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A constrained transport divergence-free finite element method for incompressible MHD equations

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arXiv 2020年

作者： Li, Lingxiao Zhang, Donghang Zheng, Weiying Institute of Applied Physics and Computational Mathematics Beijing100094 China LSEC NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Science University of Chinese Academy of Sciences Beijing100049 China

In this paper we study finite element method for three-dimensional incompressible resistive magnetohydrodynamic equations, in which the velocity, the current density, and the magnetic induction are divergence-free. It is desirable that the discrete solutions should also satisfy divergence-free conditions exactly especially for the momentum equations. Inspired by constrained transport method, we devise a new stable mixed finite element method that can achieve the goal. We also prove the well-posedness of the discrete solutions. To solve the resulting linear algebraic equations, we propose a GMRES solver with an augmented Lagrangian block preconditioner. By numerical experiments, we verify the theoretical results and demonstrate the quasi-optimality of the discrete solver with respect to the number of degrees of freedom. Copyright © 2020, The Authors. All rights reserved.

关键词： Finite element method

LOWEST-DEGREE POLYNOMIAL DE RHAM COMPLEX ON GENERAL QUADRILATERAL GRIDS

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arXiv 2020年

作者： Qimengquan Ji, Xia Zhang, Shuo University of Chinese Academy of Sciences Beijing100190 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China

This paper devotes to the construction of finite elements on grids that consist of general quadrilaterals not limited in parallelograms. Two finite elements are established for the H1 and H(rot) elliptic problems, respectively. The two finite element spaces on general quadrilateral grids, together with the space of piecewise constant functions, formulate a discretised de Rham complex. First order convergence rate can be proved for both of them under the asymptotic-parallelogram assumption on the grids. The local shape functions of the two spaces are piecewise polynomials, and the global finite element functions are nonconforming. A rigorous analysis is given in this paper that it is impossible to construct a practically useful finite element defined as Ciarlet’s triple whose shape functions are always piecewise polynomials and which can form conforming subspaces on a grid that consists of arbitrary quadrilaterals. Copyright © 2020, The Authors. All rights reserved.

关键词： Polynomials

***: A Comprehensive Genomic Visualisation Database for Malaysian Species

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***: A Comprehensive Genomic Visualisation Database for Mala...

computing (ICOCO), IEEE International Conference on

作者： Vei Siang Chan Farhan Bin Mohamed Faezah Mohd Salleh Andres Iglesias Alina Binti Wagiran Ali Bin Selamat School of Computing Faculty of Engineering Universiti Teknologi Malaysia Johor Bahru Malaysia Media and Game Innovation Center of Excellence Universiti Teknologi Malaysia Johor Bahru Malaysia Dept. of Biosciences Faculty of Science Universiti Teknologi Malaysia Johor Bahru Malaysia Dept. of Applied Mathematics and Computational Sciences University of Cantabria Santander Spain Malaysia-Japan International Institute of Technology University of Technology Malaysia Kuala Lumpur Malaysia

ISBN: (纸本)9781665489973

Malaysia is one of the most megadiverse regions in the world. Therefore, it is important to record these rich biodiversity data to safeguard and improve national conservation efforts. However, the lack of nationwide genomic sequencing hampers a more sophisticated species identification, data management, and analytics activities. Thus, this project aims to design and implement ***, a comprehensive one-stop online DNA reference database with integrated DNA visualisation and digital references to allow the users to search, retrieve and analyse the collected DNA sequencing data interactively. This paper documented the system architecture and implementation methods to create ***. The results of *** can display taxonomy information of biodiversity in the web’s user interfaces and visualise the complex set of DNA data to allow new insights. Lastly, the authors identified several future works to improve *** including improve user interaction, add visualisation methods to support more bioinformatics tasks, and conduct formal user evaluation.

关键词： Sequential analysis Annotations Taxonomy Data visualization DNA Genomics Systems architecture

Multiobjective Forecasting Model Based on the Interval Discrete Type-2 Fuzzy Sets and Genetic Algorithm 34

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Multiobjective Forecasting Model Based on the Interval Discr...

34th International Conference on Information Technologies, InfoTech 2020

作者： Demidova, Liliya Anatolievna Stepanov, Maksim Anatolievich Institute of Integrated Safety and Special Instrumentation Russian Technological University - MIREA Department of Intelligent Systems of Information Security Vernadsky Avenue78 Moscow119454 Russia Faculty of Computing Engineering Ryazan State Radio Engineering University Named after V.F. Utkin Department of Computational and Applied Mathematics Gagarin Str. 59/1 Ryazan390005 Russia

ISBN: (纸本)9781728169149

The forecasting task for the short time series has been investigated. The main problem of this task is the availability of a small amount of relevant information. Such tasks can be considered as the tasks in the conditions of uncertainty, fuzziness of the initial data. We suggest to develop the multiobjective forecasting model based on the interval discrete type-2 fuzzy sets. As the criteria which should be minimized, it is proposed to use the average relative forecasting error and the tendency mismatch indicator. The search for the optimal parameters values of the forecasting model is implemented using the genetic algorithm. The examples showing the possibilities of the proposed forecasting model have been discussed. © 2020 IEEE.

关键词： Genetic algorithms

Framework for evaluating statistical models in physics education research

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Physical Review Physics Education Research 2021年第2期17卷 020104-020104页

作者： John M. Aiken Riccardo De Bin H. J. Lewandowski Marcos D. Caballero Center for Computing in Science Education & Department of Physics University of Oslo N-0316 Oslo Norway Department of Mathematics University of Oslo N-0316 Oslo Norway Department of Physics University of Colorado Boulder Boulder Colorado 80309 USA JILA National Institute of Standards and Technology and the University of Colorado Boulder Colorado 80309 USA Department of Physics and Astronomy Department of Computational Mathematics Sciences and Engineering and CREATE for STEM Institute Michigan State University East Lansing Michigan 48824 USA

Across the field of education research there has been an increased focus on the development, critique, and evaluation of statistical methods and data usage due to recently created, very large datasets and machine learning techniques. In physics education research (PER), this increased focus has recently been shown through the 2019 Physical Review PER Focused Collection examining quantitative methods in PER. Quantitative PER has provided strong arguments for reforming courses by including interactive engagement, demonstrated that students often move away from scientistlike views due to science education, and has injected robust assessment into the physics classroom via concept inventories. The work presented here examines the impact that machine learning may have on physics education research, presents a framework for the entire process including data management, model evaluation, and results communication, and demonstrates the utility of this framework through the analysis of two types of survey data.

关键词： Research methodology

Accelerated Sparse Recovery via Gradient Descent with Nonlinear Conjugate Gradient Momentum

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arXiv 2022年

作者： Hu, Mengqi Lou, Yifei Wang, Bao Yan, Ming Yang, Xiu Ye, Qiang Department of Industrial and Systems Engineering Lehigh University 200 West Packer Avenue BethlehemPA18015 United States Department of Mathematical Sciences The University of Texas at Dallas 800 W. Campbell Rd RichardsonTX75080 United States Department of Mathematics and Scientific Computing Imaging Institute The University of Utah 72 Central Campus Dr Salt Lake CityUT84102 United States School of Data Science The Chinese University of Hong Kong Shenzhen 2001 Longxiang Blvd Guangdong Shenzhen China Department of Computational Mathematics Science and Engineering Department of Mathematics Michigan State University 428 South Shaw Lane East LansingMI48824 United States Department of Mathematics University of Kentucky LexingtonKY40513 United States

This paper applies an idea of adaptive momentum for the nonlinear conjugate gradient to accelerate optimization problems in sparse recovery. Specifically, we consider two types of minimization problems: a (single) differentiable function and the sum of a non-smooth function and a differentiable function. In the first case, we adopt a fixed step size to avoid the traditional line search and establish the convergence analysis of the proposed algorithm for a quadratic problem. This acceleration is further incorporated with an operator splitting technique to deal with the non-smooth function in the second case. We use the convex 1 and the nonconvex 1 − 2 functionals as two case studies to demonstrate the efficiency of the proposed approaches over traditional methods. © 2022, CC BY-SA.

关键词： Momentum

General liquid-crystal theory for anisotropically shaped molecules: Symmetry, orientational order parameters, and system free energy

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Physical Review E 2020年第6期102卷 062701-062701页

作者： Jie Xu Jeff Z. Y. Chen LSEC & NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing (ICMSEC) Academy of Mathematics and Systems Science (AMSS) Chinese Academy of Sciences Beijing 100190 China Department of Physics and Astronomy University of Waterloo Ontario Canada N2L 3G1

A general theory of liquid crystals is presented, starting from the group-theory symmetry analysis of the constituting molecules. A particular attention is paid to the type of elastic free-energies and their relationships with the molecular symmetries. The orientational order-parameter tensors are identified for each molecular symmetry, in a consideration of consistently keeping the leading, characteristic elastic free energies in a model. The order parameters are expressed in terms of symmetric traceless tensors, some of high orders, for all major molecular symmetries, including seven groups of axial symmetries and seven groups of polyhedral symmetries. For spatially inhomogeneous liquid crystals, the couplings of these tensors in the elastic energies are derived by expanding the interaction energies between these molecules. The aim is to provide a general view of the molecular symmetries of individual molecules, orientational order parameters characterizing the orientational distribution functions, and the elastic free energies, all under one single group-theory approach.

关键词： Bent-core liquid crystals Liquid crystals Lyotropic liquid crystals Nematic liquid crystals

H2−Korn⇔s inequality and the nonconforming elements for the strain gradient elastic model

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arXiv 2021年

作者： Li, Hongliang Ming, Pingbing Wang, Huiyu Department of Mathematics Sichuan Normal University Chengdu610066 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences No. 55 East Road Zhong-Guan-Cun Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Middle School Beijing101 China

We establish a new H2−Korn’s inequality and its discrete analog, which greatly simplify the construction of nonconforming elements for a linear strain gradient elastic model. The Specht triangle [41] and the NZT tetrahedron [45] are analyzed as two typical representatives for robust nonconforming elements in the sense that the rate of convergence is independent of the small material parameter. We construct new regularized interpolation estimate and the enriching operator for both elements, and prove the error estimates under minimal smoothness assumption on the solution. Numerical results are consistent with the theoretical prediction. © 2021, CC BY.

关键词： Finite element method

Rubric-based holistic review: A promising route to equitable graduate admissions in physics

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Physical Review Physics Education Research 2022年第2期18卷 020140-020140页

作者： Nicholas T. Young K. Tollefson Remco G. T. Zegers Marcos D. Caballero Department of Physics and Astronomy Michigan State University East Lansing Michigan 48824 USA Department of Computational Mathematics Science and Engineering Michigan State University East Lansing Michigan 48824 USA National Superconducting Cyclotron Laboratory Michigan State University East Lansing Michigan 48824 USA Joint Institute for Nuclear Astrophysics Michigan State University East Lansing Michigan 48824 USA Center for Computing in Science Education and Department of Physics University of Oslo N-0316 Oslo Norway CREATE for STEM Institute Michigan State University East Lansing Michigan 48824 USA

As systematic inequities in higher education and society have been brought to the forefront, graduate programs are interested in increasing the diversity of their applicants and enrollees. Yet, structures in place to evaluate applicants may not support such aims. One potential solution to support those aims is rubric-based holistic review. Starting in 2018, our physics department implemented a rubric-based holistic review process for all applicants to our graduate program. The rubric assessed applicants on 18 metrics covering their grades, test scores, research experiences, noncognitive competencies, and fit with the program. We then compared faculty’s ratings of applicants by admission status, sex, and undergraduate program over a three-year period. We find that the rubric scores show statistically significant differences between admitted and nonadmitted students as hoped. We also find that differences in rubric scores based on sex or undergraduate program reflected known systematic inequities such as applicants from smaller and less prestigious undergraduate universities scoring lower on the physics GRE and women performing more volunteer work in academia. Our results then suggest rubric-based holistic review as a possible route to making graduate admissions in physics more equitable.

关键词： Diversity & inclusion Educational policy Graduate students