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Anisotropic adaptive finite element method for magnetohydrodynamic flow at high Hartmann numbers

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Applied Mathematics and Mechanics(English Edition) 2016年第11期37卷 1479-1500页

作者： Jikun ZHAO Shipeng MAO Weiying ZHENG School of Mathematics and Statistics Zhengzhou University State Key Laboratory of Scientific and Engineering Computing (LSEC) and Institute of Computational Mathematics Academy of Mathematics and Systems Science (AMSS) Chinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences

This paper presents an anisotropic adaptive finite element method （FEM） to solve the governing equations of steady magnetohydrodynamic （MHD） duct flow. A resid- ual error estimator is presented for the standard FEM, and two-sided bounds on the error independent of the aspect ratio of meshes are provided. Based on the Zienkiewicz-Zhu es- timates, a computable anisotropic error indicator and an implement anisotropic adaptive refinement for the MHD problem are derived at different values of the Hartmann number. The most distinguishing feature of the method is that the layer information from some directions is captured well such that the number of mesh vertices is dramatically reduced for a given level of accuracy. Thus, this approach is more suitable for approximating the layer problem at high Hartmann numbers. Numerical results show efficiency of the algorithm.

关键词： magnetohydrodynamic （MHD） flow posteriori error estimate anisotropicadaptive finite element method （FEM）

Author Correction: Federated learning enables big data for rare cancer boundary detection

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Nature communications 2023年第1期14卷 436页

作者： Sarthak Pati Ujjwal Baid Brandon Edwards Micah Sheller Shih-Han Wang G Anthony Reina Patrick Foley Alexey Gruzdev Deepthi Karkada Christos Davatzikos Chiharu Sako Satyam Ghodasara Michel Bilello Suyash Mohan Philipp Vollmuth Gianluca Brugnara Chandrakanth J Preetha Felix Sahm Klaus Maier-Hein Maximilian Zenk Martin Bendszus Wolfgang Wick Evan Calabrese Jeffrey Rudie Javier Villanueva-Meyer Soonmee Cha Madhura Ingalhalikar Manali Jadhav Umang Pandey Jitender Saini John Garrett Matthew Larson Robert Jeraj Stuart Currie Russell Frood Kavi Fatania Raymond Y Huang Ken Chang Carmen Balaña Jaume Capellades Josep Puig Johannes Trenkler Josef Pichler Georg Necker Andreas Haunschmidt Stephan Meckel Gaurav Shukla Spencer Liem Gregory S Alexander Joseph Lombardo Joshua D Palmer Adam E Flanders Adam P Dicker Haris I Sair Craig K Jones Archana Venkataraman Meirui Jiang Tiffany Y So Cheng Chen Pheng Ann Heng Qi Dou Michal Kozubek Filip Lux Jan Michálek Petr Matula Miloš Keřkovský Tereza Kopřivová Marek Dostál Václav Vybíhal Michael A Vogelbaum J Ross Mitchell Joaquim Farinhas Joseph A Maldjian Chandan Ganesh Bangalore Yogananda Marco C Pinho Divya Reddy James Holcomb Benjamin C Wagner Benjamin M Ellingson Timothy F Cloughesy Catalina Raymond Talia Oughourlian Akifumi Hagiwara Chencai Wang Minh-Son To Sargam Bhardwaj Chee Chong Marc Agzarian Alexandre Xavier Falcão Samuel B Martins Bernardo C A Teixeira Flávia Sprenger David Menotti Diego R Lucio Pamela LaMontagne Daniel Marcus Benedikt Wiestler Florian Kofler Ivan Ezhov Marie Metz Rajan Jain Matthew Lee Yvonne W Lui Richard McKinley Johannes Slotboom Piotr Radojewski Raphael Meier Roland Wiest Derrick Murcia Eric Fu Rourke Haas John Thompson David Ryan Ormond Chaitra Badve Andrew E Sloan Vachan Vadmal Kristin Waite Rivka R Colen Linmin Pei Murat Ak Ashok Srinivasan J Rajiv Bapuraj Arvind Rao Nicholas Wang Ota Yoshiaki Toshio Moritani Sevcan Turk Joonsang Lee Snehal Prabhudesai Fanny Morón Jacob Mandel Konstantinos Kamnitsas Ben Glocker Luke V M Dixon Matthew Williams Peter Zamp Center for Biomedical Image Computing and Analytics (CBICA) University of Pennsylvania Philadelphia PA USA. Department of Radiology Perelman School of Medicine University of Pennsylvania Philadelphia PA USA. Department of Pathology and Laboratory Medicine Perelman School of Medicine University of Pennsylvania Philadelphia PA USA. Department of Informatics Technical University of Munich Munich Bavaria Germany. Intel Corporation Santa Clara CA USA. Department of Neuroradiology Heidelberg University Hospital Heidelberg Germany. Clinical Cooperation Unit Neuropathology German Cancer Consortium (DKTK) within the German Cancer Research Center (DKFZ) Heidelberg Germany. Department of Neuropathology Heidelberg University Hospital Heidelberg Germany. Division of Medical Image Computing German Cancer Research Center Heidelberg Germany. Pattern Analysis and Learning Group Department of Radiation Oncology Heidelberg University Hospital Heidelberg Germany. Neurology Clinic Heidelberg University Hospital Heidelberg Germany. Department of Radiology & Biomedical Imaging University of California San Francisco San Francisco CA USA. Symbiosis Center for Medical Image Analysis Symbiosis International University Pune Maharashtra India. Department of Neuroimaging and Interventional Radiology National Institute of Mental Health and Neurosciences Bangalore Karnataka India. Department of Radiology School of Medicine and Public Health University of Wisconsin Madison WI USA. Department of Medical Physics School of Medicine and Public Health University of Wisconsin Madison WI USA. Leeds Teaching Hospitals Trust Department of Radiology Leeds UK. Department of Radiology Brigham and Women's Hospital Harvard Medical School Boston MA USA. Athinoula A. Martinos Center for Biomedical Imaging Massachusetts General Hospital Charlestown MA USA. Catalan Institute of Oncology Badalona Spain. Consorci MAR Parc de Salut de Barcelona Catalonia Spain. Department of Radiology (IDI

A note on semidefinite programming relaxations for polynomial optimization over a single sphere

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science China Mathematics 2016年第8期59卷 1543-1560页

作者： HU Jiang JIANG Bo LIU Xin WEN ZaiWen Beijing International Center for Mathematical Research Peking University Research Center for Management Science and Data Analytics School of Information Management and EngineeringShanghai University of Finance and Economics LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems Science Chinese Academy of Sciences

We study two instances of polynomial optimization problem over a single sphere. The first problem is to compute the best rank-1 tensor approximation. We show the equivalence between two recent semidefinite relaxations methods. The other one arises from Bose-Einstein condensates(BEC), whose objective function is a summation of a probably nonconvex quadratic function and a quartic term. These two polynomial optimization problems are closely connected since the BEC problem can be viewed as a structured fourth-order best rank-1 tensor approximation. We show that the BEC problem is NP-hard and propose a semidefinite relaxation with both deterministic and randomized rounding procedures. Explicit approximation ratios for these rounding procedures are presented. The performance of these semidefinite relaxations are illustrated on a few preliminary numerical experiments.

关键词： polynomial optimization over a single sphere semidefinite programming best rank-1 tensor ap-proximation Bose-Einstein condensates

Validating quantum-classical programming models with tensor network simulations

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arXiv 2018年

作者： McCaskey, Alexander Dumitrescu, Eugene Chen, Mengsu Lyakh, Dmitry Humble, Travis S. Quantum Computing Institute Oak Ridge National Laboratory Oak RidgeTN37831 United States Computer Science and Mathematics Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Computational Sciences and Engineering Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Department of Physics Virginia Tech BlacksburgVA24060 United States National Center for Computational Sciences Oak Ridge National Laboratory Oak RidgeTN37831 United States Bredesen Center for Interdisciplinary Research University of Tennessee KnoxvilleTN37996 United States

The exploration of hybrid quantum-classical algorithms and programming models on noisy near-term quantum hardware has begun. As hybrid programs scale towards classical intractability, validation and benchmarking are critical to understanding the utility of the hybrid computational model. In this paper, we demonstrate a newly developed quantum circuit simulator based on tensor network theory that enables intermediate-scale verification and validation of hybrid quantum-classical computing frameworks and programming models. We present our tensor-network quantum virtual machine (TNQVM) simulator which stores a multi-qubit wavefunction in a compressed (factorized) form as a matrix product state, thus enabling single-node simulations of larger qubit registers, as compared to brute-force state-vector simulators. Our simulator is designed to be extensible in both the tensor network form and the classical hardware used to run the simulation (multicore, GPU, distributed). The extensibility of the TNQVM simulator with respect to the simulation hardware type is achieved via a pluggable interface for different numerical backends (e.g., ITensor and ExaTENSOR numerical libraries). We demonstrate the utility of our TNQVM quantum circuit simulator through the verification of randomized quantum circuits and the variational quantum eigensolver algorithm, both expressed within the eXtreme-scale ACCelerator (XACC) programming model. Copyright © 2018, The Authors. All rights reserved.

关键词： Tensors

Application of Bayesian networks for estimation of individual psychological characteristics

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arXiv 2017年

作者： Litvinenko, Alexander Litvinenko, Natalya Mamyrbayev, Orken Extreme Computing Research Center Center for Uncertainty Quantification in Computational Science & Engineering King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Applied research department Institute of Mathematics and Mathematical Modeling CS MES RK Almaty Kazakhstan Institute of information and computational technologies CS MES RK Almaty Kazakhstan

An accurate qualitative and comprehensive assessment of human potential is one of the most important challenges in any company or collective. We apply Bayesian networks for developing more accurate overall estimations of psychological characteristics of an individual, based on psychological test results, which identify how much an individual possesses a certain trait. Examples of traits could be a stress resistance, the readiness to take a risk, the ability to concentrate on certain complicated work. The most common way of studying psychological characteristics of each individual is testing. Additionally, the overall estimation is usually based on personal experiences and the subjective perception of a psychologist or a group of psychologists about the investigated psychological personality traits.62C10, 62C12 Copyright © 2017, The Authors. All rights reserved.

关键词： Bayesian networks

Ab initio thermodynamic properties of certain compounds in Nd-Fe-B system

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arXiv 2018年

作者： Hanindriyo, Adie Tri Sridar, Soumya Hari Kumar, K.C. Hongo, Kenta Maezono, Ryo School of Material Science Jaist Asahidai 1-1 Nomi Ishikawa923-1292 Japan Department of Metallurgical and Materials Engineering Indian Institute of Technology Madras Chennai600 036 India Computational Engineering Applications Unit RIKEN 2-1 Hirosawa Wako Saitama351-0198 Research Center for Advanced Computing Infrastructure Jaist Asahidai 1-1 Nomi Ishikawa923-1292 Japan Center for Materials Research by Information Integration Research and Services Division of Materials Data and Integrated System National Institute for Materials Science Tsukuba305-0047 Japan Presto Japan Science and Technology Agency 4-1-8 Honcho Kawaguchi-shi Saitama332-0012 Japan School of Information Science Jaist Asahidai 1-1 Nomi Ishikawa923-1292 Japan

In this work, we report the results of ab initio calculations of thermochemical properties of several compounds in the Fe-Nd, B-Nd and B-Fe-Nd systems. We have performed DFT+U calculations to compute the enthalpy of formation of the compounds NdB6, NdB4, Nd2B5, Nd2Fe17and Nd5Fe2B6. It was found that the values obtained with an effective Hubbard U correction have better agreement with the experimental data. We have also computed the vibrational contribution to the heat capacity (Cp) of the compounds as a function of temperature was computed using the quasharmonic approximation. For most of the compounds these properties have not been experimentally determined until now. Hence, the computed ab initio thermodynamic properties will serve as useful input for the Gibbs energy model parameter assessment using the CALPHAD method. Copyright © 2018, The Authors. All rights reserved.

关键词： Iron alloys

High order fast algorithm for the Caputo fractional derivative

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arXiv 2017年

作者： Wang, Kun Huang, Jizu College of Mathematics and Statistics Chongqing University Chongqing401331 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

In the paper, we present a high order fast algorithm with almost optimum memory for the Caputo fractional derivative, which can be expressed as a convolution of u′(t) with the kernel (tn- t)-α. In the fast algorithm, the interval [0, tn-1] is split into nonuniform subintervals. The number of the subintervals is in the order of log n at the n-th time step. The fractional kernel function is approximated by a polynomial function of K-th degree with a uniform absolute error on each subinterval. We save K+1 integrals on each subinterval, which can be written as a convolution of u′(t) with a polynomial base function. As compared with the direct method, the proposed fast algorithm reduces the storage requirement and computational cost from O(n) to O((K + 1) log n) at the n-th time step. We prove that the convergence rate of the fast algorithm is the same as the direct method even a high order direct method is considered. The convergence rate and efficiency of the fast algorithm are illustrated via several numerical examples. Copyright © 2017, The Authors. All rights reserved.

关键词： Polynomial approximation

On efficient second order stabilized semi-implicit schemes for the cahn-hilliard phase-field equation

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arXiv 2017年

作者： Wang, Lin Yu, Haijun School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China NCMIS LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China

Efficient and energy stable high order time marching schemes are very important but not easy to construct for the study of nonlinear phase dynamics. In this paper, we propose and study two linearly stabilized second order semi-implicit schemes for the Cahn-Hilliard phase-field equation. One uses backward differentiation formula and the other uses Crank- Nicolson method to discretize linear terms. In both schemes, the nonlinear bulk forces are treated explicitly with two second-order stabilization terms. This treatment leads to linear elliptic systems with constant coefficients, for which lots of robust and efficient solvers are available. The discrete energy dissipation properties are proved for both schemes. Rigorous error analysis is carried out to show that, when the time step-size is small enough, second order accuracy in time is obtained with a prefactor controlled by a fixed power of 1/ϵ, where ϵ is the characteristic interface thickness. Numerical results are presented to verify the accuracy and efficiency of proposed *** Codes 65M12, 65M15, 65P40 Copyright © 2017, The Authors. All rights reserved.

关键词： Energy dissipation

Recent developments in the PySCF program package

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arXiv 2020年

作者： Sun, Qiming Zhang, Xing Banerjee, Samragni Bao, Peng Barbry, Marc Blunt, Nick S. Bogdanov, Nikolay A. Booth, George H. Chen, Jia Cui, Zhi-Hao Eriksen, Janus Juul Gao, Yang Guo, Sheng Hermann, Jan Hermes, Matthew R. Koh, Kevin Koval, Peter Lehtola, Susi Li, Zhendong Liu, Junzi Mardirossian, Narbe McClain, James D. Motta, Mario Mussard, Bastien Pham, Hung Q. Pulkin, Artem Purwanto, Wirawan Robinson, Paul J. Ronca, Enrico Sayfutyarova, Elvira Scheurer, Maximilian Schurkus, Henry F. Smith, James E.T. Sun, Chong Sun, Shi-Ning Upadhyay, Shiv Wagner, Lucas K. Wang, Xiao White, Alec Whitfield, James Daniel Williamson, Mark J. Wouters, Sebastian Yang, Jun Yu, Jason M. Zhu, Tianyu Berkelbach, Timothy C. Sharma, Sandeep Sokolov, Alexander Yu. Chan, Garnet Kin-Lic AxiomQuant Investment Management LLC Shanghai200120 China Division of Chemistry and Chemical Engineering California Institute of Technology PasadenaCA91125 United States Department of Chemistry and Biochemistry The Ohio State University ColumbusOH43210 United States Beijing National Laboratory for Molecular Sciences State Key Laboratory for Structural Chemistry of Unstable and Stable Species Institute of Chemistry Chinese Academy of Sciences Beijing100190 China Simbeyond B.V. P.O. Box 513 EindhovenNL-5600 MB Netherlands Department of Chemistry Lensfield Road CambridgeCB2 1EW United Kingdom Max Planck Institute for Solid State Research Heisenbergstraße 1 Stuttgart70569 Germany Department of Physics King's College London Strand LondonWC2R 2LS United Kingdom Department of Physics University of Florida GainesvilleFL32611 United States Quantum Theory Project University of Florida GainesvilleFL32611 United States School of Chemistry University of Bristol Cantock's Close BristolBS8 1TS United Kingdom Division of Engineering and Applied Science California Institute of Technology PasadenaCA91125 United States Google Inc. Mountain ViewCA94043 United States FU Berlin Department of Mathematics and Computer Science Arnimallee 6 Berlin14195 Germany TU Berlin Machine Learning Group Marchstr. 23 Berlin10587 Germany Department of Chemistry Chemical Theory Center Supercomputing Institute University of Minnesota 207 Pleasant Street SE MinneapolisMN55455 United States Department of Chemistry and Biochemistry The University of Notre Dame du Lac 251 Nieuwland Science Hall Notre DameIN46556 United States Simune Atomistics S.L. Avenida Tolosa 76 Donostia-San Sebastian Spain HelsinkiFI-00014 Finland Key Laboratory of Theoretical and Computational Photochemistry Ministry of Education College of Chemistry Beijing Normal University Beijing100875 China Department of Chemistry The Johns Hopkins University BaltimoreMD21218 United States AMGEN

PYSCF is a Python-based general-purpose electronic structure platform that both supports first-principles simulations of molecules and solids, as well as accelerates the development of new methodology and complex computational workflows. The present paper explains the design and philosophy behind PYSCF that enables it to meet these twin objectives. With several case studies, we show how users can easily implement their own methods using PYSCF as a development environment. We then summarize the capabilities of PYSCF for molecular and solid-state simulations. Finally, we describe the growing ecosystem of projects that use PYSCF across the domains of quantum chemistry, materials science, machine learning and quantum information science. Copyright © 2020, The Authors. All rights reserved.

关键词： Python