimum point. In its neighborhood, the exponential evolution leads to a modification of the linear evolution process, which can be modelled by a direct correction of the linear residual to ensure positivity. This correction however destroys the conservation of the numerical scheme. Therefore, a second correction procedure is proposed to recover conservation. The proposed positivity-preserving algorithm is considerably less restrictive than existing algorithms. It does not rely on the existence of low-order positivity-preserving baseline schemes and the convex decomposition of volume integrals of flow quantities. It does not need to reduce the time step size for maintaining the stability either. Furthermore, it can be implemented iteratively in the implicit dual time-stepping schemes to preserve positivity of the intermediate and converged states of the sub-iterations. It is proved that the present positivity-preserving algorithm is accuracy-preserving. numerical results demonstrate that the proposed algorithm preserve the positive density and pressure in all test cases, and considerably improve the robustness of the numerical schemes. © 2023, The Author

关键词： Finite volume method

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A Viscous-Term Subcell Limiting Approach for High-Order Fr/Cpr Method in Solving Compressible Navier-Stokes Equations on Curvilinear Grids

SSRN

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SSRN 2023年

作者： Zhu, Huajun Yan, Zhen-Guo Liu, Huayong Mao, Meiliang Deng, Xiaogang State Key Laboratory of Aerodynamics China Aerodynamics Research and Development Center Sichuan Mianyang621000 China Tianfu Engineering-Oriented Numerical Simulation & Software Innovation Center Sichuan University Sichuan Chengdu610000 China Chinese Academy of Military Science Beijing100071 China

High-order flux reconstruction/correction procedure via reconstruction (FR/CPR) method has become an attractive method for simulating multi-scale flows because of their high accuracy and low dissipation. However, simulating flows with strong shocks is still challenging for FR/CPR. Recently, a priori subcell limiting based on compact nonlinear nonuniform weighted (CNNW) schemes was proposed for the CPR method to solve the Euler equations, which robustly simulates strong shocks and has good balance between high resolution and shock capturing robustness. The CPR method with subcell CNNW limiting is a hybrid scheme and also called hybrid CPR-CNNW scheme (abbr. HCCS). This paper extends HCCS to solve compressible Navier-Stokes equations on curvilinear grids. To improve the capability of HCCS in simulating hypersonic flows, a viscous-term subcell limiting (VSL) approach is proposed. The main idea of the VSL is to replace the unified high-order polynomial distribution by limited piecewise polynomial distribution in troubled cells for the viscous-term discretization, which is implemented by decomposing the troubled cells into subcells and limiting the distribution of physical variables for each subcells. In this paper, the VSL reuses the limited results of subcell CNNW schemes used in the inviscid-term discretization, which makes the approach efficient. It is shown that HCCS without the VSL blows up during simulating hypersonic flows. Then, HCCS with the VSL is extended to curvilinear grids. Discrete grid metrics and discrete Jacobian are designed to make HCCS with the VSL satisfy discrete conservation laws, discrete geometric conservation laws and fulfilling free-stream preservation, which are validated by two test cases on curvilinear grids. numerical results on several typical cases show that HCCS with the VSL has superiority in high resolution, shock capturing robustness, and accurate prediction of surface pressure, skin friction and heat transfer. © 2023, The Authors.

关键词： Navier Stokes equations

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A general positivity-preserving algorithm for implicit high-order finite volume schemes solving the Euler and Navier-Stokes equations

arXiv

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arXiv 2023年

关键词： Finite volume method

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Localization in the Incommensurate Systems: A Plane Wave Study via Effective Potentials

arXiv

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arXiv 2023年

作者： Wang, Ting Zhou, Yuzhi Zhou, Aihui LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China CAEP Software Center for High Performance Numerical Simulation Beijing100088 China Institute of Applied Physics and Computational Mathematics Beijing100094 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In this paper, we apply the effective potentials in the localization landscape theory (Filoche et al., 2012, Arnold et al., 2016) to study the spectral properties of the incommensurate systems. We uniquely develop a plane wave method for the effective potentials of the incommensurate systems and utilize that, the localization of the electron density can be inferred from the effective potentials. Moreover, we show that the spectrum distribution can also be obtained from the effective potential version of Weyl’s law. We perform some numerical experiments on some typical incommensurate systems, showing that the effective potential provides an alternative tool for investigating the localization and spectrum distribution of the systems. Copyright © 2023, The Authors. All rights reserved.

关键词： Elastic waves

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An extended plane wave framework for the electronic structure calculations of twisted bilayer material systems

arXiv

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arXiv 2023年

作者： Dai, Xiaoying Zhou, Aihui Zhou, Yuzhi LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China CAEP Software Center for High Performance Numerical Simulation Beijing100088 China Institute of Applied Physics and Computational Mathematics Beijing100088 China

In this paper, we propose an extended plane wave framework to make the electronic structure calculations of the twisted bilayer 2D material systems practically feasible. Based on the foundation in [Y. Zhou, H. Chen, A. Zhou, J. Comput. Phys. 384, 99 (2019)], following extensions take place: (1) an tensor-producted basis set, which adopts PWs in the incommensurate dimensions, and localized basis in the interlayer dimension, (2) a practical application of a novel cutoff techniques we have recently developed, and (3) a quasi-band structure picture under the small twisted angles and weak interlayer coupling limits. With (1) and (2) now the dimensions of Hamiltonian matrix are reduced by about 2 orders of magnitude compared with the original framework. And (3) enables us to better organize the calculations and understand the results. For numerical examples, we study the electronic structures of the linear bilayer graphene lattice system with the magic twisted angle (∼ 1.05◦). The famous flat bands have been reproduced with their features in quantitative agreement with those from experiments and other theoretical calculations. Moreover, the extended framework has much less computational cost compared to the commensurate cell approximations, and is more extendable compared to the traditional model hamiltonians and tight binding models. Finally this framework can readily accommodate nonlinear models thus will laid the foundations for more effective yet accurate Density Functional Theory (DFT) calculations. © 2023, CC BY.

关键词： Electronic structure

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Well-posedness analysis of the Cahn-Hilliard-Biot model

arXiv

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arXiv 2023年

作者： Riethmüller, Cedric Storvik, Erlend Both, Jakub Wiktor Radu, Florin Adrian Institute of Applied Analysis and Numerical Simulation University of Stuttgart Germany Department of Computer Science Electrical Engineering and Mathematical Sciences Western Norway University of Applied Sciences Norway Center for Modeling of Coupled Subsurface Dynamics Department of Mathematics University of Bergen Norway

We investigate the well-posedness of the recently proposed Cahn-Hilliard-Biot model. The model is a three-way coupled PDE of elliptic-parabolic nature, with several nonlinearities and the fourth order term known to the Cahn-Hilliard system. We show existence of weak solutions to the variational form of the equations and uniqueness under certain conditions of the material parameters and secondary consolidation, adding regularizing effects. Existence is shown by discretizing in space and applying ODE-theory (the Peano-Cauchy theorem) to prove existence of the discrete system, followed by compactness arguments to retain solutions of the continuous system. In addition, the continuous dependence of solutions on the data is established, in particular implying uniqueness. Both results build strongly on the inherent gradient flow structure of the model. Copyright © 2023, The Authors. All rights reserved.

关键词： Variational techniques

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Force-based gradient descent method for ab initio atomic structure relaxation

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Physical Review B 2022年第10期106卷 104101-104101页

作者： Yukuan Hu Xingyu Gao Yafan Zhao Xin Liu Haifeng Song State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China University of Chinese Academy of Sciences Beijing 100049 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing 100088 China CAEP Software Center for High Performance Numerical Simulation Beijing 100088 China

Force-based algorithms for ab initio atomic structure relaxation, such as conjugate gradient methods, usually get stuck in the line minimization processes along search directions, where expensive ab initio calculations are triggered frequently to test trial positions before locating the next iterate. We present a force-based gradient descent method, WANBB, that circumvents the deficiency. At each iteration, WANBB enters the line minimization process with a trial step size capturing the local curvature of the energy surface. The exit is controlled by a nonrestrictive criterion that tends to accept early trials. These two ingredients streamline the line minimization process in WANBB. The numerical simulations on nearly 80 systems with good universality demonstrate the considerable compression of WANBB on the cost for the unaccepted trials compared with conjugate gradient methods. We also observe across the board significant and universal speedups as well as the superior robustness of WANBB over several widely used methods. The latter point is theoretically established. The implementation of WANBB is pretty simple, in that no a priori physical knowledge is required and only three parameters are present without tuning.

关键词： Crystal structure Structural properties Density functional theory development

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Self-Supervised Entity Alignment Based on Multi-Modal Contrastive Learning

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IEEE/CAA Journal of Automatica Sinica 2022年第11期9卷 2031-2033页

作者： Bo Liu Ruoyi Song Yuejia Xiang Junbo Du Weijian Ruan Jinhui Hu the School of Software Engineering Xi’an Jiaotong UniversityXi’an 710000 the China Electronics Technology Group Corporation(CETC)Key Laboratory of Smart City Model Simulation and Intelligent Technology the Smart City Research Institute of CETC and National Center for Applied Mathematics Shenzhen(NCAMS)Shenzhen 518000China the Chinese University of Hong Kong Shenzhen 518000China Tencent Shenzhen 518000China the CETC Key Laboratory of Smart City Model Simulation and Intelligent Technology the Smart City Research Institute of CETC and National Center for Applied Mathematics Shenzhen(NCAMS)Shenzhen 518000China the Shenzhen Institute of Advanced Technology Chinese Academy of SciencesShenzhen 518055

Dear Editor,This letter proposes an unsupervised entity alignment method,which realizes integration of multiple multi-modal knowledge graphs *** recent years,Large-scale multi-modal knowledge graphs(LMKGs),containing text and image,have been widely applied in numerous knowledge-driven topics,such as question answering,entity linking,information extraction,reasoning and recommendation.

关键词： modal linking letter

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Performance assessment of the effective core potentials under the Fermionic neural network: first and second row elements

arXiv

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arXiv 2024年

作者： Wang, Mengsa Zhou, Yuzhi Wang, Han Graduate School of China Academy of Engineering Physics Beijing100088 China National Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China CAEP Software Center for High Performance Numerical Simulation Beijing100088 China Institute of Applied Physics and Computational Mathematics Beijing100088 China HEDPS CAPT College of Engineering Peking University Beijing China

The rapid development of deep learning techniques has driven the emergence of a neural network-based variational Monte Carlo method (referred to as FermiNet), which has manifested high accuracy and strong predictive power in the electronic structure calculations of atoms, molecules as well as some periodic systems. Recently, the implementation of the effective core potential (ECP) scheme in it further facilitates more efficient calculations in practice. But there still lack comprehensive assessments on the ECP’s performance under the FermiNet. In this work, we set sail to fill this gap by conducting extensive tests on the first two row elements regarding their atomic spectral and molecular properties. Our major finding is that in general the qualities of ECPs have been correctly reflected under the FermiNet. Two recently built ECP tables, namely ccECP and eCEPP, seem to prevail on the overall performance. Specifically, ccECP performs slightly better on the spectral precision and covers more elements, while eCEPP is more systematically built from both shape and energy consistency, and better treats the core polarisation. On the other hand, the high accuracy of the all-electron calculations is hindered by the absence of relativistic effects as well as the numerical instabilities in some heavier elements. Finally, with further in-depth discussions, we generate possible directions for developing and improving the FermiNet in the near future. Copyright © 2024, The Authors. All rights reserved.

关键词： Deep learning

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A physics-driven sensor placement optimization methodology for temperature field reconstruction

arXiv

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arXiv 2024年

作者： Liu, Xu Yao, Wen Peng, Wei Fu, Zhuojia Xiang, Zixue Chen, Xiaoqian Defense Innovation Institute Academy of Military Science Beijing100071 China Intelligent Game and Decision Laboratory Academy of Military Science Beijing100071 China College of Aerospace Science and Engineering National University of Defense Technology Changsha410073 China Laboratory of Ministry of Education for Coastal Disaster and Protection Hohai University Nanjing210098 China Center for Numerical Simulation Software in Engineering and Sciences College of Mechanics and Materials Hohai University Nanjing211100 China

Perceiving the global field from sparse sensors has been a grand challenge in the monitoring, analysis, and design of physical systems. In this context, sensor placement optimization is a crucial issue. Most existing works require large and sufficient data to construct data-based criteria, which are intractable in data-free scenarios without numerical and experimental data. To this end, we propose a novel physics-driven sensor placement optimization (PSPO) method for temperature field reconstruction using a physics-based criterion to optimize sensor locations. In our methodological framework, we firstly derive the theoretical upper and lower bounds of the reconstruction error under noise scenarios by analyzing the optimal solution, proving that error bounds correlate with the condition number determined by sensor locations. Furthermore, the condition number, as the physics-based criterion, is used to optimize sensor locations by the genetic algorithm. Finally, the best sensors are validated by reconstruction models, including non-invasive end-to-end models, noninvasive reduced-order models, and physics-informed models. Experimental results, both on a numerical and an application case, demonstrate that the PSPO method significantly outperforms random and uniform selection methods, improving the reconstruction accuracy by nearly an order of magnitude. Moreover, the PSPO method can achieve comparable reconstruction accuracy to the existing data-driven placement optimization methods. © 2024, CC BY.

关键词： Genetic algorithms

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