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arXiv 2025年

作者： Zhang, Juan Luo, Junyue Zhang, Fangfang Yue, Xiaoqiang Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

This paper explores the application of kernel learning methods for parameter prediction and evaluation in the Algebraic Multigrid Method (AMG), focusing on several Partial Differential Equation (PDE) problems. AMG is an efficient iterative solver for large-scale sparse linear systems, particularly those derived from elliptic and parabolic PDE discretizations. However, its performance heavily relies on numerous parameters, which are often set empirically and are highly sensitive to AMG’s effectiveness. Traditional parameter optimization methods are either computationally expensive or lack theoretical support. To address this, we propose a Gaussian Process Regression (GPR)-based strategy to optimize AMG parameters and introduce evaluation metrics to assess their effectiveness. Trained on small-scale datasets, GPR predicts nearly optimal parameters, bypassing the time-consuming parameter sweeping process. We also use kernel learning techniques to build a kernel function library and determine the optimal kernel function through linear combination, enhancing prediction accuracy. In numerical experiments, we tested typical PDEs such as the constant-coefficient Poisson equation, variable-coefficient Poisson equation, diffusion equation, and Helmholtz equation. Results show that GPR-predicted parameters match grid search results in iteration counts while significantly reducing computational time. A comprehensive analysis using metrics like mean squared error, prediction interval coverage, and Bayesian information criterion confirms GPR’s efficiency and reliability. These findings validate GPR’s effectiveness in AMG parameter optimization and provide theoretical support for AMG’s practical application. © 2025, CC BY.

关键词： Poisson equation

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Influences of Element Types on Nonlinear Finite Element Analysis of a Concrete Column Under Near-Field Blast Loading

Influences of Element Types on Nonlinear Finite Element Anal...

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Recent Advances in Applied Mechanics and Mechanical engineering - Select Proceedings of ICAMME 2022

作者： Xu, Jie Hendriks, Max A. N. Rots, Jan G. Tsouvalas, Apostolos College of Aerospace Science and Engineering National University of Defense Technology Hunan Changsha410073 China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Hunan Changsha410073 China Faculty of Civil Engineering and Geosciences Delft University of Technology Zuid Holland Delft2628 CN Netherlands

ISBN: (纸本)9789819923748

Due to the accompanying severe consequences of explosions, the blast puts a great threat to public security. Nonlinear finite element analysis is a possible method for civil engineers to check the integrity of the structures under blast loading without underestimating the limit of the structures. However, different choices of element types would generally put a great influence on the analytical results and the corresponding computational expenses. Therefore, how should civil engineers simplify their physical model into finite element models to gain relatively accurate numerical results with acceptable computational expenses is of great interest. In this article, 6 different types of elements are discussed with different orders and shapes for a certain physical situation, and the corresponding experimental results and the numerical results for a very detailed finite element model are used as the baseline for judgement, which could be helpful for civil engineers to make proper simplifications in the set-up of finite element models. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

关键词： Engineers

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Experimental device and method design for long - term compression creep of composite solid propellant

Experimental device and method design for long - term compre...

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2022 International Conference on Advanced Manufacturing Technology and Manufacturing Systems, ICAMTMS 2022

作者： Deng, Kuangwei Zhou, Weiyong Li, Haiyang College of Aerospace Science and Engineering National University of Defense Technology Hunan Changsha410073 China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Hunan Changsha410073 China

ISBN: (纸本)9781510656840

In order to research the effect of creep behavior and creep mechanical property of composite solid propellant on the structural integrity of long storage solid rocket motor, the semi-electronic compression creep experimental device and experimental method are designed. Then short-term and long-term compression creep experiments were carried out. Based on the experimental results, the compression deformation law of propellant was analysed. The results show that in the short-term compressive creep experiment, the stress-strain relationship of the propellant is still in the linear stage under the stress level of 0.5MPa. In the long-term compressive creep experiment, the stress-strain relationship is obviously nonlinear at the stress level of 0.25MPa. Long-term creep can result in a substantial reduction in propellant failure stress. Long-term creep will lead to large deformation of the propellant and plastic deformation even at relatively low stress level, which will adversely affect the motor structure. © 2022 SPIE.

关键词： Creep

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Generalized Multiscale Finite Element Method for Multicontinuum Coupled Flow and Transport Model

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Lobachevskii Journal of Mathematics 2024年第11期45卷 5343-5356页

作者： Ammosov, D.A. Huang, J. Leung, W.T. Shan, B. Computational Technologies and Artificial Intelligence North-Eastern Federal University Yakutsk 677980 Russian Federation School of Mathematics and Computational Science Xiangtan University National Center for Applied Mathematics in Hunan and Hunan Key Laboratory for Computation and Simulation in Science and Engineering Hunan Xiangtan 411105 China Department of Mathematics City University of Hong Kong Hong Kong Department of Mathematics Texas A & M University College Station 77843 TX United States

Abstract: In this paper, we consider a coupled flow and transport process described by partial differential equations for pressure and concentration. We derive the multicontinuum coupled flow and transport model using the multicontinuum homogenization method. We formulate cell problems with constraints that take into account various homogenized effects. For the resulting multicontinuum model, we develop a multiscale solver based on the Generalized Multiscale Finite Element Method. The combined approach of multicontinuum and multiscale modeling makes it possible to consider complex heterogeneous media with high contrast. We present numerical results for a model problem with two continua and heterogeneous coefficients separable into microscopic and macroscopic parts. The results show the high efficiency of the proposed multiscale approach. © Pleiades Publishing, Ltd. 2024.

关键词： coupled flow and transport generalized multiscale finite element method homogenization miscible displacement multicontinuum

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On the vanishing dissipation limit for the incompressible MHD equations on bounded domains

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science China Mathematics 2022年第1期65卷 31-50页

作者： Qin Duan Yuelong Xiao Zhouping Xin Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China College of Mathematics and Statistics Shenzhen UniversityShenzhen 518060China The Institute of Mathematical Sciences The Chinese University of Hong KongHong Kong 999077China

In this paper,we investigate the solvability,regularity and the vanishing dissipation limit of solutions to the three-dimensional viscous magnetohydrodynamic(MHD)equations in bounded *** the boundary,the velocity field fulfills a Navier-slip condition,while the magnetic field satisfies the insulating *** is shown that the initial boundary value problem has a global weak solution for a general smooth *** importantly,for a flat domain,we establish the uniform local well-posedness of the strong solution with higher-order uniform regularity and the asymptotic convergence with a rate to the solution of the ideal MHD equation as the dissipations tend to zero.

关键词： MHD equations initial boundary value problem vanishing dissipation limit

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An Efficient Saddle Search Method for Ordered Phase Transitions Involving Translational Invariance

SSRN

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SSRN 2024年

作者： Cui, Gang Jiang, Kai Zhou, Tiejun Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

In this work, we propose an efficient nullspace-preserving saddle search (NPSS) method for a class of phase transitions involving translational invariance, where the critical states are often degenerate. The NPSS method includes two stages, escaping from the basin and searching for the index-1 generalized saddle point. The NPSS method climbs upward from the generalized local minimum in segments to overcome the challenges of degeneracy. In each segment, an effective ascent direction is ensured by keeping this direction orthogonal to the nullspace of the initial state in this segment. This method can escape the basin quickly and converge to the transition states efficiently. We apply the NPSS method to the phase transitions between crystals, and between crystal and quasicrystal, based on the Landau-Brazovskii and Lifshitz-Petrich free energy functionals. Numerical results show a good performance of the NPSS method. © 2024, The Authors. All rights reserved.

关键词： Free energy

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A NEURAL MULTIGRID SOLVER FOR HELMHOLTZ EQUATIONS WITH HIGH WAVENUMBER AND HETEROGENEOUS MEDIA

arXiv

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arXiv 2024年

作者： Cui, Chen Jiang, Kai Shu, Shi Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

Solving high-wavenumber and heterogeneous Helmholtz equations presents a longstanding challenge in scientific computing. In this paper, we introduce a deep learning-enhanced multigrid solver to address this issue. By conducting error analysis on standard multigrid applied to a discrete Helmholtz equation, we devise a strategy to handle errors with different frequencies separately. For error components with frequencies distant from the wavenumber, we perform simple smoothing based on local operations at different levels to eliminate them. On the other hand, to address error components with frequencies near the wavenumber, we utilize another multigrid V-cycle to solve an advection-diffusion-reaction (ADR) equation at a coarse scale. The resulting solver, named Wave-ADR-NS, involves parameters learned through unsupervised training. Numerical results demonstrate that Wave-ADR-NS effectively resolves heterogeneous 2D Helmholtz equation with wavenumber up to 2000. Comparative experiments against classical multigrid preconditioners and existing deep learning-based multigrid preconditioners reveals the superior performance of *** Codes 65N22, 65N55, 68T07 Copyright © 2024, The Authors. All rights reserved.

关键词： Helmholtz equation

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Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers

arXiv

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arXiv 2024年

作者： Wang, Zhen Liu, Yun Cui, Chen Shu, Shi Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

Recently, designing neural solvers for large-scale linear systems of equations has emerged as a promising approach in scientific and engineering computing. This paper first introduce the Richardson(m) neural solver by employing a meta network to predict the weights of the long-step Richardson iterative method. Next, by incorporating momentum and preconditioning techniques, we further enhance convergence. Numerical experiments on anisotropic second-order elliptic equations demonstrate that these new solvers achieve faster convergence and lower computational complexity compared to both the Chebyshev iterative method with optimal weights and the Chebyshev semi-iteration method. To address the strong dependence of the aforementioned single-level neural solvers on PDE parameters and grid size, we integrate them with two multilevel neural solvers developed in recent years. Using alternating optimization techniques, we construct Richardson(m)FNS for anisotropic equations and NAG-Richardson(m)-WANS for the Helmholtz equation. Numerical experiments show that these two multilevel neural solvers effectively overcome the drawback of single-level methods, providing better robustness and computational efficiency. Copyright © 2024, The Authors. All rights reserved.

关键词： Iterative methods

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Conservative nonconforming virtual element method for stationary incompressible magnetohydrodynamics

arXiv

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arXiv 2024年

作者： Dong, Xiaojing Huang, Yunqing Wang, Tianwen Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

In this paper, we propose a conservative nonconforming virtual element method for the full stationary incompressible magnetohydrodynamics model. We leverage the virtual element satisfactory divergence-free property to ensure mass conservation for the velocity field. The condition of the well-posedness of the proposed method, as well as the stability are derived. We establish optimal error estimates in the discrete energy norm for both the velocity and magnetic field. Furthermore, by employing a new technique, we obtain the optimal error estimates in L2-norm without any additional conditions. Finally, numerical experiments are presented to validate the theoretical analysis. In the implementation process, we adopt the effective Oseen iteration to handle the nonlinear system. © 2024, CC BY-NC-ND.

关键词： Magnetohydrodynamics

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Convergent analysis of algebraic multigrid method with data-driven parameter learning for non-selfadjoint elliptic problems

arXiv

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arXiv 2024年

作者： Zhang, Juan Luo, Junyue Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

In this paper, we apply the practical GADI-HS iteration as a smoother in algebraic multigrid (AMG) method for solving second-order non-selfadjoint elliptic problem. Additionally, we prove the convergence of the derived algorithm and introduce a data-driven parameter learing method called Gaussian process regression (GPR) to predict optimal parameters. Numerical experimental results show that using GPR to predict parameters can save a significant amount of time cost and approach the optimal parameters accurately. © 2024, CC BY.

关键词： Algebra

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