检索结果-内蒙古大学图书馆

Potential numerical techniques and challenges for atmospheric modeling

学校读者我要写书评

暂无评论

Potential numerical techniques and challenges for atmospheri...

作者： Li, J. Steppeler, J. Fang, F. Pain, C.C. Zhu, J. Peng, X. Dong, L. Li, Y. Tao, L. Leng, W. Wang, Y. Zheng, J. International Center for Climate and Environment Sciences Institute of Atmospheric Physics Chinese Academy of Sciences Beijing China Hamburg Germany Applied Modelling and Computation Group Department of Earth Science and Engineering Imperial College London London United Kingdom International Center for Climate and Environment Sciences Institute of Atmospheric Physics Chinese Academy of Sciences Department of Atmospheric Sciences University of Chinese Academy of Sciences Beijing China State Key Laboratory of Severe Weather Chinese Academy of Meteorological Sciences Beijing China State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric Physics Chinese Academy of Sciences Beijing China State Key Laboratory of Scientific and Engineering Computing Chinese Academy of Sciences Beijing China School of Mathematics and Statistics Henan University Kaifeng China Center for Excellence in Regional Atmospheric Environment Institute of Urban Environment Chinese Academy of Sciences Xiamen China

Operator Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equations Characterized by Sharp Solutions

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Lin, Bin Mao, Zhiping Wang, Zhicheng Karniadakis, George Em School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University Xiamen361005 China Laboratory of Ocean Energy Utilization Ministry of Education School of Energy and Power Engineering Dalian University of Technology Dalian China Division of Applied Mathematics Brown University ProvidenceRI02906 United States

Physics-informed Neural Networks (PINNs) have been shown as a promising approach for solving both forward and inverse problems of partial differential equations (PDEs). Meanwhile, the neural operator approach, including methods such as Deep Operator Network (DeepONet) and Fourier neural operator (FNO), has been introduced and extensively employed in approximating solution of PDEs. Nevertheless, to solve problems consisting of sharp solutions poses a significant challenge when employing these two approaches. To address this issue, we propose in this work a novel framework termed Operator Learning Enhanced Physics-informed Neural Networks (OL-PINN). Initially, we utilize DeepONet to learn the solution operator for a set of smooth problems relevant to the PDEs characterized by sharp solutions. Subsequently, we integrate the pre-trained DeepONet with PINN to resolve the target sharp solution problem. We showcase the efficacy of OL-PINN by successfully addressing various problems, such as the nonlinear diffusion-reaction equation, the Burgers equation and the incompressible Navier-Stokes equation at high Reynolds number. Compared with the vanilla PINN, the proposed method requires only a small number of residual points to achieve a strong generalization capability. Moreover, it substantially enhances accuracy, while also ensuring a robust training process. Furthermore, OL-PINN inherits the advantage of PINN for solving inverse problems. To this end, we apply the OL-PINN approach for solving problems with only partial boundary conditions, which usually cannot be solved by the classical numerical methods, showing its capacity in solving ill-posed problems and consequently more complex inverse problems. Copyright © 2023, The Authors. All rights reserved.

关键词： Partial differential equations

Unconditionally optimal convergence of an energy-conserving and linearly implicit scheme for nonlinear wave equations

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Cao, Waixiang Li, Dongfang Zhang, Zhimin School of Mathematical Sciences Beijing Normal University Beijing100875 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 Beijing Computational Science Research Center Beijing100193 China Department of Mathematics Wayne State University DetroitMI48202 United States

In this paper, we present and analyze an energy-conserving and linearly implicit scheme for solving the nonlinear wave equations. Optimal error estimates in time and superconvergent error estimates in space are established without time-step dependent on the spatial mesh size. The key is to estimate directly the solution bounds in the H2-norm for both the nonlinear wave equation and the corresponding fully discrete scheme, while the previous investigations rely on the temporal-spatial error splitting approach. Numerical examples are presented to confirm energy-conserving properties, unconditional convergence, and optimal error estimates, respectively, of the proposed fully discrete *** Codes 65M60, 65M12, 65N12 © 2021, CC0.

关键词： Wave equations

Anomalous time-scaling of extreme events in infinite systems and birkhoff sums of infinite observables

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Galatolo, Stefano Holland, Mark Persson, Tomas Zhang, Yiwei Dipartimento di Matematica Via Buonattoti 1 Pisa56127 Italy North Park Road EXETEREX4 4QF United Kingdom Centre for Mathematical Sciences Lund University Box 118 Lund221 00 Sweden Scool of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Sciences and Technology Wuhan430074 China

We establish quantitative results for the statistical behaviour of infinite systems. We consider two kinds of infinite system: i) a conservative dynamical system (f, X, µ) preserving a σ-finite measure µ such that µ(X) = ∞;ii) the case where µ is a probability measure but we consider the statistical behaviour of an observable φ: X → [0, ∞) which is non-integrable: R φ dµ = ∞. In the first part of this work we study the behaviour of Birkhoff sums of systems of the kind ii). For certain weakly chaotic systems, we show that these sums can be strongly oscillating. However, if the system has superpolynomial decay of correlations or has a Markov structure, then we show this oscillation cannot happen. In this case we prove a general relation between the behavior of φ, the local dimension of µ, and the scaling rate of the growth of Birkhoff sums of φ as time tends to infinity. We then establish several important consequences which apply to infinite systems of the kind i). This includes showing anomalous scalings in extreme event limit laws, or entrance time statistics. We apply our findings to non-uniformly hyperbolic systems preserving an infinite measure, establishing anomalous scalings in the case of logarithm laws of entrance times, dynamical Borel-Cantelli lemmas, almost sure growth rates of extremes, and dynamical run length functions.37A40, 37A50, 37A25, 60G75, 37D25 Copyright © 2018, The Authors. All rights reserved.

关键词： Chaotic systems

Large deviations principle for stochastic delay differential equations with super-linearly growing coefficients

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Jin, Diancong Chen, Ziheng Zhou, Tau 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 School of Mathematics and Statistics Yunnan University Kunming650500 China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

We utilize the weak convergence method to establish the Freidlin-Wentzell large deviations principle (LDP) for stochastic delay differential equations (SDDEs) with super-linearly growing coefficients, which covers a large class of cases with non-globally Lipschitz coefficients. The key ingredient in our proof is the uniform moment estimate of the controlled equation, where we handle the super-linear growth of the coefficients by an iterative argument. Our results allow both the drift and diffusion coefficients of the considered equations to super-linearly grow not only with respect to the delay variable but also to the state variable. This work extends the existing results which develop the LDPs for SDDEs with super-linearly growing coefficients only with respect to the delay *** Codes 60H10, 60F10, 60H30 Copyright © 2022, The Authors. All rights reserved.

关键词： Stochastic systems

Freezing dynamics of wetting droplet under a uniform electric field

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Huang, Jiangxu Li, Hanqing Che, Jiaqi Chai, Zhenhua Wang, Lei Shi, Baochang 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 Marine Design & Research Institute of China China The State Key Laboratory of Digital Manufacturing Equipment and Technology Huazhong University of Science and Technology Wuhan430074 China School of Mathematics and Physics China University of Geosciences Wuhan430074 China

Electrofreezing is a powerful technique that employs the electric field to control and enhance the freezing process. In this work, a phase-field-based lattice Boltzmann (LB) method is developed to study the electrofreezing process of sessile droplet on a cooled substrate. The accuracy of the present LB method is first validated through performing some simulations of the three-phase Stefan problem, the droplet freezing on a cold wall, and the droplet deformation under a uniform electric field. Then it is used to investigate the effect of an electric field on the freezing of a wetting droplet on a cold substrate, and the numerical results show that the electric field has a significant influence on the freezing time of the droplet mainly through changing the morphology of the droplet. In particular, under the effect of the electric field, the freezing time is increased for the droplet with a prolate pattern, while the freezing time of the droplet with an oblate pattern is decreased. These numerical results bring some new insights on the electrofreezing and provide a valuable guidance for the precise regulation of droplet freezing. Copyright © 2024, The Authors. All rights reserved.

关键词： Wetting

Spectral gap of sparse bistochastic matrices with exchangeable rows

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Bordenave, Charles Qiu, Yanqi Zhang, Yiwei Institut de Mathématiques de Marseille CNRS Aix-Marseille University 39 Rue Frédéric Joliot Curie Marseille13013 France Institute of Mathematics and Hua Loo-Keng Key Laboratory of Mathematics AMSS Chinese Academy of Sciences Beijing100190 China CNRS Institut de Mathématiques de Toulouse University of Toulouse III School of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Sciences and Technology Wuhan430074 China

We consider a random bistochastic matrix of size n of the form MQ where M is a uniformly distributed permutation matrix and Q is a given bistochastic matrix. Under sparsity and regularity assumptions on Q, we prove that the second largest eigenvalue of MQ is essentially bounded by the normalized Hilbert-Schmidt norm of Q when n grows large. We apply this result to random walks on random regular digraphs.60B20, 60C05, 05C80, 05C38 Copyright © 2018, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

A prediction-correction based iterative convolution-thresholding method for topology optimization of heat transfer problems

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Chen, Huangxin Dong, Piaopiao Wang, Dong Wang, Xiao-Ping School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing Xiamen University Fujian361005 China School of Science and Engineering The Chinese University of Hong Kong Guangdong Shenzhen518172 China Shenzhen International Center for Industrial and Applied Mathematics Shenzhen Research Institute of Big Data Guangdong518172 China

In this paper, we propose an iterative convolution-thresholding method (ICTM) based on prediction-correction for solving the topology optimization problem in steady-state heat transfer equations. The problem is formulated as a constrained minimization problem of the complementary energy, incorporating a perimeter/surface-area regularization term, while satisfying a steady-state heat transfer equation. The decision variables of the optimization problem represent the domains of different materials and are represented by indicator functions. The perimeter/surface-area term of the domain is approximated using Gaussian kernel convolution with indicator functions. In each iteration, the indicator function is updated using a prediction-correction approach. The prediction step is based on the variation of the objective functional by imposing the constraints, while the correction step ensures the monotonically decreasing behavior of the objective functional. Numerical results demonstrate the efficiency and robustness of our proposed method, particularly when compared to classical approaches based on the ICTM. Copyright © 2024, The Authors. All rights reserved.

关键词： Convolution

Structural stability of the transonic shock problem in a divergent three-dimensional axi-symmetric perturbed nozzle

学校读者我要写书评

暂无评论

arXiv 2019年

作者： Weng, Shangkun Xie, Chunjing Xin, Zhouping School OfMathematics and Statistics Wuhan University Wuhan Hubei Province430072 China School of Mathematical Sciences Institute of Natural Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China Institute of Mathematical Sciences Chinese University of Hong Kong Shatin NT Hong Kong

In this paper, we investigate the structural stability of the transonic shock problem in an axisymmetric perturbed nozzle. The axisymmetric perturbation of supersonic incoming flow including the swirl velocity is also considered. We obtain the existence and uniqueness of the piecewise smooth transonic shock solution in a general 3D axisymmetric De Laval nozzle. Due to the singularity on the axis, a key issue is to find an invertible Lagrange transformation to straighten the stream line. Copyright © 2019, The Authors. All rights reserved.

关键词： Lagrange multipliers