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SSRN 2023年

作者： Hu, Lijun Tan, Shide Li, Long Yuan, Haizhuan School of Mathematics and Statistics Hengyang Normal University Hunan Hengyang421002 China School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan Xiangtan411105 China

The Roe's flux difference splitting scheme has been a popular shock-capturing method in computational fluid dynamics due to its high resolution for various discontinuities. However, it fails to satisfy the entropy condition and will encounter different forms of instability while calculating shock wave problems, such as the occurrence of post-shock oscillation in simulations of slowly moving shock waves and the carbuncle phenomenon in simulations of multidimensional strong shock waves. A simple flux difference splitting scheme based on the idea of convection-pressure splitting is proposed in the present work. The flux of the 3D Euler equations is split into the convection part and the pressure part with application of the Toro-Vazquez splitting procedure. The pressure subsystem has a complete set of linearly independent eigenvectors and thus it is solved by the conventional flux difference splitting method which is based on the eigenstructure of the system. The weakly hyperbolic convection subsystem, however, does not have a complete set of linearly independent eigenvectors and it is solved by the flux difference splitting scheme based on the generalized eigenvectors. In order to improve the resolution for contact discontinuities, a strategy combining the THINC reconstruction with the BVD algorithm is employed to minimize the density difference in the numerical dissipation term of the convection flux. Results of stability analysis show that the proposed scheme can effectively attenuate the numerical error and thus suppress the multidimensional shock instability. A comprehensive range of numerical simulations for classical 1D, 2D and 3D benchmark test problems demonstrate that the proposed scheme satisfies the entropy condition and positivity-preserving, possesses high resolution for contact discontinuities, and, more importantly, is free from the post-shock oscillation of slowly moving shock waves and the instability of multidimensional strong shock waves. © 2023, Th

关键词： Eigenvalues and eigenfunctions

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

SSRN

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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

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Two-Relaxation-Time Regularized Lattice Boltzmann Model for Navier-Stokes Equations

SSRN

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SSRN 2024年

作者： Yu, Yuan Qin, Zuojian Gu, Qingqing 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 School of Energy and Power Engineering University of Shanghai for Science and Technology Shanghai200093 China

In this paper, we develop a two-relaxation-time regularized lattice Boltzmann (TRT-RLB) model for simulating weakly compressible isothermal flows, which demonstrates superior stability and accuracy over existing models such as the regularized lattice Boltzmann (RLB) and two-relaxation-time (TRT) models. In this model, 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. Theoretical analysis and numerical experiments both confirm the model’s ability to eliminate non-physical numerical slip associated with the half-way bounce-back scheme. Our simulations of the double shear layer problem and Taylor-Green vortex flow exhibit pronounced advantages in terms of stability and accuracy, even under super-high Reynolds numbers as high as Re = 107. Additionally, the simulation of creeping flow around a square cylinder showcases the model’s precision in computing ultra-low Reynolds numbers down to Re = 10−7. This robust capability confirms the proposed model as a highly effective and adaptable tool in computational fluid dynamics. © 2024, The Authors. All rights reserved.

关键词： Navier Stokes equations

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Identifying possible lncRNA-disease associations based on deep learning and positive-unlabeled learning

Identifying possible lncRNA-disease associations based on de...

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IEEE International Conference on Bioinformatics and Biomedicine (BIBM)

作者： Lihong Peng Liangliang Huang Yuankang Lu Guangyi Liu Min Chen Guosheng Han School of Computer Science Hunan University of Technology Zhuzhou China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan China

ISBN: (数字)9781665468190

ISBN: (纸本)9781665468206

lncRNAs are involved in many biological processes, and their mutations and disorders are closely related to many diseases. Identification of LncRNA-Disease Associations (LDAs) helps us understand the pathogenesis of diseases and improve their diagnosis and treatment. However, experiments to determine LDAs are expensive, so it is essential to exploit effective computational methods to screen possible LDAs. In this study, we developed an LDA prediction model (LDA-DLPU) based on deep learning and positive-unlabeled (PU) learning. First, LDA-DLPU extracted features of lncRNAs and diseases based on singular value decomposition and regression model. Second, it selected negative LDAs based on PU learning and graph autoencoder. Finally, it classified unknown lncRNA-disease pairs based on deep neural network. LDA-DLPU obtained the best performance on two datasets. We predict that BCYRN1 and IFNG-AS1 may associate with leukemia.

关键词： Deep learning Computational modeling Neural networks Biological processes Predictive models Feature extraction Bioinformatics

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Two-Relaxation-Time Regularized Lattice Boltzmann Model for Navier-Stokes Equations

SSRN

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SSRN 2024年

作者： Yu, Yuan Qin, Zuojian Chen, Siwei Shu, Shi Yuan, Hai-Zhuan aSchool of Mathematics and Computational Science Xiangtan University Xiangtan 411105 China bNational Center for Applied Mathematics in Hunan Xiangtan 411105 China cHunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan 411105 China

In this paper, we propose a novel two-relaxation-time regularized lattice Boltzmann (TRTRLB) model for simulating weakly compressible isothermal flows. A free relaxation parameter, τs,2, is employed to relax the regularized non-equilibrium third-order terms. ChapmanEnskog 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. © 2024, The Authors. All rights reserved.

关键词： Navier Stokes equations

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

arXiv

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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

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FOURIER NEURAL SOLVER FOR LARGE SPARSE LINEAR ALGEBRAIC SYSTEMS

arXiv

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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

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

arXiv

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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

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

arXiv

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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

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

arXiv

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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

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