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

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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Attitude and Orbit Control for Closely Observing Attitude-Dodging Target

Attitude and Orbit Control for Closely Observing Attitude-Do...

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International Conference on Guidance, Navigation and Control, ICGNC 2022

作者： Huang, Xuan Zhang, Jin Zhang, Hanyu Liu, Yuanhe College of Aerospace Science and Engineering National University of Defense Technology Changsha410072 China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Changsha410072 China

ISBN: (纸本)9789811966125

Aiming at the situation that the non-cooperative spacecraft keeps the specific surface facing away from the active spacecraft through attitude dodging, the six-degree-of-freedom (6-DOF) attitude and orbit control of the active spacecraft for proximity observation is studied. Based on the relative orbit and attitude dynamics model, an orbit maneuver strategy is proposed, which uses the target's control time delay to fly around the target first at an accelerated angular rate and then at a constant angular rate. Then the desired attitude of the active spacecraft is designed, so as to realize continuous tracking observation of the specific surface of the target. A 6-DOF fly-around-observation hyperbolic-tangent sliding mode controller (HTSMC) considering unknown bounded disturbances is designed, and the stability of the HTSMC is proven. The simulations indicate that the fly-around observation strategy is reasonable and feasible, and the HTSMC has a short convergence time and high control accuracy. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

关键词： Time delay

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A Task Allocation Algorithm of Loitering Munition Group for Regional Blockade Based on Event-Driven 1

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3rd International Conference on Autonomous Unmanned Systems, ICAUS 2023

作者： Zhu, Yunchong Li, Kebo Liu, Yuanhe Liang, Yan’gang College of Aerospace Science and Engineering National University of Defense Technology Changsha410073 China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Mission Changsha410073 China

ISBN: (数字)9789819710874

ISBN: (纸本)9789819710867

Propose an event-driven online task allocation algorithm to solve the problem of online task allocation for the Loitering Munition Group, which has no information about any targets in operational area. Firstly, analyzing the properties of enemy and friendly equipment in typical regional blockade operations and designing the process of unknown regional blockade operations. Secondly, propose the concept of "benefit-cost ratio" to drive the dynamic scrolling of the task allocation window, and achieve a fast response to sudden events such as new target appearance or projectile damage execution, and timely adjust the task allocation plan. Then, construct a simulation system for the Loitering Munition Group's regional blockade operation, conduct Monte Carlo simulation to verify the effectiveness and reliability of the online task allocation method. © Beijing HIWING Scientific and Technological Information Institute 2024.

关键词： Monte Carlo methods

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GTO Maneuver Trajectory Optimization Based on Analytical Model Iteration

GTO Maneuver Trajectory Optimization Based on Analytical Mod...

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International Conference on Guidance, Navigation and Control, ICGNC 2022

作者： Zhang, Hanyu Zhang, Jin Huang, Xuan College of Aerospace Science and Engineering National University of Defense Technology Changsha410073 China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Changsha410073 China

ISBN: (纸本)9789811966125

This paper proposes a fast, efficient, and applicable optimization method for geosynchronous transfer orbit (GTO) maneuvers. The strategy with combined maneuvers executed at apogees is adopted, and the maneuver parameters are calculated using the geometric relationship of velocity vectors and orbital parameters. The initial guess is calculated based on the J2 analytical dynamics model, and then the targeting iterative method based on analytical impulse calculation and numerical orbital integration is used for local optimization to obtain the high-precision solution. Finally, the trajectory optimization problems for GTO maneuvers launched from four different launch sites are simulated to verify the applicability and efficiency of the method. The results show that the proposed method has good convergence ability, the calculating time is less than 60 s, and the required number of numerical integration is less than 100. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

关键词： Analytical models

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Guidance Law Design for Varying-Speed Missile Based on Classic Differential Geometric Principle

Guidance Law Design for Varying-Speed Missile Based on Class...

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International Conference on Guidance, Navigation and Control, ICGNC 2022

作者： Liu, Yuanhe Li, Kebo Qin, Xuesheng Liang, Yan’gang College of Aerospace Science and Engineering National University of Defense Technology Changsha410072 China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Changsha410072 China

ISBN: (纸本)9789811966125

For the guidance law design problem of the varying-speed missile against the stationary target, a differential geometric guidance law (DGGL) design approach is proposed in this paper. The missile kinematic model and guidance model in the arc-length domain are first derived through the differential geometric curve theory (DGCT). The concept of guidance curvature is introduced. Then, considering the nonlinearity of the guidance model, the error dynamic approach is extended to the arc-length domain, and several typical desired error dynamic equations are introduced. On this basis, taking the optimal error dynamics approach as an example, the corresponding DGGLs are derived. The optimality of the designed guidance law is extended to the scenarios of nonlinearity and varying speed. Finally, the corresponding DGGLs are simulated and compared in varying-speed missile scenarios to demonstrate the effectiveness of the proposed approach. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

关键词： Geometry

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Minimum-Effort Waypoint-Following Differential Geometric Guidance Law Design for UAVs

Minimum-Effort Waypoint-Following Differential Geometric Gui...

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2022 IEEE International Conference on Unmanned Systems, ICUS 2022

作者： Qin, Xue-Sheng Zhang, Tao-Tao Li, Ke-Bo Liang, Yan-Gang Liu, Yuan-He College of Aerospace Science and Engineering National University of Defense Technology Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Changsha China College of Weapons Engineering Naval University of Engineering Wuhan China

ISBN: (数字)9781665484565

ISBN: (纸本)9781665484565

The minimum-effort waypoint-following differential geometric guidance (MEWFDGG) for unmanned aerial vehicles (UAVs) is proposed in this paper. Using the classic differential geometry curve theory, the optimal guidance problem of UAV is transformed into the optimal space curve design problem where the guidance command is the curvature of the space curve. The speed change of UAV is decoupled from the corresponding guidance law design problem. The commonly adopted constant speed hypothesis is released, and hence the performance of the proposed MEWFDGG will not be influenced by varying-speed of UAV. The theoretical analysis demonstrates that MEWFDGG could be applied to general waypoint-following tasks with arbitrary waypoint number. The superiority and effectiveness of MEWFDGG are verified by numerical simulation examples. © 2022 IEEE.

关键词： Antennas

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APF-Based Control for On-Orbit Swarm Guard Against Multiple Threat Targets 7th

APF-Based Control for On-Orbit Swarm Guard Against Multiple ...

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7th Chinese Conference on Swarm Intelligence and Cooperative Control, CCSICC 2023

作者： Wang, Hanwei Zhang, Jiacheng Zhu, Yuehe Luo, Yazhong Jin, Ke Zhang, Yu Fu, Lifeng College of Aerospace Science and Engineering National University of Defense Technology Changsha410073 China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Changsha410073 China

ISBN: (纸本)9789819733279

With the number of satellites and space debris growing fast, it is significant to develop a swarm-to-swarm defense method to protect the on-orbit high value spacecraft. In order to solve the difficulties of swarm assignment combinations, unpredictable threat target maneuvers, non-Euclidean dynamics, and real-time control requirements, a novel method mainly based on Hungarian algorithm and artificial potential fields is proposed. The method involves rapidly searching the one-to-one mission assignment scheme and generating control laws of defenders in real time. Both a positive and a conservative defend strategy are proposed. Case studies show that the computation time of the instantaneous target assignment and control scheme is 0.08 ms. When defenders are not less than threat targets and their maneuverability are the same, the interception number is 100%. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.

关键词： Space debris

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

arXiv

引用

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

arXiv

引用

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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