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High-order energy stable schemes of incommensurate phase-field crystal model

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arXiv 2020年

作者： Jiang, Kai Si, Wei School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan Xiangtan411105 China

This article focuses on the development of high-order energy stable schemes for the multi-length-scale incommensurate phase-field crystal model which is able to study the phase behavior of aperiodic structures. These high-order schemes based on the scalar auxiliary variable (SAV) and spectral deferred correction (SDC) approaches are suitable for the L2 gradient flow equation, i.e., the Allen-Cahn dynamic equation. Concretely, we propose a second-order Crank-Nicolson (CN) scheme of the SAV system, prove the energy dissipation law, and give the error estimate in the almost periodic function sense. Moreover, we use the SDC method to improve the computational accuracy of the SAV/CN scheme. Numerical results demonstrate the advantages of high-order numerical methods in numerical computations and show the influence of length-scales on the formation of ordered structures. Copyright © 2020, The Authors. All rights reserved.

关键词： Numerical methods

An adaptive virtual element method for the polymer self-consistent field theory

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arXiv 2020年

作者： Wei, Huayi Wang, Xin Chen, Chunyu Jiang, Kai School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan411105 China

In this paper, we develop a high-order adaptive virtual element method (VEM) to simulate the self-consistent field theory (SCFT) model in arbitrary domains. The VEM is very flexible in handling general polygon elements and can treat hanging nodes as polygon vertices without additional processing. Besides, to effectively simulate the phase separation behavior in strong segregation systems, an adaptive method on polygonal mesh equipped with a new marking strategy is developed. This new marking strategy will indicate the times of marked elements to be refined and coarsened, making full use of the information contained in the current numerical results. Using the halfedge data structure, we can apply the adaptive method to the arbitrary polygonal mesh. Numerical results demonstrate that the developed method is efficient in simulating polymers’ phase behavior in complex geometric domains. The accuracy is consistent with theoretical results. The adaptive method can greatly reduce computational costs to obtain prescribed numerical accuracy for strong segregation systems. Copyright © 2020, The Authors. All rights reserved.

关键词： Mean field theory

High-order energy stable schemes of incommensurate phase-field crystal model

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arXiv 2018年

作者： Jiang, Kai Si, Wei School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan411105 China

关键词： Numerical methods

Numerical methods for the mass-conserved Ohta-Kawasaki equation

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arXiv 2019年

作者： Zhang, Juan Li, Shifeng Jiang, Kai School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan Xiangtan411105 China

In this paper, we propose a numerical method to solve the mass-conserved Ohta-Kawasaki equation with finite element discretization. An unconditional stable convex splitting scheme is applied to time approximation. The Newton method and its variant are used to address the implicitly nonlinear term. We rigorously analyze the convergence of the Newton iteration methods. Theoretical results demonstrate that two Newton iteration methods have the same convergence rate, and the Newton method has a smaller convergent factor than the variant one. To reduce the condition number of discretized linear system, we design two efficient block preconditioners and analyze their spectral distribution. Finally, we offer numerical examples to support the theoretical analysis and indicate the efficiency of the proposed numerical methods for the mass-conserved Ohta-Kawasaki equation. Copyright © 2019, The Authors. All rights reserved.

关键词： Newton-Raphson method

The Parallel Generation of 2-D Hilbert Space-filling Curve on GPU

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The Parallel Generation of 2-D Hilbert Space-filling Curve o...

International Conference on Biomedical engineering and Informatics

作者： Chunsheng Feng Shi Shu Junxian Wang Zheng Li Hunan Key Laboratory for Computation & Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan China

ISBN: (纸本)9781467311830

In this paper, we propose two parallel Hilbert Space-filling Curve(HSFC) generation algorithms BMIMp and SDDMp based on block matrix iteration method(BMIM) and state diagrams driver method(SDDM) in the CUDA parallel programming mode. Numerical results show that both of them obtain high parallel speedup. Especially, the speedup of BMIMp and SDDMp can reach 207 and 290 respectively for the 14-order HSFC. Furthermore, BMIMp outperforms SDDMp when considering the total computation time.

关键词： Hilbert Space-filling Curve block matrix iteration method state diagrams driver method CUDA C parallel computation

A Reinforcement Learning Method to Trajectory Design for Manned Lunar Mission via Reshaping Rewards

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A Reinforcement Learning Method to Trajectory Design for Man...

International Conference on Guidance, Navigation and Control, ICGNC 2022

作者： Yang, Luyi Li, Haiyang Li, Xingyong Li, Zeyue Lu, Lin College of Aerospace Science and Engineering National University of Defense Technology Changsha410073 China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Hunan Changsha410073 China

ISBN: (纸本)9789811966125

This paper applies the reinforcement learning (RL) to multi-stage impulsive trajectory design of the manned lunar mission. The manned spacecraft is modeled as the agent and the nonlinear dynamics in the cislunar space is the interaction environment of the agent. Then the Markov decision model is mathematically built for the spacecraft and the optimization goal is to minimize the total impulses in the whole mission. The Q-learning method is used to learn the optimal policy and to better train the agent to explore and exploit the environment, a reshaping reward is designed to improve the convergency and effectiveness of the algorithm. Numerical results give the integrated designs of the lunar transfer orbit, Earth transfer orbit and three-impulsive lunar injection/ejection orbit. The proposed reshaping reward function shows better performance compared with the non-reshaping reward. The conclusions could provide a reference for China’s future manned lunar project. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

关键词： Reinforcement learning

Numerical prediction of inner turbulent flow in conical diffuser by using a new five-point scheme and DLR k-ε turbulence model

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Numerical prediction of inner turbulent flow in conical diff...

The 9th National Conference on Rheology

作者：蒋光彪何永森舒适肖映雄 College of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University

The internal turbulent flow in conical diffuser is a very complicated adverse pressure gradient *** k-ε turbulence model was adopted to study *** every terms of the Laplace operator in DLR k-ε turbulence model and pressure Poisson equation were discretized by upwind difference scheme.A new full implicit difference scheme of 5-point was constructed by using finite volume method and finite difference method.A large sparse matrix with five diagonals was formed and was stored by three arrays of one dimension in a compressed *** iterative methods do not work well with large sparse *** algebraic multigrid method(AMG),linear algebraic system of equations was solved and the precision was set at *** computation results were compared with the experimental *** results show that the computation results have a good agreement with the experiment *** precision of computational results and numerical simulation efficiency are greatly improved.

关键词： conical diffuser turbulent flow DLR k-ε turbulence model 5-point scheme algebraic multigrid method（AMG）

Superconvergence and asymptotic expansion for semidiscrete bilinear finite volume element approximation of the parabolic problem

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Computers & Mathematics with Applications 2013年第1期66卷 91-104页

作者： Cunyun Nie Shi Shu Haiyuan Yu Yuyue Yang Department of Mathematics and Physics Hunan Institution of Engineering Hunan 411104 China Hunan Key Laboratory for Computation & Simulation in Science and Engineering Xiangtan University Hunan 411105 China Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education Xiangtan University Hunan 411105 China

We first derive the asymptotic expansion of the bilinear finite volume element for the linear parabolic problem by employing the energy-embedded method on uniform grids, and then obtain a high accuracy combination pointwise formula of the derivatives for the finite volume element approximation based on the above asymptotic expansion. Furthermore, we prove that the approximate derivatives have the convergence rate of order two. Numerical experiments confirm the theoretical results.

关键词： Linear parabolic problem Bilinear finite volume element Error asymptotic expansion Superconvergence

Stability of three-dimensional icosahedral quasicrystals in multi-component systems

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arXiv 2019年

作者： Jiang, Kai Si, Wei School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University 411105 China

The relative stability of three-dimensional icosahedral quasicrystals in multi-component systems has been investigated based on a phenomenological coupled-mode Swift-Hohenberg model with two-length-scales. A recently developed projection method, Which provides a unified numerical framework to study periodic crystals and quasicrystals, Is used to compute free energy to high accuracy. Compared with traditional approaches, the advantage of the projection method has also been discussed in detail. A rigorous and systematic computation demonstrates that threedimensional icosahedral quasicrystal and two-dimensional decagonal quasicrystal are both stable phases in such a simple multi-component coupled-mode Swift-Hohenberg model. The result extends the two length-scales interaction mechanism of stabilizing quasicrystals from single-component to multi-component systems. Copyright © 2019, The Authors. All rights reserved.

关键词： Quasicrystals