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Convergence Analysis of an Unconditionally Energy Stable Linear Crank-Nicolson Scheme for the Cahn-Hilliard 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 Ncmis and Lsec Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190

Efficient and unconditionally stable high order time marching schemes are very important but not easy to construct for nonlinear phase dynamics. In this paper, we propose and analysis an efficient stabilized linear Crank-Nicolson scheme for the Cahn-Hilliard equation with provable unconditional stability. In this scheme the nonlinear bulk force are treated explicitly with two second-order linear stabilization terms. The semi-discretized equation is a linear elliptic system with constant coefficients, thus robust and efficient solution procedures are guaranteed. Rigorous error analysis show that, when the time step-size is small enough, the scheme is second order accurate in time with a prefactor controlled by some lower degree polynomial of 1/". Here " is the interface thickness parameter. Numerical results are presented to verify the accuracy and efficiency of the *** Codes 65M12, 65M15, 65P40 Copyright © 2017, The Authors. All rights reserved.

关键词： Phase interfaces

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

Sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact lines

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arXiv 2017年

作者： Xu, Xianmin Di, Yana Yu, Haijun School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 Ncmis and Lsec Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190

The sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact line problem are studied by asymptotic analysis and numerical simulations. The effects of the mobility number as well as a phenomenological relaxation parameter in the boundary condition are considered. In asymptotic analysis, we focus on the case that the mobility number is the same order of the Cahn number and derive the sharp-interface limits for several setups of the boundary relaxation parameter. It is shown that the sharp interface limit of the phase field model is the standard two-phase incompressible Navier-Stokes equations coupled with several different slip boundary conditions. Numerical results are consistent with the analysis results and also illustrate the different convergence rates of the sharp-interface limits for different scalings of the two parameters. Copyright © 2017, The Authors. All rights reserved.

关键词： Asymptotic analysis

Multiscale approach and the convergence for the time-dependent Maxwell-Schrödinger system in heterogeneous nanostructures

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arXiv 2017年

作者： Cao, Liqun Ma, Chupeng Luo, Jianlan Zhang, Lei LSEC NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Physics and Nuclear Energy Engineering Beijing University of Aeronautics and Astronautics Beijing100191 China Department of Logistics Management Logistics Academy Beijing100858 China

This paper discusses the multiscale approach and the convergence of the timedependent Maxwell-Schrödinger system with rapidly oscillating discontinuous coefficients arising from the modeling of a heterogeneous nanostructure with a periodic microstructure. The homogenization method and the multiscale asymptotic method for the nonlinear coupled equations are presented. The efficient numerical algorithms based on the above methods are proposed. Numerical simulations are then carried out to validate the method presented in this paper. Copyright © 2017, The Authors. All rights reserved.

关键词： Finite element method

computational MICROMAGNETICS WITH COMMICS

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arXiv 2018年

作者： Pfeiler, Carl-Martin Ruggeri, Michele Stiftner, Bernhard Lukas, E.X.L. Hochsteger, Matthias Hrkac, Gino Schöberl, Joachim Mauser, Norbert J. Praetorius, Dirk College of Engineering Mathematics and Physical Sciences University of Exeter North Park Road Exeter United Kingdom Faculty of Mathematics University of Vienna Oskar-Morgenstern-Platz 1 Vienna1090 Austria Institute for Analysis and Scientific Computing TU Wien Wiedner Hauptstrasse 8–10 Vienna1040 Austria Wolfgang Pauli Institute c/ Faculty of Mathematics University of Vienna Oskar-Morgenstern-Platz 1 Vienna1090 Austria

We present our open-source Python module Commics for the study of the magnetization dynamics in ferromagnetic materials via micromagnetic simulations. It implements state-of-the-art unconditionally convergent finite element methods for the numerical integration of the Landau–Lifshitz–Gilbert equation. The implementation is based on the multiphysics finite element software Netgen/NGSolve. The simulation scripts are written in Python, which leads to very readable code and direct access to extensive post-processing. Together with documentation and example scripts, the code is freely available on GitLab. Copyright © 2018, The Authors. All rights reserved.

关键词： Python

Mathematical and numerical analysis of the time-dependent Maxwell-Schrödinger Equations in the Coulomb gauge

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arXiv 2017年

作者： Ma, Chupeng Cao, Liqun Huang, Jizu Lin, Yanping Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Department of Applied Mathematics Hong Kong Polytechnic University Kowloon Hong Kong

In this paper, we consider the initial-boundary value problem for the time-dependent Maxwell-Schrödinger equations in the Coulomb gauge. We first prove the global existence of weak solutions to the equations. Next we propose an energy-conserving fully discrete finite element scheme for the system and prove the existence and uniqueness of solutions to the discrete system. The optimal error estimates for the numerical scheme without any time-step restrictions are then derived. Numerical results are provided to support our theoretical analysis. Copyright © 2017, The Authors. All rights reserved.

关键词： Initial value problems

Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions

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arXiv 2023年

作者： Alexeev, Yuri Amsler, Maximilian Barroca, Marco Antonio Bassini, Sanzio Battelle, Torey Camps, Daan Casanova, David Choi, Young Jai Chong, Frederic T. Chung, Charles Codella, Christopher Córcoles, Antonio D. Cruise, James Di Meglio, Alberto Duran, Ivan Eckl, Thomas Economou, Sophia Eidenbenz, Stephan Elmegreen, Bruce Fare, Clyde Faro, Ismael Fernández, Cristina Sanz Ferreira, Rodrigo Neumann Barros Fuji, Keisuke Fuller, Bryce Gagliardi, Laura Galli, Giulia Glick, Jennifer R. Gobbi, Isacco Gokhale, Pranav de la Puente Gonzalez, Salvador Greiner, Johannes Gropp, Bill Grossi, Michele Gull, Emanuel Healy, Burns Hermes, Matthew R. Huang, Benchen Humble, Travis S. Ito, Nobuyasu Izmaylov, Artur F. Javadi-Abhari, Ali Jennewein, Douglas Jha, Shantenu Jiang, Liang Jones, Barbara de Jong, Wibe Albert Jurcevic, Petar Kirby, William Kister, Stefan Kitagawa, Masahiro Klassen, Joel Klymko, Katherine Koh, Kwangwon Kondo, Masaaki Kürkçüoglu, Doga Murat Kurowski, Krzysztof Laino, Teodoro Landfield, Ryan Leininger, Matt Leyton-Ortega, Vicente Li, Ang Lin, Meifeng Liu, Junyu Lorente, Nicolas Luckow, Andre Martiel, Simon Martin-Fernandez, Francisco Martonosi, Margaret Marvinney, Claire Medina, Arcesio Castaneda Merten, Dirk Mezzacapo, Antonio Michielsen, Kristel Mitra, Abhishek Mittal, Tushar Moon, Kyungsun Moore, Joel Mostame, Sarah Motta, Mario Na, Young-Hye Nam, Yunseong Narang, Prineha Ohnishi, Yu-Ya Ottaviani, Daniele Otten, Matthew Pakin, Scott Pascuzzi, Vincent R. Pednault, Edwin Piontek, Tomasz Pitera, Jed Rall, Patrick Ravi, Gokul Subramanian Robertson, Niall Rossi, Matteo A.C. Rydlichowski, Piotr Ryu, Hoon Samsonidze, Georgy Sato, Mitsuhisa Saurabh, Nishant Sharma, Vidushi Sharma, Kunal Shin, Soyoung Slessman, George Steiner, Mathias Sitdikov, Iskandar Suh, In-Saeng Switzer, Eric D. Tang, Wei Thompson, Joel Todo, Synge Tran, Minh C. Trenev, Dimitar Trott, Christian Tseng, Huan-Hsin Tubman, Norm M. Tureci, Esin Valiñas, David García Vallecorsa, Sofia Wever, Christopher Wojciechowski, Konrad Wu, Xiaodi Yoo, Shinjae Yoshioka, Argonne National Laboratory LemontIL60439 United States Corporate Sector Research and Advance Engineering Robert Bosch GmbH Robert-Bosch-Campus 1 RenningenD-71272 Germany IBM Research RJ Rio de Janeiro20031-170 Brazil Centro Brasileiro de Pesquisas Físicas RJ Rio de Janeiro22290-180 Brazil CINECA via Magnanelli 6/3 BO Casalecchio di Reno40033 Italy Arizona State University TempeAZ United States National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA United States Euskadi Donostia-San Sebastián20018 Spain Ikerbasque Basque Foundation for Science Bilbao48009 Spain Department of Physics Yonsei University Seoul03722 Korea Republic of University of Chicago ChicagoIL United States IBM Quantum IBM T.J. Watson Research Center Yorktown Heights NY10598 United States Cambridge Consultants part of Capgemini Invent Cambridge United Kingdom Geneva1211 Switzerland Virginia Tech BlacksburgVA24061 United States Los Alamos National Laboratory Los AlamosNM87545 United States Osaka University Osaka560-8531 Japan Department of Chemistry Chicago Center for Theoretical Chemistry University of Chicago ChicagoIL United States Fraunhofer ITWM Rheinland-Pfalz Kaiserslautern67663 Germany Infleqtion ChicagoIL60622 United States University of Illinois Urbana-Champaign United States University of Michigan Ann ArborMI48109 United States Research Office Oak Ridge National Laboratory One Bethel Valley Road Oak RidgeTN37831 United States Hyogo Kobe650-0047 Japan Chemical Physics Theory Group Department of Chemistry University of Toronto TorontoONM5S 3H6 Canada Department of Physical and Environmental Sciences University of Toronto Scarborough TorontoONM1C 1A4 Canada Brookhaven National Laboratory UptonNY United States Rutgers University New BrunswickNJ United States IBM Quantum Almaden Research Center San JoseCA95120 United States Applied Mathematics and Computational Research Division

computational models are an essential tool for the design, characterization, and discovery of novel materials. computationally hard tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their resources for simulation, analysis, and data processing. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. In this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions. Copyright © 2023, The Authors. All rights reserved.

关键词： Characterization (materials science)

Genetic drivers of heterogeneity in type 2 diabetes pathophysiology

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Nature 2024年第8003期627卷 347-357页

作者： Ken Suzuki Konstantinos Hatzikotoulas Lorraine Southam Henry J Taylor Xianyong Yin Kim M Lorenz Ravi Mandla Alicia Huerta-Chagoya Giorgio E M Melloni Stavroula Kanoni Nigel W Rayner Ozvan Bocher Ana Luiza Arruda Kyuto Sonehara Shinichi Namba Simon S K Lee Michael H Preuss Lauren E Petty Philip Schroeder Brett Vanderwerff Mart Kals Fiona Bragg Kuang Lin Xiuqing Guo Weihua Zhang Jie Yao Young Jin Kim Mariaelisa Graff Fumihiko Takeuchi Jana Nano Amel Lamri Masahiro Nakatochi Sanghoon Moon Robert A Scott James P Cook Jung-Jin Lee Ian Pan Daniel Taliun Esteban J Parra Jin-Fang Chai Lawrence F Bielak Yasuharu Tabara Yang Hai Gudmar Thorleifsson Niels Grarup Tamar Sofer Matthias Wuttke Chloé Sarnowski Christian Gieger Darryl Nousome Stella Trompet Soo-Heon Kwak Jirong Long Meng Sun Lin Tong Wei-Min Chen Suraj S Nongmaithem Raymond Noordam Victor J Y Lim Claudia H T Tam Yoonjung Yoonie Joo Chien-Hsiun Chen Laura M Raffield Bram Peter Prins Aude Nicolas Lisa R Yanek Guanjie Chen Jennifer A Brody Edmond Kabagambe Ping An Anny H Xiang Hyeok Sun Choi Brian E Cade Jingyi Tan K Alaine Broadaway Alice Williamson Zoha Kamali Jinrui Cui Manonanthini Thangam Linda S Adair Adebowale Adeyemo Carlos A Aguilar-Salinas Tarunveer S Ahluwalia Sonia S Anand Alain Bertoni Jette Bork-Jensen Ivan Brandslund Thomas A Buchanan Charles F Burant Adam S Butterworth Mickaël Canouil Juliana C N Chan Li-Ching Chang Miao-Li Chee Ji Chen Shyh-Huei Chen Yuan-Tsong Chen Zhengming Chen Lee-Ming Chuang Mary Cushman John Danesh Swapan K Das H Janaka de Silva George Dedoussis Latchezar Dimitrov Ayo P Doumatey Shufa Du Qing Duan Kai-Uwe Eckardt Leslie S Emery Daniel S Evans Michele K Evans Krista Fischer James S Floyd Ian Ford Oscar H Franco Timothy M Frayling Barry I Freedman Pauline Genter Hertzel C Gerstein Vilmantas Giedraitis Clicerio González-Villalpando Maria Elena González-Villalpando Penny Gordon-Larsen Myron Gross Lindsay A Guare Sophie Hackinger Liisa Hakaste Sohee Han Andrew T Hattersley Christian Herder Momoko Horikoshi Annie-Green Howard Willa Centre for Genetics and Genomics Versus Arthritis Centre for Musculoskeletal Research Division of Musculoskeletal and Dermatological Sciences University of Manchester Manchester UK. Department of Diabetes and Metabolic Diseases Graduate School of Medicine University of Tokyo Tokyo Japan. Department of Statistical Genetics Osaka University Graduate School of Medicine Suita Japan. Institute of Translational Genomics Helmholtz Zentrum München German Research Center for Environmental Health Neuherberg Germany. konstantinos.hatzikotoulas@helmholtz-munich.de. Institute of Translational Genomics Helmholtz Zentrum München German Research Center for Environmental Health Neuherberg Germany. Center for Precision Health Research National Human Genome Research Institute National Institutes of Health Bethesda MD USA. British Heart Foundation Cardiovascular Epidemiology Unit Department of Public Health and Primary Care University of Cambridge Cambridge UK. Heart and Lung Research Institute University of Cambridge Cambridge UK. Department of Epidemiology School of Public Health Nanjing Medical University Nanjing China. Department of Biostatistics and Center for Statistical Genetics University of Michigan Ann Arbor MI USA. Corporal Michael J. Crescenz VA Medical Center Philadelphia PA USA. Department of Systems Pharmacology and Translational Therapeutics University of Pennsylvania Perelman School of Medicine Philadelphia PA USA. Department of Genetics University of Pennsylvania Perelman School of Medicine Philadelphia PA USA. Programs in Metabolism and Medical and Population Genetics Broad Institute of Harvard and MIT Cambridge MA USA. Diabetes Unit and Center for Genomic Medicine Massachusetts General Hospital Boston MA USA. TIMI Study Group Division of Cardiovascular Medicine Brigham and Women's Hospital Harvard Medical School Boston MA USA. William Harvey Research Institute Barts and the London School of Medicine and Dentistry Queen Mary University of London L

Type 2 diabetes (T2D) is a heterogeneous disease that develops through diverse pathophysiological processes and molecular mechanisms that are often specific to cell type. Here, to characterize the genetic contribution to these processes across ancestry groups, we aggregate genome-wide association study data from 2,535,601 individuals (39.7% not of European ancestry), including 428,452 cases of T2D. We identify 1,289 independent association signals at genome-wide significance (P < 5 × 10) that map to 611 loci, of which 145 loci are, to our knowledge, previously unreported. We define eight non-overlapping clusters of T2D signals that are characterized by distinct profiles of cardiometabolic trait associations. These clusters are differentially enriched for cell-type-specific regions of open chromatin, including pancreatic islets, adipocytes, endothelial cells and enteroendocrine cells. We build cluster-specific partitioned polygenic scores in a further 279,552 individuals of diverse ancestry, including 30,288 cases of T2D, and test their association with T2D-related vascular outcomes. Cluster-specific partitioned polygenic scores are associated with coronary artery disease, peripheral artery disease and end-stage diabetic nephropathy across ancestry groups, highlighting the importance of obesity-related processes in the development of vascular outcomes. Our findings show the value of integrating multi-ancestry genome-wide association study data with single-cell epigenomics to disentangle the aetiological heterogeneity that drives the development and progression of T2D. This might offer a route to optimize global access to genetically informed diabetes care.

关键词：

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