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Achieving coherent perfect absorption based on flat-band plasmonic Friedrich-Wintgen BIC in borophene metamaterials

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arXiv 2023年

作者： Zhang, Yan-Xi Lin, Qi Yan, Xiao-Qiang Wang, Ling-Ling Liu, Gui-Dong School of Physics and Optoelectronics Xiangtan University Xiangtan411105 China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan411105 China School of Physics and Electronics Hunan University Changsha410082 China

Many applications involve the phenomenon of a material absorbing electromagnetic radiation. By exploiting wave interference, the efficiency of absorption can be significantly enhanced. Here, we propose Friedrich-Wintgen bound states in the continuum (F-W BICs) based on borophene metamaterials to realize coherent perfect absorption with a dual-band absorption peak in commercially important communication bands. The metamaterials consist of borophene gratings and a borophene sheet that can simultaneously support a Fabry-Perot plasmon resonance and a guided plasmon mode. The formation and dynamic modulation of the F-W BIC can be achieved by adjusting the width or carrier density of the borophene grating, while the strong coupling leads to the anti-crossover behavior of the absorption spectrum. Due to the weak angular dispersion originating from the intrinsic flat-band characteristic of the deep sub-wavelength periodic structure, the proposed plasmonic system exhibits almost no change in wavelength and absorption at large incident angles (within 70 degrees). In addition, we employ the temporal coupled-mode theory including near- and far-field coupling to obtain strong critical coupling, successfully achieve coherent perfect absorption, and can realize the absorption switch by changing the phase difference between the two coherent beams. Our findings can offer theoretical support for absorber design and all-optical tuning. Copyright © 2023, The Authors. All rights reserved.

关键词： Absorption spectroscopy

Paired 2-Disjoint Path Covers of Burnt Pancake Graphs with Faulty Elements

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SSRN

SSRN 2024年

作者： Li, Pingshan Chen, Congzhen Liu, Xianglin Xiangtan University China School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China Key Laboratory of Intelligent Computing & Information Processing of Education China Key Laboratory for Computation and Simulation in Science and Engineering China National Center for Applied Mathematics in Hunan China Guangxi Vocational University of Agriculture Guangxi Nanning530007 China

It is a key issue in parallel processing to find $k$-disjoint paths in the underlying graph of an interconnected network such that these disjoint paths pass through all vertices of the network, this is known as paired $k$-disjoint path cover problems or unpaired $k$-disjoint path cover problems. In 2024, Dvo\v{r}\'{a}k and Gu (Theoretical Computer science, $986 (2024) 114327$) showed that there exist two disjoint paths whose vertices partition the vertex of the burnt pancake graph even if it contains at most $n-4$ faulty elements (vertices or edges) and they proposed an open problem: is it possible to improve the upper bound $n-4$ to $n-3$? In this paper, we provide a positive answer to this problem. © 2024, The Authors. All rights reserved.

关键词： Hamiltonians

Multitask kernel-learning parameter prediction method for solving time-dependent linear systems

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arXiv 2022年

作者： Jiang, Kai Zhang, Juan Zhou, Qi 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

Matrix splitting iteration methods play a vital role in solving large sparse linear systems. Their performance heavily depends on the splitting parameters, however, the approach of selecting optimal splitting parameters has not been well developed. In this paper, we present a multitask kernel-learning parameter prediction method to automatically obtain relatively optimal splitting parameters, which contains simultaneous multiple parameters prediction and a data-driven kernel learning. For solving time-dependent linear systems, including linear differential systems and linear matrix systems, we give a new matrix splitting Kronecker product method, as well as its convergence analysis and preconditioning strategy. Numerical results illustrate our methods can save an enormous amount of time in selecting the relatively optimal splitting parameters compared with the exists methods. Moreover, our iteration method as a preconditioner can effectively accelerate GMRES. As the dimension of systems increases, all the advantages of our approaches becomes significantly. Especially, for solving the differential Sylvester matrix equation, the speedup ratio can reach tens to hundreds of times when the scale of the system is larger than one hundred thousand. Copyright © 2022, The Authors. All rights reserved.

关键词： Linear systems

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

Fully-Connected LEO Hybrid Constellation Design with Global Uniform Coverage

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Fully-Connected LEO Hybrid Constellation Design with Global ...

Asian Aerospace and Astronautics Conference (AAAC)

作者： Yao Xiao Shuai Guo Yazhong Luo Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions College of Aerospace Science and Engineering (of National University of Defense Technology) Changsha China

ISBN: (数字)9798350355833

ISBN: (纸本)9798350355840

Low Earth orbit mega-constellations have been deployed with the development of small satellite technology, and the decrease in satellite manufacturing and launch costs. The network connectivity and coverage performance are important factors in evaluating the low Earth orbit mega-constellation system. This study considers the problem of designing a low Earth orbit hybrid mega-constellation to achieve global uniform coverage considering the constraint of constellation connectivity. First, the precondition of establishing inter-satellite links is analyzed and characterized by inter-satellite angular distance. The constraint of the satellite phase and the topology design method among sub-constellations are derived. Then, the coverage longitude width model is established and the coverage ratio of latitudes is proposed. Finally, the coverage uniformity and connectivity models are proposed as the objective and constraint respectively in the hybrid constellation optimization model. A hybrid constellation design example is provided, which achieves a uniformity metric of 0.0186 and a maximum transmission hop of 6.

关键词： Measurement simulation Optimization models Design methodology Low earth orbit satellites Small satellites Orbits Topology Manufacturing Optimization

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

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

FOURIER NEURAL SOLVER FOR LARGE SPARSE LINEAR ALGEBRAIC SYSTEMS

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arXiv 2022年

作者： Cui, Chen Jiang, Kai Liu, Yun 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

Large sparse linear algebraic systems can be found in a variety of scientific and engineering fields, and many scientists strive to solve them in an efficient and robust manner. In this paper, we propose an interpretable neural solver, the Fourier Neural Solver (FNS), to address them. FNS is based on deep learning and Fast Fourier transform. Because the error between the iterative solution and the ground truth involves a wide range of frequency modes, FNS combines a stationary iterative method and frequency space correction to eliminate different components of the error. Local Fourier analysis reveals that the FNS can pick up on the error components in frequency space that are challenging to eliminate with stationary methods. Numerical experiments on the anisotropy diffusion equation, convection-diffusion equation, and Helmholtz equation show that FNS is more efficient and more robust than the state-of-the-art neural *** Codes 65F10 65N22 68T07 35Q68 Copyright © 2022, The Authors. All rights reserved.

关键词： Fourier analysis

γ-DEEPDSM FOR INTERFACE RECONSTRUCTION: OPERATOR LEARNING AND A LEARNING-AUTOMATED FEM PACKAGE

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arXiv 2024年

作者： Zheng, Yangyang Wei, Huayi Cao, Shuhao Guo, Ruchi School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan China 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 School of Science and Engineering University of Missouri-Kansas City Kansas CityMO United States School of Mathematics Sichuan University Sichuan Chengdu China

In this work, we propose an Operator Learning (OpL) method for solving boundary value inverse problems in partial differential equations (PDEs), focusing on recovering diffusion coefficients from boundary data. Inspired by the classical Direct Sampling Method (DSM), our operator learner, named γ-deepDSM, has two key components: (1) a data-feature generation process that applies a learnable fractional Laplace-Beltrami operator to the boundary data, and (2) a convolutional neural network that operates on these data features to produce reconstructions. To facilitate this workflow, leveraging FEALPy [52], a cross-platform Computed-Aided-engineering engine, our another contribution is to develop a set of finite element method (FEM) modules fully integrated with PyTorch, called Learning-Automated FEM (LA-FEM). The new LA-FEM modules in FEALPy conveniently allows efficient parallel GPU computing, batched computation of PDEs, and auto-differentiation, without the need for additional loops, data format conversions, or device-to-device transfers. With LA-FEM, the PDE solvers with learnable parameters can be directly integrated into neural network models. Copyright © 2024, The Authors. All rights reserved.

关键词： Convolutional neural networks