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Parallel finite-volume discrete Boltzmann method for inviscid compressible flows on unstructured grids

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Physical Review E 2021年第2期103卷 023306-023306页

作者： Lei Xu Rongliang Chen Xiao-Chuan Cai Shenzhen Institutes of Advanced Technology Chinese Academy of Sciences Shenzhen 518055 China Shenzhen Key Laboratory for Exascale Engineering and Scientific Computing Shenzhen 518055 China Department of Mathematics University of Macau Macau China

In this paper, a finite-volume discrete Boltzmann method based on a cell-centered scheme for inviscid compressible flows on unstructured grids is presented. In the new method, the equilibrium distribution functions are obtained from the circle function in two-dimensions (2D) and the spherical function in three-dimensions (3D). Moreover, the advective fluxes are evaluated by Roe's flux-difference splitting scheme, the gradients of the density and total energy distribution functions are computed with a least-squares method, and the Venkatakrishnan limiter is employed to prevent oscillations. To parallelize the method we use a graph-based partitioning approach that also guarantees the load balancing. The method is validated by seven benchmark problems: (a) a 2D flow pasting a bump, (b) a 2D Riemann problem, (c) a 2D flow passing the RAE2822 airfoil, (d) flows passing the NACA0012 airfoil, (e) 2D supersonic flows around a cylinder, (f) an explosion in a 3D box, and (g) a 3D flow around the ONERA M6 wing. The benchmark tests show that the results obtained by the proposed method match well with the published results, and the parallel numerical experiments show that the proposed parallel implementation has close to linear strong scalability, and parallel efficiencies of 95.31% and 94.56% are achieved for 2D and 3D problems on a supercomputer with up to 4800 processor cores, respectively.

关键词： Aerodynamics High-speed flow Lattice-Boltzmann methods

An Inexact Preconditioned Zeroth-order Proximal Method for Composite Optimization

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arXiv 2024年

作者： Liu, Shanglin Wang, Lei Xiao, Nachuan Liu, Xin State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing101408 China Department of Statistics Pennsylvania State University University Park16802 United States Institute of Operational Research and Analytics National University of Singapore Singapore117597 Singapore

In this paper, we consider the composite optimization problem, where the objective function integrates a continuously differentiable loss function with a nonsmooth regularization term. Moreover, only the function values for the differentiable part of the objective function are available. To efficiently solve this composite optimization problem, we propose a preconditioned zeroth-order proximal gradient method in which the gradients and preconditioners are estimated by finite-difference schemes based on the function values at the same trial points. We establish the global convergence and worst-case complexity for our proposed method. Numerical experiments exhibit the superiority of our developed method. Copyright © 2024, The Authors. All rights reserved.

关键词： Gradient methods

Phase-field based lattice Boltzmann method for containerless freezing

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arXiv 2024年

作者： Huang, Jiangxu Wang, Lei Chai, Zhenhua Shi, Baochang School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China School of Mathematics and Physics China University of Geosciences Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science 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

In this paper, a phase-field based lattice Boltzmann (LB) method is proposed to simulate solid-liquid phase change phenomena in multiphase systems. The method couples the thermal properties of the solidification front with the dynamics of the droplet interface, which enables the description of the complex interfacial changes during solid-liquid phase change process. The volume expansion or shrinkage of the droplet caused by the change of density during phase change is represented by adding a mass source term to the continuum equation. We first test the developed LB method by the three-phase Stefan problem and the droplet solidification on a cold surface, and the numerical results are in good agreement with the analytical and experimental solutions. Then the LB method is used to study the solidification problem with bubbles. The results show that the model can accurately capture the effect of bubbles on the solidification process, which is in good agreement with the previous work. Finally, a parametric study is carried out to examine the influences of some physical parameters on the sessile droplet solidification, and it is found that the time of droplet solidification increases with the increase of droplet volume and contact angle. Copyright © 2024, The Authors. All rights reserved.

关键词： Freezing

A Consistent and Conservative Axisymmetric Lattice Boltzmann Method for Multiphase Electro-Hydrodynamic Flows

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SSRN

SSRN 2024年

作者： Liu, Xi Chai, Zhenhua Shi, Baochang Yuan, Xiaolei School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science 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 College of Mathematics and Information Science Hebei University Baoding071002 China

In this paper, a consistent and conservative mathematical model is first developed for multiphase electro-hydrodynamic (EHD) flows, which has some distinct features in the volume conservation, the consistency of reduction, and the consistency of mass-momentum transport. Then a two-relaxation-time axisymmetric lattice Boltzmann (LB) method is proposed for multiphase EHD flows, and the present LB method consists of three LB models, which are used to solve the axisymmetric reduction-consistent and conservative Allen-Cahn equation for the multiphase field, the axisymmetric Poisson equation for the electric potential, and the axisymmetric consistent and conservative Navier-Stokes equations for the flow field. Owing to the reduction-consistent property, the present LB method can be used to handle a set of M (1≤M≤N) EHD fluids in N-phase system. To test the capacity of the LB method, the deformations of a single two-phase droplet and a ternary-phase compound droplet under a uniform electric field are considered. It is found that different from a single droplet with two deformation modes, the compound droplet has four deformation modes, and additionally, the effects of the electric strength, the conductivity ratio and the permittivity ratio on the compound droplet are also investigated. Finally, the compound droplet in the quaternary-phase system is also explored, and there are eight deformation modes that have not been reported in the available literature. © 2024, The Authors. All rights reserved.

关键词： Navier Stokes equations

Enhanced Contrastive Learning with Multi-Aspect Information for Recommender Systems

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SSRN

SSRN 2022年

作者： Hu, Linfeng Zhou, Wei Luo, Fengji Ni, Shuang Wen, Junhao School of Bigdata and Software Engineering Chongqing University Daxuecheng South Rd. 55 Chognqing400044 China Key Laboratory of Dependable Service Computing in Cyber Physical Society MOE Chognqing400044 China School of Civil Engineering The University of Sydney SydneyNSW2006 Australia

In recent years, graph neural networks (GNNs) as the state-of-art have advanced the solutions of recommender systems. However, the embedding representations of nodes obtained from GNNs-based models are always suboptimal when facing sparse interaction data. Contrastive learning on graphs is proven effective in alleviating the influence of data sparsity. Most related works perform contrastive learning through self-discrimination while ignoring the self-supervised signals from neighboring nodes, which can also be quite crucial in optimizing the representations. To tackle these issues, we propose a model named Enhanced Contrast Learning with Multi-Aspect Information (ECMI) for recommender systems, which aims to capture the self-supervised signals from both the nodes themselves and their neighbors. Specifically, we conducted contrastive learning in the two-layer space separately. We consider structurally directly connected homophilic node pairs as positive examples in explicit space while introducing a social relationship network and an item entity network in implicit space. These two networks can be combined with the interaction network to conduct a two-channel tri-training procedure. This procedure can build more effective contrastive learning by exploring the similar potential neighbors of the target node. We conduct experiments on three public datasets, and the results consistently validate the effectiveness of ECMI. © 2022, The Authors. All rights reserved.

关键词： Recommender systems

Efficient CI-Based One-Bit Precoding for Multiuser Downlink Massive MIMO Systems with PSK Modulation

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arXiv 2021年

作者： Wu, Zheyu Jiang, Bo Liu, Ya-Feng Shao, Mingjie Dai, Yu-Hong The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The Ministry of Education Key Laboratory for NSLSCS School of Mathematical Sciences Nanjing Normal University Nanjing210023 China The School of Information Science and Engineering Shandong University Qingdao China

In this paper, we consider the one-bit precoding problem for the multiuser downlink massive multiple-input multiple-output (MIMO) system with phase shift keying (PSK) modulation. We focus on the celebrated constructive interference (CI)-based problem formulation. We first establish the NP-hardness of the problem (even in the single-user case), which reveals the intrinsic difficulty of globally solving the problem. Then, we propose a novel negative 1 penalty model for the considered problem, which penalizes the one-bit constraint into the objective by a negative 1-norm term, and show the equivalence between (global and local) solutions of the original problem and the penalty problem when the penalty parameter is sufficiently large. We further transform the penalty model into an equivalent min-max problem and propose an efficient alternating proximal/projection gradient descent ascent (APGDA) algorithm for solving it, which performs a proximal gradient decent over one block of variables and a projection gradient ascent over the other block of variables alternately. The APGDA algorithm enjoys a low per-iteration complexity and is guaranteed to converge to a stationary point of the min-max problem and a local minimizer of the penalty problem. To further reduce the computational cost, we also propose a low-complexity implementation of the APGDA algorithm, where the values of the variables will be fixed in later iterations once they satisfy the one-bit constraint. Numerical results show that, compared to the state-of-the-art CI-based algorithms, both of the proposed algorithms generally achieve better bit-error-rate (BER) performance with lower computational cost. Copyright © 2021, The Authors. All rights reserved.

关键词： Gradient methods

ASYMPTOTIC ERROR DISTRIBUTION OF ACCELERATED EXPONENTIAL EULER METHOD FOR PARABOLIC SPDES

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arXiv 2024年

作者： Hong, Jialin Jin, Diancong Wang, Xu Yang, Guanlin LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 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

The asymptotic error distribution of numerical methods applied to stochastic ordinary differential equations has been well studied, which characterizes the evolution pattern of the error distribution in the small step-size regime. It is still open for stochastic partial differential equations whether the normalized error process of numerical methods admits a nontrivial limit distribution. We answer this question by presenting the asymptotic error distribution of the temporal accelerated exponential Euler (AEE) method when applied to parabolic stochastic partial differential equations. In order to overcome the difficulty caused by the infinite-dimensional setting, we establish a uniform approximation theorem for convergence in distribution. Based on it, we derive the limit distribution of the normalized error process of the AEE method by studying the limit distribution of its certain appropriate finite-dimensional approximation process. As applications of our main result, the asymptotic error distribution of a fully discrete AEE method for the original equation and that of the AEE method for a stochastic ordinary differential equation are also obtained. Copyright © 2024, The Authors. All rights reserved.

关键词： Ordinary differential equations

Emergent orbital skyrmion lattice in a triangular atom array

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Physical Review Research 2023年第4期5卷 L042042-L042042页

作者： Rui Cao Jinsen Han Jianmin Yuan Xiaopeng Li Yongqiang Li Department of Physics National University of Defense Technology Changsha 410073 People's Republic of China Department of Physics Graduate School of China Academy of Engineering Physics Beijing 100193 People's Republic of China State Key Laboratory of Surface Physics Key Laboratory of Micro and Nano Photonic Structures (MOE) and Department of Physics Fudan University Shanghai 200433 China Institute for Nanoelectronic Devices and Quantum Computing Fudan University Shanghai 200433 China Shanghai Qi Zhi Institute AI Tower Xuhui District Shanghai 200232 China Hunan Key Laboratory of Extreme Matter and Applications National University of Defense Technology Changsha 410073 China

Multiorbital optical lattices have been attracting rapidly growing research interest in the last several years, providing fascinating opportunities for orbital-based quantum simulations. Here, we consider bosonic atoms loaded in the degenerate p-orbital bands of a two-dimensional triangular optical lattice. This system is described by a multiorbital Bose-Hubbard model. We find the confined atoms in this system develop spontaneous orbital polarization, which forms a chiral Skyrmion lattice pattern in a large regime of the phase diagram. This is an orbital version of the skyrmion, reminiscent of those in spin systems. The emergence of the Skyrmion lattice is confirmed in both bosonic dynamical mean-field theory (BDMFT) and exact diagonalization (ED) calculations. By analyzing the quantum-tunneling-induced orbital-exchange interaction in the strong interaction limit, we find the Skyrmion lattice state arises due to the interplay of p-orbital symmetry and the geometric frustration of the triangular lattice. We provide experimental consequences of the orbital Skyrmion state that can be readily tested in cold atom experiments. Our study implies orbital-based quantum simulations could bring exotic scenarios unexpected from their spin analog.

关键词： Bose-Einstein condensates Cold gases in optical lattices Orbital order 2-dimensional systems Triangular lattice Ultracold gases Dynamical mean field theory Exact diagonalization

Polaron-assisted nonadiabatic dynamics in protonated TiO_(2) with surface water molecule

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ChemPhysMater 2023年第4期2卷 331-336页

作者： Zhongfei Xu Chuanjia Tong Rutong Si Gilberto Teobaldi Limin Liu The Key Laboratory of Resources and Environmental System Optimization Ministry of EducationCollege of Environmental Science and EngineeringNorth China Electric Power UniversityBeijing 102206China School of Physics and Electronics Central South UniversityChangsha 410083China Beijing Computational Science Research Center Beijing 100193China The Abdus Salam International Centre for Theoretical Physics Trieste 34151Italy Scientific Computing Department Science and Technology Facilities Council UK Research and Innovation(STFC-UKRI)Rutherford Appleton LaboratoryHarwell CampusDidcot OX110QXUnited Kingdom School of Chemistry University of SouthamptonHighfieldSouthampton SO171BJUnited Kingdom School of Physics Beihang UniversityBeijing 100191China

We investigated the polaron-assisted nonadiabatic dynamics in protonated TiO_(2),as well as the polaron-H_(2)O coupling and its effects on the relaxation of photogenerated *** observed that different polaron hopping regimes result in varied nonadiabatic couplings and relaxations of excited electrons from the conduction band minimum to the gap states of protonated TiO_(2),with a weak dependence on the actual trapping site of the ***-adsorbed H_(2)O molecules can attract polarons toward the adsorbed Ti sites,with the coupling between H_(2)O and the polaron being inversely proportional to their *** findings suggest that the lifetime of the photogenerated charge carriers can be extended by reducing the polaron-H_(2)O distances,with expected benefits to the efficiency of the reduced TiO 2 samples for photocatalytic applications.

关键词： Protonated Polaron-H_(2)O coupling Nonadiabatic molecule dynamics Lifetime Anatase