检索结果-内蒙古大学图书馆

Quantum simulation of discrete linear dynamical systems and simple iterative methods in linear algebra via Schrödingerisation

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Jin, Shi Liu, Nana Institute of Natural Sciences Shanghai Jiao Tong University Shanghai200240 China School of Mathematical Sciences Shanghai Jiao Tong University Shanghai200240 China Ministry of Education Key Laboratory in Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China Shanghai Artificial Intelligence Laboratory Shanghai China University of Michigan Shanghai Jiao Tong University Joint Institute Shanghai200240 China

Quantum simulation is known to be capable of simulating certain dynamical systems in continuous time – Schrödinger’s equations being the most direct and well-known – more efficiently than classical simulation. Any linear dynamical system can in fact be transformed into a system of Schrödinger’s equations via a method called Schrödingerisation [1]. Building on the observation that iterative methods in linear algebra, and more generally discrete linear dynamical systems, can be viewed as discrete time approximations of dynamical systems which evolve continuously in time, we can apply the Schrödingerisation technique. Thus quantum simulation can be directly applied to the continuous-time limits of some of the simplest iterative methods. This applies to general (explicit) iterative schemes or discrete linear dynamical systems. In particular, we introduce the quantum Jacobi and quantum power methods for solving the quantum linear systems of equations and for estimating the maximum eigenvector and eigenvalue of a matrix respectively. The proposed quantum simulation can be performed on either discrete-variable quantum systems or on hybrid continuous-variable and discrete-variable quantum systems. This framework provides an interesting alternative method to solve linear algebra problems using quantum simulation. © 2023, CC BY.

关键词： Iterative methods

Parallel exponential time differencing methods for geophysical flow simulations

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Lan, Rihui Leng, Wei Wang, Zhu Ju, Lili Gunzburger, Max Department of Mathematics University of South Carolina ColumbiaSC29208 United States State Key Laboratory of Scientific and Engineering Computing Chinese Academy of Sciences Beijing100190 China Department of Scientific Computing Florida State University TallahasseeFL32306 United States

Two ocean models are considered for geophysical flow simulations: the multi-layer shallow water equations and the multi-layer primitive equations. For the former, we investigate the parallel performance of exponential time differencing (ETD) methods, including exponential Rosenbrock-Euler, ETD2wave, and B-ETD2wave. For the latter, we take advantage of the splitting of barotropic and baroclinic modes and propose a new two-level method in which an ETD method is applied to solve the fast barotropic mode. These methods could improve the computational efficiency of numerical simulations because ETD methods allow for much larger time step sizes than traditional explicit time-stepping techniques that are commonly used in existing computational ocean models. Several standard benchmark tests for ocean modeling are performed and comparison of the numerical results demonstrate a great potential of applying the parallel ETD methods for simulating real-world geophysical flows. © 2021, CC BY-NC-ND.

关键词： Numerical methods

STABILITY OF GLOBAL MAXWELLIAN FOR NON-LINEAR VLASOV-POISSON-FOKKER-PLANCK EQUATIONS

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2019年第1期39卷 127-138页

作者： Jie LIAO Qianrong WANG Xiongfeng YANG Department of Mathematics East China University of Science and Technology School of Mathematical Sciences Key Laboratory of Scientific and Engineering Computing (MOE) Shanghai Jiao Tong University

In this article, we establish the exponential time decay of smooth solutions around a global Maxwellian to the non-linear Vlasov–Poisson–Fokker–Planck equations in the whole space by uniform-in-time energy estimates. The non-linear coupling of macroscopic part and Fokker–Planck operator in the model brings new difficulties for the energy estimates, which is resolved by adding tailored weighted-in-v energy estimates suitable for the Fokker–Planck operator.

关键词： non-linear Vlasov–Poisson–Fokker–Planck equation global Maxwellian global a priori estimates exponential convergence

Non-invasive assessment of intracranial wall shear stress using high-resolution magnetic resonance imaging in combination with computational fluid dynamics technique

学校读者我要写书评

暂无评论

Fundamental Research 2022年第2期2卷 329-334页

作者： Yuwen Chen Jia Liu Mingli Li Yannan Yu Zhengzheng Yan Wenshin Shiu Bokai Wu Zaiheng Cheng Yao Meng Yang Liu Weizhuang Yuan Zongmuyu Zhang Weihai Xu Department of Neurology State Key Laboratory of Complex Severe and Rare DiseasesPeking Union Medical Cllege HospitalChinese Academy of Medical Sciences and Peking Union Medical College1 ShuaifuyuanBeijing 100005China Department of Cardiology Second Afliated Hospital of Zhejiang University School of MedicineHangzhouZhejiang 310009China Shenzhen Instiutes of Advanced Technology Chinese Academy of SciencesShenzhen 518055China Shenzhen Key Laboratory for Exascale Engineering and Scientific Computing Shenzhen 518055China Department of Radiology Peking Union Medical College HospitalChinese Acadermy of Medical Sciences1 ShuaifiryuanBeijing 100005China Department of Radiology Stanford UniversityCaliformia 94305United States Department of Neurology Saarland UniversityKirrberger StraSe 66421Germany

In vivo studies on association between wall shear stress(WSS)and intracranial plaque are *** on the three-dimensional T1-weighted high-resolution magnetic resonance imaging(3DT1 HR-MRI)data of patients with low-grade stenotic(<50%)atherosclerotic middle cerebral artery(MCA)and subjects with normal MCA,we built a three-dimensional reconstructed WSS model by computational fluid dynamics(CFD)***-dimensional registration of the CFD model to the HR-MRI was performed with projections based on the resolution and thickness of the *** relationships between the Wss at each side of the vessel wall and plaque location were analyzed.A total of 94 MCA plaques from 43 patients and 50 normal MCAs were *** the normal MCAs,WSS was lower at the ventral-inferior wall than at the dorsal-superior wall(proximal segment,p<0.001;middle segment,p<0.001)and lower at the inner wall than at the outer wall of the MCA curve(p<0.001).In atherosclerotic MCAs,similar low Wss regions were observed where plaques *** WSS ratio of the ventral-inferior wall to the dorsal-superior wall in atherosclerotic MCAs was lower than that in normal MCAs(p=0.002).The WSS_(inmer-outer)ratio in atherosclerotic MCAs was lower than that in normal MCAs(p=0.002).Low WSS was associated with MCA atherosclerosis formation and occurred mainly at the ventral inferior wall,which was anatomically opposite the orifices of penetrating arteries,and at the inner wall of the MCA ***,the results were well consistent with the low WSS theory in atherosclerosis *** reconstructed WSS model is a promising novel method for assessing an individualized vascular profile once validated by further studies.

关键词： Intracranial atherosclerosis Wall shear stress Atherosclerotic plaque High-resolution magnetic resonance imaging Computational fluid dynamics

A high-order discrete energy decay and maximum-principle preserving scheme for time fractional Allen-Cahn equation

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Zhang, Guoyu Huang, Chengming Alikhanov, Anatoly A. Yin, Baoli School of Mathematical Sciences Inner Mongolia University Hohhot010021 China School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China North-Caucasus Center for Mathematical Research North-Caucasus Federal University Stavropol355017 Russia

The shifted fractional trapezoidal rule (SFTR) with a special shift is adopted to construct a finite difference scheme for the time-fractional Allen-Cahn (tFAC) equation. Some essential key properties of the weights of SFTR are explored for the first time. Based on these properties, we rigorously demonstrate the discrete energy decay property and maximum-principle preservation for the scheme. Numerical investigations show that the scheme can resolve the intrinsic initial singularity of such nonlinear fractional equations as tFAC equation on uniform meshes without any correction. Comparison with the classic fractional BDF2 and L2-1σ method further validates the superiority of SFTR in solving the tFAC equation. Experiments concerning both discrete energy decay and discrete maximum-principle also verify the correctness of the theoretical results. © 2023, CC BY-NC-SA.

关键词： Maximum principle

Structure-Preserving Operator Learning: Modeling the Collision Operator of Kinetic Equations

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Lee, Jae Yong Schotthöfer, Steffen Xiao, Tianbai Krumscheid, Sebastian Frank, Martin Center for Artificial Intelligence and Natural Sciences Korea Institute for Advanced Study Seoul Korea Republic of Oak Ridge National Laboratory Computer Science and Mathematics Division Oak RidgeTN United States State Key Laboratory of High Temperature Gas Dynamics Centre for Interdisciplinary Research in Fluids Institute of Mechanics Chinese Academy of Sciences Beijing China School of Engineering Science University of Chinese Academy of Sciences Beijing China Karlsruhe Institute of Technology Scientific Computing Center Karlsruhe76131 Germany

This work explores the application of deep operator learning principles to a problem in statistical physics. Specifically, we consider the linear kinetic equation, consisting of a differential advection operator and an integral collision operator, which is a powerful yet expensive mathematical model for interacting particle systems with ample applications, e.g., in radiation transport. We investigate the capabilities of the Deep Operator network (DeepONet) approach to modelling the high dimensional collision operator of the linear kinetic equation. This integral operator has crucial analytical structures that a surrogate model, e.g., a DeepONet, needs to preserve to enable meaningful physical simulation. We propose several DeepONet modifications to encapsulate essential structural properties of this integral operator in a DeepONet model. To be precise, we adapt the architecture of the trunk-net so the DeepONet has the same collision invariants as the theoretical kinetic collision operator, thus preserving conserved quantities, e.g., mass, of the modeled many-particle system. Further, we propose an entropy-inspired data-sampling method tailored to train the modified DeepONet surrogates without requiring an excessive expensive simulation-based data generation. © 2024, CC BY-NC-SA.

关键词： Kinetic energy

Detecting and Exploiting Unit Commitment Structures in MIPs

学校读者我要写书评

暂无评论

Detecting and Exploiting Unit Commitment Structures in MIPs

International Conference on Power and Energy Technology (ICPET)

作者： Zhao-Gang Su Sheng-Jie Chen Yu-Fei Li Liang Chen Caixia Kou Zhi Cai Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China College of Sciences Beijing University of Posts and Telecommunications Beijing China Beijing Key Laboratory of Research and System Evaluation of Power Dispatching Automation Technology China Electric Power Research Institute Beijing China

ISBN: (数字)9798350375855

ISBN: (纸本)9798350375862

The unit commitment (UC) problem has been extensively researched in the literature, which is typically formulated as a mixed integer programming (MIP) problem. However, current studies lack effective methods to identify potential UC problem structures within a general MIP problem, making it challenging to leverage well-established valid inequalities for UC problems to accelerate the solution process. In this paper, we present a novel detection method that automatically identifies UC structures within an MIP problem by analyzing the relationships between variables and constraints. Moreover, we enhance the MIP formulation by incorporating three well-studied classes of valid inequalities as cutting planes, based on the identified UC structures. Our experiments demonstrate that our proposed UC detection method greatly improves computational efficacy of a standard MIP solver compared to the default setting.

关键词： Integer programming Production Generators Time factors Standards

Asymptotic-preserving schemes for kinetic-fluid modeling of mixture flows with distinct particle sizes

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Jin, Shi Lin, Yiwen School of Mathematical Sciences Shanghai Jiao Tong University Shanghai200240 China Institute of Natural Sciences Shanghai Jiao Tong University Shanghai200240 China Ministry of Education Key Laboratory in Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China

We consider coupled models for particulate flows, where the disperse phase is made of particles with distinct sizes. We are thus led to a system coupling the incompressible Navier-Stokes equations to the multi-component Vlasov-Fokker-Planck equations. We design an asymptotic-preserving numerical scheme to approximate the system. The scheme is based on suitable implicit treatment of the stiff drag force term as well as the Fokker-Planck operator, and can be formally shown to capture the hydrodynamic limit with time step and mesh size independent of the Stokes number. Numerical examples illustrate the accuracy and asymptotic behavior of the scheme, with several interesting applications. Copyright © 2022, The Authors. All rights reserved.

关键词： Navier Stokes equations

Linearly Implicit and High-Order Energy-Preserving Schemes for Highly Oscillatory Hamiltonian Systems

学校读者我要写书评

暂无评论

SSRN

SSRN 2022年

作者： Li, Dongfang Li, Xiaoxi Zhang, Zhimin School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Department of Mathematics Wayne State University DetroitMI48202 United States

In this paper, a family of novel energy-preserving schemes are presented for numerically solving highly oscillatory Hamiltonian systems. These schemes are constructed by using the relaxation idea in the extrapolated Runge–Kutta (ERK) methods. After obtaining the relaxation parameter, it is shown that the methods can be arbitrarily high order accurate, linearly implicit and keep the original discrete energy conserved, while the previous energy-preserving schemes for highly oscillatory Hamiltonian systems are usually fully implicit. Numerical comparisons with various typical energy-preserving schemes are presented. The numerical results show that the proposed schemes are highly competitive and effective. © 2022, The Authors. All rights reserved.

关键词： Runge Kutta methods