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A Fourth-Order Degradation Tensor for an Anisotropic Damage Phase Field Model

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SSRN

SSRN 2023年

作者： Bittencourt, Marco Lúcio Petrini, Ana L.E.R. Esteves, Carlos L.C.S. Boldrini, José L. Department of Integrated Systems School of Mechanical Engineering University of Campinas SP 13083-970 Brazil Department of Applied Mathematics Institute of Mathematics Statistics and Scientific Computing University of Campinas SP 13083-859 Brazil

This work proposes a thermodynamically consistent phase-field model for anisotropic brittle material under the hypotheses of plane stress, small deformation and constant temperature. The model is derived from the principle of virtual power, the first and second laws of thermodynamics in the form of the Clausius-Duhem inequality. The degradation effect on the material behavior is given by a fourth-order degradation tensor introduced as an internal variable that evolves according to the current strain state rather than the conventional scalar degradation function of phase-field models. Therefore, local anisotropy can be induced, changing the material mechanical behavior differently in all directions organically. The proposed degradation tensor is defined in the global coordinate system and therefore is sensitive to any change in the principal directions of the strain and stress states. To demonstrate the model's capability of representing damage in isotropic and transversely isotropic materials, some benchmark examples were carried out. The evolution of the damage components was also analyzed. © 2023, The Authors. All rights reserved.

关键词： Tensors

Spectral Galerkin method for solving elastic wave scattering problems with multiple open arcs

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arXiv 2022年

作者： Jerez-Hanckes, Carlos Pinto, José Yin, Tao Facultad de Ingeniería y Ciencias Universidad Adolfo Ibáñez Santiago Chile LSEC 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, CC BY-NC-SA.

关键词： Elastic waves

Large-Scale Materials Modeling at Quantum Accuracy: Ab Initio Simulations of Quasicrystals and Interacting Extended Defects in Metallic Alloys 23

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Large-Scale Materials Modeling at Quantum Accuracy: Ab Initi...

2023 International Conference for High Performance computing, Networking, Storage and Analysis, SC 2023

作者： Das, Sambit Kanungo, Bikash Subramanian, Vishal Panigrahi, Gourab Motamarri, Phani Rogers, David Zimmerman, Paul Gavini, Vikram Department of Mechanical Engineering University of Michigan Ann Arbor United States Department of Materials Science & Engineering University of Michigan Ann Arbor United States Department of Computational and Data Sciences Indian Institute of Science Bangalore India Scientific Computing Group Oak Ridge National Laboratory Oak Ridge United States Department of Chemistry University of Michigan Ann Arbor United States Department of Materials Science & Engineering University of Michigan Ann Arbor United States

ISBN: (纸本)9798400701092

Ab initio electronic-structure has remained dichotomous between achievable accuracy and length-scale. Quantum many-body (QMB) methods realize quantum accuracy but fail to scale. Density functional theory (DFT) scales favorably but remains far from quantum accuracy. We present a framework that breaks this dichotomy by use of three interconnected modules: (i) invDFT: a methodological advance in inverse DFT linking QMB methods to DFT;(ii) MLXC: a machine-learned density functional trained with invDFT data, commensurate with quantum accuracy;(iii) DFT-FE-MLXC: an adaptive higher-order spectral finite-element (FE) based DFT implementation that integrates MLXC with efficient solver strategies and HPC innovations in FE-specific dense linear algebra, mixed-precision algorithms, and asynchronous compute-communication. We demonstrate a paradigm shift in DFT that not only provides an accuracy commensurate with QMB methods in ground-state energies, but also attains an unprecedented performance of 659.7 PFLOPS (43.1% peak FP64 performance) on 619,124 electrons using 8,000 GPU nodes of Frontier supercomputer. © 2023 ACM.

关键词： Inverse problems

Nonlinear Perturbation-based Non-Convex Optimization over Time-Varying Networks

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arXiv 2024年

作者： Doostmohammadian, Mohammadreza Gabidullina, Zulfiya R. Rabiee, Hamid R. The Faculty of Mechanical Engineering Semnan University Semnan Iran Centre for International Scientific Studies and Collaborations Tehran Iran The Institute of Computational Mathematics and Information Technologies Kazan Federal University Russia The School of Computer Engineering Sharif University of Technology Tehran Iran

Decentralized optimization strategies are helpful for various applications, from networked estimation to distributed machine learning. This paper studies finite-sum minimization problems described over a network of nodes and proposes a computationally efficient algorithm that solves distributed convex problems and optimally finds the solution to locally non-convex objective functions. In contrast to batch gradient optimization in some literature, our algorithm is on a single-time scale with no extra inner consensus loop. It evaluates one gradient entry per node per time. Further, the algorithm addresses link-level nonlinearity representing, for example, logarithmic quantization of the exchanged data or clipping of the exchanged data bits. Leveraging perturbation-based theory and algebraic Laplacian network analysis proves optimal convergence and dynamics stability over time-varying and switching networks. The time-varying network setup might be due to packet drops or link failures. Despite the nonlinear nature of the dynamics, we prove exact convergence in the face of odd sign-preserving sector-bound nonlinear data transmission over the links. Illustrative numerical simulations further highlight our contributions. © 2024, CC BY.

关键词： Consensus algorithm

Shape of my heart: Cardiac models through learned signed distance functions

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arXiv 2023年

作者： Verhülsdonk, Jan Grandits, Thomas Costabal, Francisco Sahli Pinetz, Thomas Krause, Rolf Auricchio, Angelo Haase, Gundolf Pezzuto, Simone Effland, Alexander Institute for Applied Mathematics University of Bonn Germany Department of Mathematics and Scientific Computing University of Graz Austria Institute for Biological and Medical Engineering Pontificia Universidad Católica de Chile Chile Center for Computational Medicine in Cardiology Università della Svizzera italiana Switzerland FernUni Schweiz Brig Switzerland Instituto Cardiocentro Ticino EOC Switzerland Department of Mathematics University of Trento Italy

The efficient construction of anatomical models is one of the major challenges of patient-specific in-silico models of the human heart. Current methods frequently rely on linear statistical models, allowing no advanced topological changes, or requiring medical image segmentation followed by a meshing pipeline, which strongly depends on image resolution, quality, and modality. These approaches are therefore limited in their transferability to other imaging domains. In this work, the cardiac shape is reconstructed by means of three-dimensional deep signed distance functions with Lipschitz regularity. For this purpose, the shapes of cardiac MRI reconstructions are learned to model the spatial relation of multiple chambers. We demonstrate that this approach is also capable of reconstructing anatomical models from partial data, such as point clouds from a single ventricle, or modalities different from the trained MRI, such as the electroanatomical mapping (EAM). Copyright © 2023, The Authors. All rights reserved.

关键词： Image resolution

A new piecewise quadratic approximation approach for L_0 norm minimization problem

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Science China mathematics 2019年第1期62卷 185-204页

作者： Qian Li Yanqin Bai Changjun Yu Ya-xiang Yuan Department of Mathematics Shanghai University Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of Sciences

In this paper, we consider the problem of finding sparse solutions for underdetermined systems of linear equations, which can be formulated as a class of L_0 norm minimization problem. By using the least absolute residual approximation, we propose a new piecewis, quadratic function to approximate the L_0 ***, we develop a piecewise quadratic approximation(PQA) model where the objective function is given by the summation of a smooth non-convex component and a non-smooth convex component. To solve the(PQA) model,we present an algorithm based on the idea of the iterative thresholding algorithm and derive the convergence and the convergence rate. Finally, we carry out a series of numerical experiments to demonstrate the performance of the proposed algorithm for(PQA). We also conduct a phase diagram analysis to further show the superiority of(PQA) over L_1 and L_(1/2) regularizations.

关键词： sparse optimization non-convex approximation iterative thresholding algorithm

Lyapunov exponents and Lagrangian chaos suppression in compressible homogeneous isotropic turbulence

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arXiv 2023年

作者： Yu, Haijun Fouxon, Itzhak Wang, Jianchun Li, Xiangru Yuan, Li Mao, Shipeng Mond, Michael NCMIS & LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Department of Mechanical Engineering Ben-Gurion University of the Negev Beer-Sheva84105 Israel Department of Computational Science and Engineering Yonsei University Seoul03722 Korea Republic of Department of Mechanics and Aerospace Engineering Southern University of Science and Technology Shenzhen518055 China

We study Lyapunov exponents of tracers in compressible homogeneous isotropic turbulence at different turbulent Mach number Mt and Taylor-scale Reynolds number Reλ. We demonstrate that statistics of finite-time Lyapunov exponents have the same form as in incompressible flow due to density-velocity coupling. The modulus of the smallest Lyapunov exponent λ3 provides the principal Lyapunov exponent of the time-reversed flow, which is usually wrong in a compressible flow. This exponent, along with the principal Lyapunov exponent λ1, determines all the exponents due to vanishing of the sum of all Lyapunov exponents. Numerical results by high-order schemes for solving the Navier-Stokes equations and tracking particles verify these theoretical predictions. We found that: 1) The largest normalized Lyapunov exponent λ1τη, where τη is the Kolmogorov timescale, is a decreasing function of Mt. Its dependence on Reλ is weak when the driving force is solenoidal, while it is an increasing function of Reλ when the solenoidal and compressible forces are comparable. Similar facts hold for |λ3|, in contrast with well-studied short-correlated model;2) The ratio of the first two Lyapunov exponents λ1/λ2 decreases with Reλ, and is virtually independent of Mt for Mt ≤ 1 in the case of solenoidal force but decreases as Mt increases when solenoidal and compressible forces are comparable;3) For purely solenoidal force, λ1 : λ2 : λ3 ≈ 4: 1: −5 for Reλ > 80, which is consistent with incompressible turbulence studies;4) The ratio of dilation-to-vorticity is a more suitable parameter to characterize Lyapunov exponents than Mt © 2023, CC BY-NC-ND.

关键词： Navier Stokes equations

An Artificial Intelligence Approach for Solving Stochastic Transportation Problems

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Computers, Materials & Continua 2022年第1期70卷 817-829页

作者： Prachi Agrawal Khalid Alnowibet Talari Ganesh Adel F.Alrasheedi Hijaz Ahmad Ali Wagdy Mohamed Department of Mathematics and Scientific Computing National Institute of Technology HamirpurHimachal Pradesh177005India Statistics and Operations Research Department College of ScienceKing Saud UniversityRiyadh11451Kingdom of Saudi Arabia Section of Mathematics International Telematic University UninettunoRoma00186Italy Operations Research Department Faculty of Graduate Studies for Statistical ResearchCairo UniversityGiza12613Egypt Wireless Intelligent Networks Center(WINC) School of Engineering and Applied SciencesNile UniversityGizaEgypt

Recent years witness a great deal of interest in artificial intelligence(AI)tools in the area of *** has developed a large number of tools to solve themost difficult search-and-optimization problems in computer science and operations ***,metaheuristic-based algorithms are a sub-field of *** study presents the use of themetaheuristic algorithm,that is,water cycle algorithm(WCA),in the transportation problem.A stochastic transportation problem is considered in which the parameters supply and demand are considered as random variables that follow the Weibull *** the parameters are stochastic,the corresponding constraints are *** are converted into deterministic constraints using the stochastic programming *** this study,we propose evolutionary algorithms to handle the difficulties of the complex high-dimensional optimization *** is influenced by the water cycle process of how streams and rivers flow toward the sea(optimal solution).WCA is applied to the stochastic transportation problem,and obtained results are compared with that of the new metaheuristic optimization algorithm,namely the neural network algorithm which is inspired by the biological nervous *** is concluded that WCA presents better results when compared with the neural network algorithm.

关键词： Artificial intelligence metaheuristic algorithm stochastic programming transportation problem water cycle algorithm weibull distribution

Bibliometric Study on Virtual Reality Applied to Military Training

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Bibliometric Study on Virtual Reality Applied to Military Tr...

International Conference on Electrical, Communication, and Computer engineering (ICECCE)

作者： Diogo Pacheco Salazar Araujo Romullo Girardi Jauvane C. de Oliveira Paulo Fernando Ferreira Rosa Department of Computer Engineering (SE19) Military Institute of Engineering (IME) Rio de Janeiro Brazil Coordination of Mathematical and Computational Methods National Laboratory for Scientific Computing (LNCC) Rio de Janeiro Brazil Laboratory of AI Robotics and Cybernetics (LIARC) Military Institute of Engineering (IME) Rio de Janeiro Brazil

ISBN: (数字)9798331529437

ISBN: (纸本)9798331529444

In the defense domain, the adoption of Virtual Reality (VR)-based training simulators has significantly increased in recent years in response to the limitations of traditional military training methods. This paper presents a quantitative approach study based on bibliometric metrics to assess the use of VR in defense. Using the Scopus and Web of Science databases as references, the study aimed to identify various aspects related to the research field: distribution of publications, most relevant sources, dynamics of interaction among these sources, prominent topics in recent research, as well as prevalent application areas and supporting technologies. Thus, the study provides valuable insights into the current state and research trends of VR applied to the military context.

关键词： Training Measurement Databases Bibliometrics Virtual reality Market research