检索结果-内蒙古大学图书馆

Spectral Galerkin Method for Solving Elastic Wave Scattering Problems with Multiple Open Arcs

学校读者我要写书评

暂无评论

SSRN

SSRN 2022年

作者： Jerez-Hanckes, Carlos Pinto, José Yin, Tao Faculty of Engineering and Sciences Universidad Adolfo Ibáñez Diagonal Las Torres 2700 Peñalolén Santiago Chile Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

We study the elastic time-harmonic wave scattering problems on unbounded domains with boundaries composed of finite collections of disjoints finite open arcs (or cracks) in two dimensions. Specifically, we present a fast spectral Galerkin method for solving the associated weakly- and hyper-singular boundary integral equations (BIEs) arising from Dirichlet and Neumann boundary conditions, respectively. Discretization bases of the resulting BIEs employ weighted Chebyshev polynomials that capture the solutions’ edge behavior. We show that these bases guarantee exponential convergence in the polynomial degree when assuming analyticity of sources and arcs geometries. Numerical examples demonstrate the accuracy and robustness of the proposed method with respect to number of arcs and wavenumber. © 2022, The Authors. All rights reserved.

关键词： Boundary integral equations

Meson spectroscopy from spectral densities in lattice gauge theories

学校读者我要写书评

暂无评论

Physical Review D 2024年第7期110卷 074509页

作者： Ed Bennett Luigi Del Debbio Niccolò Forzano Ryan C. Hill Deog Ki Hong Ho Hsiao Jong-Wan Lee C.-J. David Lin Biagio Lucini Alessandro Lupo Maurizio Piai Davide Vadacchino Fabian Zierler Swansea Academy of Advanced Computing Higgs Centre for Theoretical Physics School of Physics and Astronomy Department of Physics Faculty of Science and Engineering School of Physics and Astronomy Department of Physics Extreme Physics Institute Institute of Physics Particle Theory and Cosmology Group Center for Theoretical Physics of the Universe Centre for High Energy Physics Centre for Theoretical and Computational Physics Department of Mathematics Faculty of Science and Engineering Université de Toulon CNRS CPT Marseille France Centre for Mathematical Sciences

Spectral densities encode nonperturbative information that enters the calculation of a plethora of physical observables in strongly coupled field theories. Phenomenological applications encompass aspects of standard-model hadronic physics, observable at current colliders, as well as correlation functions characterizing new physics proposals, testable in future experiments. By making use of numerical data produced in a Sp(4) lattice gauge theory with matter transforming in an admixture of fundamental and 2-index antisymmetric representations of the gauge group, we perform a systematic study to demonstrate the effectiveness of recent technological progress in the reconstruction of spectral *** this purpose, we write and test new software packages that use energy-smeared spectral densities to analyze the mass spectrum of mesons. We assess the effectiveness of different smearing kernels and optimize the smearing parameters to the characteristics of available lattice ensembles. For concreteness, we analyze the Sp(4) lattice gauge theory with matter transforming in an admixture of fundamental and 2-index antisymmetric representations of the gauge group. We generate new ensembles for the theory in consideration, with lattices that have a longer extent in the time direction with respect to the spatial ones. We run our tests on these ensembles, obtaining new results about the spectrum of light mesons and their excitations. We make available our algorithm and software for the extraction of spectral densities, that can be applied to theories with other gauge groups, including the theory of strong interactions (QCD) governing hadronic physics in the standard model.

关键词： Hybrid Monte Carlo algorithm Lattice field theory

On the hyper-singular boundary integral equation methods for dynamic poroelasticity: three dimensional case

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Zhang, Lu Xu, Liwei Yin, Tao School of Mathematical Sciences University of Electronic Science and Technology of China Sichuan Chengdu611731 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

In our previous work [SIAM J. Sci. Comput. 43(3) (2021) B784-B810], an accurate hyper-singular boundary integral equation method for dynamic poroelasticity in two dimensions has been developed. This work is devoted to studying the more complex and difficult three-dimensional problems with Neumann boundary condition and both the direct and indirect methods are adopted to construct combined boundary integral equations. The strongly-singular and hyper-singular integral operators are reformulated into compositions of weakly-singular integral operators and tangential-derivative operators, which allow us to prove the jump relations associated with the poroelastic layer potentials and boundary integral operators in a simple manner. Relying on both the investigated spectral properties of the strongly-singular operators, which indicate that the corresponding eigenvalues accumulate at three points whose values are only dependent on two Lamé constants, and the spectral properties of the Calderón relations of the poroelasticity, we propose low-GMRES-iteration regularized integral equations. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed methodology by means of a Chebyshev-based rectangular-polar solver. Copyright © 2022, The Authors. All rights reserved.

关键词： Boundary integral equations

QUASI-LINEAR FRACTIONAL-ORDER OPERATORS IN LIPSCHITZ DOMAINS

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Borthagaray, Juan Pablo Li, Wenbo Nochetto, Ricardo H. Instituto de Matemática y Estadística "Rafael Laguardia" Facultad de Ingeniería Universidad de la República Montevideo Uruguay Institute of Computational Mathematics and Scientific/Engineering Computing The Chinese Academy of Sciences Beijing100190 China Department of Mathematics Institute for Physical Science and Technology University of Maryland College ParkMD20742 United States

We prove Besov boundary regularity for solutions of the homogeneous Dirichlet problem for fractional-order quasi-linear operators with variable coefficients on Lipschitz domains Ω of Rd. Our estimates are consistent with the boundary behavior of solutions on smooth domains and apply to fractional p-Laplacians and operators with finite horizon. The proof exploits the underlying variational structure and uses a new and flexible local translation operator. We further apply these regularity estimates to derive novel error estimates for finite element approximations of fractional p-Laplacians and present several simulations that reveal the boundary behavior of solutions. © 2023, CC BY.

关键词： Mathematical operators

Joint design of hybrid beamforming and reflection coefficients in RIS-aided mmWave MIMO systems

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Li, Renwang Guo, Bei Tao, Meixia Liu, Ya-Feng Yu, Wei Department of Electronic Engineering Shanghai Jiao Tong University Shanghai China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Department of Electrical and Engineering University of Toronto TorontoONM5S 3G4 Canada

This paper considers a reconfigurable intelligent surface (RIS)-aided millimeter wave (mmWave) downlink communication system where hybrid analog-digital beamforming is employed at the base station (BS). We formulate a power minimization problem by jointly optimizing hybrid beamforming at the BS and the response matrix at the RIS, under the signalto-interference-plus-noise ratio (SINR) constraints at all users. The problem is highly challenging to solve due to the nonconvex SINR constraints as well as the unit-modulus phase shift constraints for both the RIS reflection coefficients and the analog beamformer. A two-layer penalty-based algorithm is proposed to decouple variables in SINR constraints, and manifold optimization is adopted to handle the non-convex unitmodulus *** also propose a low-complexity sequential optimization method, which optimizes the RIS reflection coefficients, the analog beamformer, and the digital beamformer sequentially without iteration. Furthermore, the relationship between the power minimization problem and the max-min fairness (MMF) problem is discussed. Simulation results show that the proposed penalty-based algorithm outperforms the stateof-the-art semidefinite relaxation (SDR)-based algorithm. Results also demonstrate that the RIS plays an important role in the power reduction. Copyright © 2022, The Authors. All rights reserved.

关键词： Millimeter waves

PROJECTION METHOD FOR QUASIPERIODIC ELLIPTIC EQUATIONS AND APPLICATION TO QUASIPERIODIC HOMOGENIZATION

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Jiang, Kai Li, Meng Zhang, Juan Zhang, Lei 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 School of Mathematical Sciences Institute of Natural Sciences MOE-LSC Shanghai Jiao Tong University Shanghai200240 China

In this study, we address the challenge of solving elliptic equations with quasiperiodic coefficients. To achieve accurate and efficient computation, we introduce the projection method, which enables the embedding of quasiperiodic systems into higher-dimensional periodic systems. To enhance the computational efficiency, we propose a compressed storage strategy for the stiffness matrix by its multi-level block circulant structure, significantly reducing memory requirements. Furthermore, we design a diagonal preconditioner to efficiently solve the resulting high-dimensional linear system by reducing the condition number of the stiffness matrix. These techniques collectively contribute to the computational effectiveness of our proposed approach. Convergence analysis shows the spectral accuracy of the proposed method. We demonstrate the effectiveness and accuracy of our approach through a series of numerical examples. Moreover, we apply our method to achieve a highly accurate computation of the homogenized coefficients for a quasiperiodic multiscale elliptic *** Codes 65D05, 65D15, 65F08, 35B15, 35B27 Copyright © 2024, The Authors. All rights reserved.

关键词： Stiffness matrix

Convergence analysis of PM-BDF2 method for quasiperiodic parabolic equations

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Jiang, Kai Li, Meng Zhang, Juan Zhang, Lei Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing Ministry of Education Department of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China School of Mathematical Sciences Institute of Natural Sciences MOE-LSC Shanghai Jiao Tong University Shanghai200240 China

Numerically solving parabolic equations with quasiperiodic coefficients is a significant challenge due to the potential formation of space-filling quasiperiodic structures that lack translational symmetry or decay. In this paper, we introduce a highly accurate numerical method for solving time-dependent quasiperiodic parabolic equations. We discretize the spatial variables using the projection method (PM) and the time variable with the second-order backward differentiation formula (BDF2). We provide a complexity analysis for the resulting PM-BDF2 method. Furthermore, we conduct a detailed convergence analysis, demonstrating that the proposed method exhibits spectral accuracy in space and second-order accuracy in time. Numerical results in both one and two dimensions validate these convergence results, highlighting the PMBDF2 method as a highly efficient algorithm for addressing quasiperiodic parabolic equations. Copyright © 2024, The Authors. All rights reserved.

关键词： Convergence of numerical methods

Vaccine efficacy and SARS-CoV-2 control in California and *** the session 2020e2026:A modeling study

学校读者我要写书评

暂无评论

Infectious Disease Modelling 2022年第1期7卷 62-81页

作者： Md Shahriar Mahmud Md Kamrujjaman Md Mashih Ibn Yasin Adan Md Alamgir Hossain Md Mizanur Rahman Md Shahidul Islam Muhammad Mohebujjaman Md Mamun Molla Department of Computer Science and Engineering State University of BangladeshDhaka1205Bangladesh Department of Mathematics University of DhakaDhaka1000Bangladesh Department of Mathematics and Statistics University of CalgaryCalgaryABCanada Computational Biology Research Lab(CBRL) Department of PharmacyJagannath UniversityDhaka1100Bangladesh Hitotsubashi Institute for Advanced Study Hitotsubashi UniversityNaka KunitachiTokyo186-8601Japan Department of Mathematics and Physics Texas A&M International UniversityLaredoTX78041USA Department of Mathematics&Physics North South UniversityDhaka1229Bangladesh Center for Applied Scientific Computing(CASC) North South UniversityDhaka1229Bangladesh

Background:Besides maintaining health precautions,vaccination has been the only prevention from SARS-CoV-2,though no clinically proved 100%effective vaccine has been developed till *** this stage,to withhold the debris of this pandemic-experts need to know the impact of the vaccine efficacy rates,the threshold level of vaccine effectiveness and how long this pandemic may extent with vaccines that have different efficacy *** this article,a mathematical model study has been done on the importance of vaccination and vaccine efficiency rate during an ongoing ***:We simulated a five compartment mathematical model to analyze the pandemic scenario in both California,and whole *** considered four vaccines,Pfizer(95%),Moderna(94%),AstraZeneca(79%),and Johnson&Johnson(72%),which are being used rigorously to control the SARS-CoV-2 pandemic,in addition with two special cases:a vaccine with 100%efficacy rate and no vaccine under ***-CoV-2 related data of California,and *** used in this ***:Both the infection and death rates are very high in *** model suggests that the pandemic situation in California will be under control in the last quartile of the year 2023 if vaccination program is continued with the Pfizer *** this time,six waves may happen from the beginning of the immunization where the case fatality and recovery rates will be 1.697%and 98.30%,***,according to the considered model,this period might be extended to the mid of 2024 when vaccines with lower efficacy rates are *** the other hand,the daily cases and deaths in the *** be under control at the end of 2026 with multiple *** the number of susceptible people will fall down to none in the beginning of 2027,there is less chance to stop the vaccination program if vaccinated with a vaccine other than a 100%effective vaccine or Pfizer,and at that case vaccination program must run till the mid of *** to this s

关键词： Vaccine Model California Control measurement SARS-CoV-2

Securing Neural Network in the Cloud: A Systematic Approach of Cloud Security Based on ANN-SVM Model

学校读者我要写书评

暂无评论

Securing Neural Network in the Cloud: A Systematic Approach ...

Sustainable Expert Systems (ICSES), International Conference on

作者： Ar Arunarani V. Vijayagopal L. Kartheesan Vijay Kumar Dwivedi Rajesh Kumar A Neerav Nishant Department of Computational Intelligence School of Computing College of Engineering SRM Institute of Science and Technology Chennai Tamilnadu India Faculty of Computer Applications Dr. M.G.R. Educational and Research Institute Chennai Tamilnadu India Department of Computer Science and Engineering School of Computing Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology Chennai Tamilnadu India Department of Mathematics Vishwavidyalaya Engineering College Surguja Chhattisgarh India Department of Computer Science and Engineering N.S.N. College of Engineering and Technology Karur Tamilnadu India Department of Computer Science and Engineering School of Engineering Babu Banarasi Das University Lucknow India

ISBN: (数字)9798331540364

ISBN: (纸本)9798331540371

Many services have made the transition to the cloud because of the increased reliability and efficiency of cloud computing. Due to their capacity to ease service access while also securing communications in the public network, the three-factor Mutual Authentication and Key Agreement (MAKA) protocols are seeing increased use in multi-server designs. A lack of formal security proof or high communication and computation costs makes the limited three-factor MAKA protocols that are currently available susceptible to a wide range of attacks. The proposed approach consists of three phases, which are preprocessing, feature selection, and model training. Text scheduling and normalization make up preprocessing. In feature selection, the PSO is an optimization method that uses a population-based approach to find optimal solutions. An ANN-SVM was employed throughout the model's training phase. With an average accuracy of 93.30%, the proposed technique surpasses ANN and SVM.

关键词： Training Support vector machines Protocols Accuracy Systematics Cloud computing security Neural networks Feature extraction Vectors Reliability