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PROJECTION METHOD FOR QUASIPERIODIC ELLIPTIC EQUATIONS AND APPLICATION TO QUASIPERIODIC HOMOGENIZATION

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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

The Basics of Quantum computing for Chemists

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arXiv 2022年

作者： Claudino, Daniel Quantum Computing Institute Oak Ridge National Laboratory Oak RidgeTN37831 United States Computational Sciences and Engineering Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Computer Science and Mathematics Division Oak Ridge National Laboratory Oak RidgeTN37831 United States

The rapid and successful strides in quantum chemistry in the past decades can be largely credited to a conspicuous synergy between theoretical and computational advancements. However, the architectural computer archetype that enabled such a progress is approaching a state of more stagnant development. One of the most promising technological avenues for the continuing progress of quantum chemistry is the emerging quantum computing paradigm. This revolutionary proposal comes with several challenges, which span a wide array of disciplines. In chemistry, it implies, among other things, a need to reformulate some of its long established cornerstones in order to adjust to the operational demands and constraints of quantum computers. Due to its relatively recent emergence, much of quantum computing may still seem fairly nebulous and largely unknown to most chemists. It is in this context that here we review and illustrate the basic aspects of quantum information and their relation to quantum computing insofar as enabling simulations of quantum chemistry. We consider some of the most relevant developments in light of these aspects and discuss the current landscape when of relevance to quantum chemical simulations in quantum computers. © 2022, CC BY.

关键词： Quantum optics

Convergence analysis of PM-BDF2 method for quasiperiodic parabolic equations

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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

High-resolution boundary variation diminishing scheme for two-phase compressible flow with cavitation and evaporation

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Journal of computational Physics 2024年 513卷

作者： Wakimura, Hiro Li, Tatsuin Shyue, Keh-Ming Aoki, Takayuki Xiao, Feng Department of Mechanical Engineering Tokyo Institute of Technology 2-12-1 i6-29 Ookayama Meguro-ku Tokyo152-8550 Japan Department of Mathematics Institute of Applied Mathematical Sciences National Taiwan University Taipei10617 Taiwan Global Scientific Information and Computing Center Tokyo Institute of Technology 2-12-1 i7-3 Ookayama Meguro-ku Tokyo152-8550 Japan

We propose high-resolution numerical schemes for two-phase compressible flow simulations to reproduce dynamically created gas/vapor-liquid interfaces with phase change. In the Godunov-type finite volume framework, suppressing numerical dissipation errors in numerical schemes is crucial for capturing the discontinuous solutions. The MUSCL scheme has second-order accuracy for smooth solutions and non-oscillatory behavior near discontinuous solutions. However, the MUSCL scheme introduces excessive numerical dissipation and diffuses the discontinuities nonphysically, leading to difficulties in distinguishing gas/vapor and liquid phases, and thus causing a blur in the interfaces during the multi-phase flow simulations. The hybrid-type boundary variation diminishing (BVD) scheme in this paper combines the MUSCL scheme and the THINC scheme to reduce the numerical dissipation errors near the discontinuities. The MUSCL-THINC-BVD scheme applies the MUSCL scheme for smooth solutions and the THINC scheme for discontinuous solutions, resulting in the successful capture of the discontinuities including the dynamically created gas/vapor-liquid interfaces. The Adaptive THINC-BVD scheme, which switches two types of THINC schemes with different values of gradient parameter, also captures the discontinuities clearly. The numerical results of the benchmark tests show that the proposed BVD schemes can lucidly reproduce the vapor-liquid interfaces newly created during the dynamical process of phase change. © 2024 Elsevier Inc.

关键词： Finite volume method

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

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

Supercomputing Conference

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

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.

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Evaluation of approaches to solving electrocardiographic imaging problem

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Evaluation of approaches to solving electrocardiographic ima...

Computers in Cardiology (CinC)

作者： M Milanic V Jazbinsek DF Wang J Sinstra RS MacLeod DH Brooks R Hren Jozef Stefan Institute Ljubljana Slovenia Institute of Mathematics Physics and Mechanics University of Ljubljana Ljubljana Slovenia Scientific Computing and Imaging Institute University of Utah Salt Lake UT USA Nora Eccles Harrison Cardiovascular Research and Training Institute University of Utah Salt Lake UT USA Department of Electrical and Computer Engineering Northeastern University Boston MA USA Univerza v Ljubljani Ljubljana SI

ISBN: (纸本)9781424472819

Electrocardiographic imaging (ECGI) is a widely used method of computing potentials on the epicardium from measured or simulated potentials on the torso surface. The main challenge of the electrocardiographic imaging problem lies in its intrinsic ill-posedness, and many regularization techniques have been developed to smooth out the solution. It is still an ongoing research subject to choose proper regularization methods and to determine their proper amount for obtaining clinically acceptable solutions. This study systematically compares various regularization techniques for the ECGI problem under a unified simulation framework. The framework consists of an electrolytic human torso tank containing a live canine heart, with the cardiac source being modeled by potentials measured on a cylindrical cage placed around the heart. We tested 14 different regularization techniques to solve the inverse problem of recovering epicardial potentials, and found that non-quadratic methods (total variation algorithms) were the most robust and resulted in the lowest reconstruction errors.

关键词： Torso Heart computational modeling Humans Testing Inverse problems Robustness Image reconstruction

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

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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

Versatile stabilized finite element formulations for nearly and fully incompressible solid mechanics

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arXiv 2019年

作者： Karabelas, Elias Haase, Gundolf Plank, Gernot Augustin, Christoph M. Institute for Mathematics and Scientific Computing NAWI Graz University of Graz Graz Austria Gottfried Schatz Research Center Division of Biophysics Medical University of Graz Graz Austria BioTechMed-Graz Graz Austria Department of Mechanical Engineering University of California Berkeley BerkeleyCA United States /IV Graz8010 Austria

computational formulations for large strain, polyconvex, nearly incompressible elasticity have been extensively studied, but research on enhancing solution schemes that offer better tradeoffs between accuracy, robustness, and computational efficiency remains to be highly relevant. In this paper, we present two methods to overcome locking phenomena, one based on a displacement-pressure formulation using a stable finite element pairing with bubble functions, and another one using a simple pressure-projection stabilized P1 − P1 finite element pair. A key advantage is the versatility of the proposed methods: with minor adjustments they are applicable to all kinds of finite elements and generalize easily to transient dynamics. The proposed methods are compared to and verified with standard benchmarks previously reported in the literature. Benchmark results demonstrate that both approaches provide a robust and computationally efficient way of simulating nearly and fully incompressible materials. Copyright © 2019, The Authors. All rights reserved.

关键词： Finite element method

Evidence of Large Recoil Velocity from a Black Hole Merger Signal

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Physical Review Letters 2022年第19期128卷 191102-191102页

作者： Vijay Varma Sylvia Biscoveanu Tousif Islam Feroz H. Shaik Carl-Johan Haster Maximiliano Isi Will M. Farr Scott E. Field Salvatore Vitale Max Planck Institute for Gravitational Physics (Albert Einstein Institute) Am Mühlenberg 1 Potsdam 14476 Germany LIGO Laboratory Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA Department of Physics and Kavli Institute for Astrophysics and Space Research Massachusetts Institute of Technology 77 Massachusetts Ave Cambridge Massachusetts 02139 USA Department of Mathematics University of Massachusetts Dartmouth Massachusetts 02747 USA Center for Scientific Computing and Data Science Research University of Massachusetts Dartmouth Massachusetts 02747 USA Center for Computational Astrophysics Flatiron Institute New York New York 10010 USA Department of Physics and Astronomy Stony Brook University Stony Brook New York 11794 USA

The final black hole left behind after a binary black hole merger can attain a recoil velocity, or a “kick,” reaching values up to 5000 km/s. This phenomenon has important implications for gravitational wave astronomy, black hole formation scenarios, testing general relativity, and galaxy evolution. We consider the gravitational wave signal from the binary black hole merger GW200129_065458 (henceforth referred to as GW200129), which has been shown to exhibit strong evidence of orbital precession. Using numerical relativity surrogate models, we constrain the kick velocity of GW200129 to vf∼1542−1098+747 km/s or vf≳698 km/s (one-sided limit), at 90% credibility. This marks the first identification of a large kick velocity for an individual gravitational wave event. Given the kick velocity of GW200129, we estimate that there is a less than 0.48% (7.7%) probability that the remnant black hole after the merger would be retained by globular (nuclear star) clusters. Finally, we show that kick effects are not expected to cause biases in ringdown tests of general relativity for this event, although this may change in the future with improved detectors.

关键词： Gravitational waves