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A general alternating-direction implicit Newton method for solving complex continuous-time algebraic Riccati matrix equation

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arXiv 2022年

作者： Li, Shifeng Jiang, Kai Zhang, Juan 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, applying the Newton method, we transform the complex continuous-time algebraic Riccati matrix equation into a Lyapunov equation. Then, we introduce an efficient general alternating-direction implicit (GADI) method to solve the Lyapunov equation. The inexact Newton-GADI method is presented to save computational amount effectively. Moreover, we analyze the convergence of the Newton-GADI method. The convergence rate of the Newton-GADI and Newton-ADI methods is compared by analyzing their spectral radii. Furthermore, we give a way to select the quasi-optimal parameter. Corresponding numerical tests are shown to illustrate the effectiveness of the proposed algorithms. © 2022, CC BY-SA.

关键词： Newton-Raphson method

A MULTI-CATEGORY INVERSE DESIGN NEURAL NETWORK AND ITS APPLICATION TO DIBLOCK COPOLYMERS

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arXiv 2022年

作者： Wei, Dan Zhou, Tiejun Huang, Yunqing Jiang, Kai 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 design a multi-category inverse design neural network to map ordered periodic structure to physical parameters. The neural network model consists of two parts, a classifier and Structure-Parameter-Mapping (SPM) subnets. The classifier is used to identify structure, and the SPM subnets are used to predict physical parameters for desired structures. We also present an extensible reciprocal-space data augmentation method to guarantee the rotation and translation invariant of periodic structures. We apply the proposed network model and data augmentation method to two-dimensional diblock copolymers based on the Landau-Brazovskii model. Results show that the multi-category inverse design neural network is high accuracy in predicting physical parameters for desired structures. Moreover, the idea of multi-categorization can also be extended to other inverse design *** Codes 68T07, 35R30, 35Q68, 74E15, 03C64 Copyright © 2022, The Authors. All rights reserved.

关键词： Block copolymers

Two-relaxation-time regularized lattice Boltzmann model for convection-diffusion equation with variable coefficients

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arXiv 2023年

作者： Yu, Yuan Qin, Zuojian Yuan, Haizhuan Shu, Shi School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China National Center for Applied Mathematics in Hunan Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China

In this paper, a new two-relaxation-time regularized (TRT-R) lattice Boltzmann (LB) model for convection-diffusion equation (CDE) with variable coefficients is proposed. Within this framework, we first derive a TRT-R collision operator by constructing a new regularized procedure through the high-order Hermite expansion of non-equilibrium. Then a first-order discrete-velocity form of discrete source term is introduced to improve the accuracy of the source term. Finally and most importantly, a new first-order space-derivative auxiliary term is proposed to recover the correct CDE with variable coefficients. To evaluate this model, we simulate a classic benchmark problem of the rotating Gaussian pulse. The results show that our model has better accuracy, stability and convergence than other popular LB models, especially in the case of a large time step. Copyright © 2023, The Authors. All rights reserved.

关键词： Boltzmann equation

Two-relaxation-time regularized lattice Boltzmann model for Navier-Stokes equations

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arXiv 2023年

作者： Yu, Yuan Qin, Zuojian Chen, Siwei Shu, Shi Yuan, Hai-Zhuan School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China National Center for Applied Mathematics in Hunan Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China

In this paper, we develop a two-relaxation-time regularized lattice Boltzmann (TRT-RLB) model for simulating weakly compressible isothermal flows. A free relaxation parameter, τs,2, is employed to relax the regularized non-equilibrium third-order terms. Chapman-Enskog analysis reveals that our model can accurately recover the Navier-Stokes equations (NSEs). Theoretical analysis of the Poiseuille flow problem demonstrates that the slip velocity magnitude in the proposed model is controlled by a magic parameter, which can be entirely eliminated under specific values, consistent with the classical TRT model. Our simulations of the double shear layer problem, Taylor-Green vortex flow, and force-driven Poiseuille flow confirm that the stability and accuracy of our model significantly surpass those of both the regularized lattice Boltzmann (RLB) and two-relaxation-time (TRT) models, even under super-high Reynolds numbers as Re = 107. Concurrently, the TRT-RLB model exhibits superior performance in very high viscosity scenarios. The simulations of creeping flow around a square cylinder demonstrates the model's capability to accurately compute ultra-low Reynolds numbers as Re = 10−7. This study establishes the TRT-RLB model as a flexible and robust tool in computational fluid dynamics. Copyright © 2023, The Authors. All rights reserved.

关键词： Navier Stokes equations

Missile guidance law design based on free-time convergent error dynamics

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arXiv 2023年

作者： Yuanhe, Liu Nianhao, Xie Kebo, Li Yangang, Liang 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

The design of guidance law can be considered a kind of finite-time error-tracking problem. A unified free-time convergent guidance law design approach based on the error dynamics and the free-time convergence method is proposed in this paper. Firstly, the desired free-time convergent error dynamics approach is proposed, and its convergent time can be set freely, which is independent of the initial states and the guidance parameters. Then, the illustrative guidance laws considering the leading angle constraint, impact angle constraint, and impact time constraint are derived based on the proposed free-time convergent error dynamics respectively. The connection and distinction between the proposed and the existing guidance laws are analyzed theoretically. Finally, the performance of the proposed guidance laws is verified by simulation comparison. Copyright © 2023, The Authors. All rights reserved.

关键词： Errors

ANISOTROPIC ANALYSIS OF VEM FOR TIME-HARMONIC MAXWELL EQUATIONS IN INHOMOGENEOUS MEDIA WITH LOW REGULARITY

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arXiv 2023年

作者： Chen, Chunyu Guo, Ruchi Wei, Huayi School of Mathematics and Computational Science Xiangtan University National Center for Applied Mathematics in Hunan Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan411105 China Department of Mathematics University of California IrvineCA92697 United States

It has been extensively studied in the literature that solving Maxwell equations is very sensitive to the mesh structure, space conformity and solution regularity. Roughly speaking, for almost all the methods in the literature, optimal convergence for low-regularity solutions heavily relies on conforming spaces and highly-regular simplicial meshes. This can be a significant limitation for many popular methods based on polytopal meshes in the case of inhomogeneous media, as the discontinuity of electromagnetic parameters can lead to quite low regularity of solutions near media interfaces, and potentially worsened by geometric singularities, making many popular methods based on broken spaces, non-conforming or polytopal meshes particularly challenging to apply. In this article, we present a virtual element method for solving an indefinite time-harmonic Maxwell equation in 2D inhomogeneous media with quite arbitrary polytopal meshes, and the media interface is allowed to have geometric singularity to cause low regularity. There are two key novelties: (i) the proposed method is theoretically guaranteed to achieve robust optimal convergence for solutions with merely Hθ regularity, θ ∈ (1/2, 1];(ii) the polytopal element shape can be highly anisotropic and shrinking, and an explicit formula is established to describe the relationship between the shape regularity and solution regularity. Extensive numerical experiments will be given to demonstrate the effectiveness of the proposed method. Copyright © 2023, The Authors. All rights reserved.

关键词： Maxwell equations

Stability of diverse dodecagonal quasicrystals in T-shaped liquid crystalline molecules

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arXiv 2024年

作者： Wang, Xin Shi, An-Chang Zhang, Pingwen Jiang, Kai 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 Department of Physics and Astronomy McMaster University HamiltonONL8S4M1 Canada School of Mathematics and Statistics Wuhan University Wuhan430072 China

Quasicrystals are intriguing ordered structures characterized by the lack of translational symmetry and the existence of rotational symmetry. The tiling of different geometric units such as triangles and squares in two-dimensional space can result in a great variety of quasicrystals that could be realized by the self-assembly of liquid crystalline molecules. In this study, we introduce three self-similar dodecagonal tilings, including a novel Diamond-Square-Triangle pattern, composed of triangular and quadrangular tiles and examine their thermodynamic stability by using the self-consistent field theory applied to T-shaped liquid crystalline molecules. Specifically, we detail the inflation rules for the construction of these dodecagonal tilings and analyze their self-similarity, and show that these tilings can be viewed as projections of higher-dimensional periodic lattice points with projection windows. Using these dodecagonal tilings as initial configurations of the SCFT results in solutions corresponding to quasicrystals that could form from the T-shaped liquid crystalline molecules. The relative stability of these aperiodic phases is analyzed to obtain design rules that could stabilize quasicrystals. Meanwhile, we provide two criteria for distinguishing three dodecagonal quasicrystals and their approximants by analyzing their diffraction peaks. These findings shed new lighten on the discovery of new quasicrystals in soft materials. Copyright © 2024, The Authors. All rights reserved.

关键词： Quasicrystals

Design and Characterization of Low-Carbon Supersulfated Cement Prepared Using As-Received Electrolysis Manganese Dioxide Residue

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SSRN

SSRN 2023年

作者： Ma, Wenbo Bai, Tianwen Zhu, Wei Guo, Shuaicheng School of Mechanical Engineering and Mechanics Xiangtan University Xiangtan411105 China College of Civil Engineering Xiangtan University Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China Key Laboratory of Building Safety and Energy Efficiency of the Ministry of Education Hunan University Changsha410082 China International Science Innovation Collaboration Base for Green & Advanced Civil Engineering Materials of Hunan Province Hunan University Changsha410082 China Key Laboratory for Green & Advanced Civil Engineering Materials and Application Technology of Hunan Province College of Civil Engineering Hunan University Changsha410082 China

Utilizing electrolysis manganese dioxide residue (EMDR) to prepare the supersulfated cement can achieve effective waste recycling, and its application can reduce the carbon emission caused by Portland cement. This study aims to quantitatively build the correlation between the mechanical performance and cementitious matrix composition of EMDR-based supersulfated cement. The supersulfated cement containing clinker, slag and as received EMDR is designed and prepared based on the simplex centroid design method. The compressive strength, tensile strength and flexural strength of the EMDR based supersulfated cement paste were measured at 3-day, 7-day and 28-day ages. The compressive strength of the electrolysis manganese dioxide residue (EMDR) based supersulfated cement first increases and then decreases with the mass ratio between slag and EMDR. The added cement clinker can increase the compressive strength at 3-day and 7-day ages, but the 28-day age strength first decrease and then increase with the cement clinker content. Meanwhile, the flexural and tensile performances of the EMDR based supersulfated cement generally increase with the clinker content. The measured elastic modulus results indicated the added clinker could enhance the stiffness of the stiffness development. Then the strength development mechanisms of EMDR-based supersulfated cement are analyzed based on phase and microstructure characterization. It is found the clinker can accelerate the reaction rate between the slag and EMDR, and the consumption rate of the gypsum contained in EMDR. The calcium silicate hydrate (CSH) gel phase's contribution to tensile strength is more significant than that of ettringite phase. Based on the mechanism analysis, the index of [SO3]/[Al2O3] molar ratio is proposed for the matrix design of EMDR based SSC. This study can support the design and application of EMDR-based supersulfated cement. © 2023, The Authors. All rights reserved.

关键词： Aluminum oxide

ACCURATELY RECOVER GLOBAL QUASIPERIODIC SYSTEMS BY FINITE POINTS

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arXiv 2023年

作者： Jiang, Kai Zhou, Qi Zhang, Pingwen 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 School of Mathematics and Statistics Wuhan University Wuhan430072 China School of Mathematical Sciences Peking University Beijing100871 China

Quasiperiodic systems, related to irrational numbers, are space-filling structures without decay nor translation invariance. How to accurately recover these systems, especially for non-smooth cases, presents a big challenge in numerical computation. In this paper, we propose a new algorithm, finite points recovery (FPR) method, which is available for both smooth and non-smooth cases, to address this challenge. The FPR method first establishes a homomorphism between the lower-dimensional definition domain of the quasiperiodic function and the higher-dimensional torus, then recovers the global quasiperiodic system by employing interpolation technique with finite points in the definition domain without dimensional lifting. Furthermore, we develop accurate and efficient strategies of selecting finite points according to the arithmetic properties of irrational numbers. The corresponding mathematical theory, convergence analysis, and computational complexity analysis on choosing finite points are presented. Numerical experiments demonstrate the effectiveness and superiority of FPR approach in recovering both smooth quasiperiodic functions and piecewise constant Fibonacci quasicrystals. While existing spectral methods encounter difficulties in accurately recovering non-smooth quasiperiodic *** Codes 11J68, 65D05, 65D15, 68W25 © 2023, CC BY-NC-ND.

关键词： Interpolation