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A New Triangular Spectral Element Method II: Mixed Formulation and hp-Error Estimates

Numerical Mathematics(Theory,Methods and Applications) 2019年第1期12卷 72-97页

作者： Bingzhen Zhou Bo Wang Li-Lian Wang Ziqing Xie Key Laboratory of High Performance Computing and Stochastic Information Processing(HPCSIP) College of Mathematics and StatisticsHunan Normal UniversityChangsha 410081P.R.China Division of Mathematical Sciences School of Physical and Mathematical SciencesNanyang Technological University637371Singapore

Mixed triangular spectral element method using nodal basis on unstructured meshes is investigated in this *** method is based on equivalent first order system of the elliptic problem and rectangle-triangle *** fully enjoys the ten-sorial structure and flexibility in handling complex domains by using nodal basis and unstructured triangular *** from the usual Galerkin formulation,the mixed form is particularly advantageous in this context,since it can avoid the singularity in-duced by the rectangle-triangle transform in the calculation of the matrices,and does not require the evaluation of the stiffness *** hp a priori error estimate is pres-ented for the proposed *** implementation details and some numerical exam-ples are provided to validate the accuracy and flexibility of the method.

关键词： Triangular spectral element method hp error analysis mixed form interpolation error in H^(1)-norm

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Analysis of Video Quality Datasets via Design of Minimalistic Video Quality Models

arXiv

引用

arXiv 2023年

作者： Sun, Wei Wen, Wen Min, Xiongkuo Lan, Long Zhai, Guangtao Ma, Kede The Institute of Image Communication and Information Processing Shanghai Jiao Tong University Shanghai200240 China The Department of Computer Science City University of Hong Kong Kowloon Hong Kong The Institute for Quantum Information State Key Laboratory of High Performance Computing College of Computer Science and Technology National University of Defense Technology Changsha410073 China The Institute of Image Communication and Information Processing The MoE Key Lab of Artificial Intelligence AI Institute Shanghai Jiao Tong University Shanghai200240 China The Department of Computer Science The Shenzhen Research Institute City University of Hong Kong Kowloon Hong Kong

Blind video quality assessment (BVQA) plays an indispensable role in monitoring and improving the end-users’ viewing experience in various real-world video-enabled media applications. As an experimental field, the improvements of BVQA models have been measured primarily on a few human-rated VQA datasets. Thus, it is crucial to gain a better understanding of existing VQA datasets in order to properly evaluate the current progress in BVQA. Towards this goal, we conduct a first-of-its-kind computational analysis of VQA datasets via designing minimalistic BVQA models. By minimalistic, we restrict our family of BVQA models to build only upon basic blocks: a video preprocessor (for aggressive spatiotemporal downsampling), a spatial quality analyzer, an optional temporal quality analyzer, and a quality regressor, all with the simplest possible instantiations. By comparing the quality prediction performance of different model variants on eight VQA datasets with realistic distortions, we find that nearly all datasets suffer from the easy dataset problem of varying severity, some of which even admit blind image quality assessment (BIQA) solutions. We additionally justify our claims by comparing our model generalization capabilities on these VQA datasets, and by ablating a dizzying set of BVQA design choices related to the basic building blocks. Our results cast doubt on the current progress in BVQA, and meanwhile shed light on good practices of constructing next-generation VQA datasets and models. Code is available at https://***/sunwei925/***. Copyright © 2023, The Authors. All rights reserved.

关键词： Deep neural networks

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A Complexity-Reduced Block-Selective Algebraic Multigrid Method for Implicitly Coupled Velocity-Pressure System on high performance Computers

SSRN

引用

SSRN 2023年

作者： Liang, Yuechao Guo, Xiao-Wei Li, Chao Yuan, Fan Song, Min Zhang, Qingyang Chen, Xinhai Liu, Jie Science and Technology on Parallel and Distributed Processing Laboratory National University of Defense Technology Changsha410073 China Laboratory of Digitizing Software for Frontier Equipment National University of Defense Technology Changsha410073 China Institute for Quantum Information State Key Laboratory of High Performance Computing College of Computer Science and Technology National University of Defense Technology Changsha410073 China School of Mathematics and Computational Sciences Xiangtan University Xiangtan411105 China College of Computer Science and Technology National University of Defense Technology Changsha410073 China

The implicitly coupled pressure-based algorithm is widely acknowledged for its superior convergence and robustness in solving incompressible flow problems. However, the increased expansion scale of equations and difficulty in solving the resulting equation system has limited the widespread use of the coupling algorithm. This paper presents an optimized block-SAMG method, referred to as Red-SAMG, to significantly reduce computational complexity and memory consumption. Our approach employs a parallel modified independent set algorithm, allowing each process to perform matrix coarsening individually. An aggressive coarsening strategy further reduces complexity to address larger-scale problems. We conducted numerical experiments on a serial two-dimensional backward-facing step case and a parallel three-dimensional tunnel between rod bundles in the reactor core problem. The results demonstrate that the Red-SAMG method with aggressive coarsening reduces solution time by 12\% on the backward-facing step case. For large-scale three-dimensional problems under the same parallel conditions, the Red-SAMG method shortens the solution time by 14\% compared to the existing SAMG method. The Red-SAMG method with aggressive coarsening further reduces solution time by 49\%. Our optimized Red-SAMG method effectively reduces the complexity of the linear system arising from the implicitly coupled algorithm. The aggressive coarsening strategy also represents a significant advancement in improving the computational efficiency of the SAMG method. © 2023, The Authors. All rights reserved.

关键词： Coarsening

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Correction to: Bifurcations in a Hamiltonian system with two degrees of freedom associated to the reversible hyperbolic umbilic

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Nonlinear Dynamics 2021年第3期105卷 2849-2849页

作者： Zhou, Xing Li, Xuemei Key Laboratory of High Performance Computing and Stochastic Information Processing College of Mathematics and Statistics Hunan Normal University Changsha China

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On Rank Factorizations and Factor Prime Factorizations for Multivariate Polynomial Matrices

引用

Journal of Systems Science & Complexity 2018年第6期31卷 1647-1658页

作者： GUAN Jiancheng LI Weiqing OUYANG Baiyu College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China)Hunan Normal UniversityChangsha 410081China Department of Mathematics Xiangnan UniversityChenzhou 423000China College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China)Hunan Normal UniversityChangsha 410081China

In this paper,rank factorizations and factor left prime factorizations are *** authors prove that any polynomial matrix with full row rank has factor left prime *** for a class of polynomial matrices,the authors give an algorithm to decide whether they have rank factorizations or factor left prime factorizations and compute these factorizations if they exist.

关键词： Factor prime factorizations multivariate polynomial matrices rank factorizations

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Existence of Multiple Positive Solutions for Third-Order Three-Point Boundary Value Problem

引用

Journal of Applied Mathematics and Physics 2019年第7期7卷 1463-1472页

作者： Qiufeng Chen Jianli Li Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) Changsha China School of Mathematics and Statistics Hunan Normal University Changsha China

In this paper, we study the existence of positive solutions for a class of third-order three-point boundary value problem. By employing the fixed point theorem on cone, some new criteria to ensure the three-point boundary value problem has at least three positive solutions are obtained. An example illustrating our main result is given. Moreover, some previous results will be improved significantly in our paper.

关键词： Third-Order Three-Point Boundary Value Problem Fixed Point Theorem Three Positive Solutions

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DTCWT-based zinc fast roughing working condition identification

引用

Chinese Journal of Chemical Engineering 2018年第8期26卷 1721-1726页

作者： Zhuo He Zhaohui Tang Zhihao Yan Jinping Liu College of Information Science and Enineering Central South University Changsha 410083China Key Laboratory of High Performance Computing and Stochastic Information Processing of Ministry of Education of China College of Mathematics and Computer ScienceHunan Normal UniversityChangsha 410081China

The surface texture of mineral flotation froth is well acknowledged as an important index of the flotation *** surface texture feature closely relates to the flotation working conditions and hence can be used as a visual indicator for the zinc fast roughing working condition. A novel working condition identification method based on the dual-tree complex wavelet transform(DTCWT) is proposed for process monitoring of zinc fast ***-level DTCWT is implemented to decompose the froth image into different directions and resolutions in advance, and then the energy parameter of each sub-image is extracted as the froth texture feature. Then, an improved random forest integrated classification(i RFIC) with 10-fold cross-validation model is introduced as the classifier to identify the roughing working condition, which effectively improves the shortcomings of the single model and overcomes the characteristic redundancy but achieves higher generalization performance. Extensive experiments have verified the effectiveness of the proposed method.

关键词： DTCWT Working condition Integrated classification model Zinc fast roughing

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Norm estimates of the partial derivatives for harmonic and harmonic elliptic mappings

arXiv

引用

arXiv 2020年

作者： Chen, Shaolin Ponnusamy, Saminathan Wang, Xiantao College of Mathematics and Statistics Hengyang Normal University HengyangHunan421008 China Department of Mathematics Indian Institute of Technology Madras Chennai600 036 India Key Laboratory of High Performance Computing and Stochastic Information Processing College of Mathematics and Statistics Hunan Normal University ChangshaHunan410081 China

Let f = P[F] denote the Poisson integral of F in the unit disk D with F being absolutely continuous in the unit circle T and F∈ Lp(0, 2π), where F (eit) = dtd F (eit) and p ≥ 1. Recently, the author in [12] proved that (1) if f is a harmonic mapping and 1 ≤ p z and fz ∈ Bp(D), the classical Bergman spaces of D [12,_ Theorem 1.2];(2) if f is a harmonic quasiregular mapping and 1 ≤ p ≤ ∞, then fz, fz ∈ Hp(D), the classical Hardy spaces of D [12, Theorem 1.3]. These are the main results in [12]. The purpose of this paper is to generalize these two results. First, we prove that, under the same assumptions, [12, Theorem 1.2] is true when 1 ≤ p MSC Codes Primary: 30C62, 31A05, Secondary: 30H10, 30H20 Copyright © 2020, The Authors. All rights reserved.

关键词： Harmonic analysis

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A Fast Iterative Shrinkage Thresholding Algorithm for Single Particle Reconstruction of Cryo-EM 3

A Fast Iterative Shrinkage Thresholding Algorithm for Single...

引用

3rd IEEE International Conference on Image, Vision and computing, ICIVC 2018

作者： Pan, Huan Wei-Wen, You Zeng, Tieyong College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing Hunan Normal University Changsha Hunan410081 China

ISBN: (纸本)9781538649916

Single particle reconstruction (SPR) from cryo-electron microscopy (cryo-EM) is an emerging technique for determining the three-dimensional (3D) structure of macromolecules. A major challenge in single particle reconstruction from cryo-electron microscopy is to establish a reliable ab initio three-dimensional model using two-dimensional projection images. In this paper we introduce a fast proximal gradient method (FISTA) to solve the corresponding optimization problem of Single particle reconstruction. Numerical experiments with simulated images demonstrate that the proposed methods significantly reduce the estimation error and improved reconstruction quality. © 2018 IEEE.

关键词： Gradient methods

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Temperature dependence of commensurate magnetic resonance in cuprate superconductors 5th

Temperature dependence of commensurate magnetic resonance in...

引用

5th Conference on New Advances in Condensed Matter Physics, NACMP 2018

作者： Lan, Yu Kuang, Lülin Hunan Provincial Key Laboratory of Intelligent Information Processing and Application College of Physics and Electronic Engineering Hengyang Normal University Hengyang421002 China National Research Center for High-Performance Computing Engineering Technology Sugon Beijing100193 China

ISBN: (纸本)9783035713275

Within the kinetic energy driven superconducting mechanism, we have studied the temperature dependence of commensurate magnetic resonance in cuprate superconductors. It is shown that the commensurate magnetic resonance peak at the antiferromagnetic wave vector point persists in the superconducting state until the temperature rises to the superconducting transition temperature Tc. The intensity of the resonance peak decreases with increasing temperature which is just like the temperature dependence of the superconducting gap parameter. Our results are in qualitative agreement with the inelastic neutron scattering experimental data and reflect that the commensurate magnetic resonance is closely related to the creation of the charge carrier pairs and thus the superconducting mechanism of cuprate superconductors. © 2018 Trans Tech Publications, Switzerland

关键词： Temperature distribution

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