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A second-order reduced multiscale method for nonlinear shell structures with orthogonal periodic configurations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2022年第1期123卷 128-157页

作者： Yang, Zhiqiang Liu, Yizhi Sun, Yi Ma, Qiang Harbin Inst Technol Dept Astronaut Sci & Mech Harbin 150001 Peoples R China Sichuan Univ Coll Math Chengdu 610043 Peoples R China

This article develops an efficient second-order reduced multiscale (SORM) method to study the nonlinear shell structure with orthogonal periodic configurations. The heterogenous shell structure is periodically distributed in orthogonal curvilinear coordinate systems. At first, the nonlinear problems for the shell structure are introduced, and the detailed higher-order nonlinear multiscale formulas based on the asymptotic homogenization approach are given including microscale unit cell functions, effective material parameter and the homogenized equation. Also, since it requires a large number of computation cost to solve the nonlinear multiscale problems by the traditional high-order homogenization methods, the novel reduced order multiscale model is constructed. Further, according to the reduced-order multiscale models and higher-order nonlinear formulas, an effective SORM algorithm is provided for studying the nonlinear shell structures. The main characteristics of the proposed algorithm are that the novel reduced forms established to investigate the nonlinear shell structures and an efficient higher-order homogenized solution evaluated by postprocessing that does not need higher-order continuities of the homogenization solutions. Finally, according to some typical nonlinear examples including block structures, cylindrical shell and double-curved shallow shell, the availabilities of the SORM algorithm are confirmed.

关键词： homogenization inelastic problems multiscale algorithms shell structures

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A multiscale DOMAIN DECOMPOSITION ALGORITHM FOR BOUNDARY VALUE PROBLEMS FOR EIKONAL EQUATIONS (vol 17, pg 620, 2019)

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multiscale MODELING & SIMULATION 2019年第4期17卷 1301-1302页

作者： Martin, Lindsay Tsai, Yen-Hsi R. Univ Texas Austin Dept Math Austin TX 78712 USA Univ Texas Austin Dept Math Austin TX 78712 USA Univ Texas Austin Oden Inst Computat Engn & Sci Austin TX 78712 USA KTH Royal Inst Technol Stockholm Sweden

This note is an erratum to the article [L. Martin and Y.-H. R. Tsai, multiscale Model. Simul., 17 (2019), pp. 620-649]. We correct the complexity and speed-up of the proposed algorithm given in section 4.3.

关键词： Eikonal equation parallel algorithms domain decomposition multiscale algorithms

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multiscale high-order/low-order (HOLO) algorithms and applications

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JOURNAL OF COMPUTATIONAL PHYSICS 2017年 330卷 21-45页

作者： Chacon, L. Chen, G. Knoll, D. A. Newman, C. Park, H. Taitano, W. Willert, J. A. Womeldorff, G. Los Alamos Natl Lab Los Alamos NM 87545 USA Inst Def Anal Alexandria VA 22311 USA

We review the state of the art in the formulation, implementation, and performance of so-called high-order/low-order (HOLO) algorithms for challenging multiscale problems. HOLO algorithms attempt to couple one or several high-complexity physical models (the high order model, HO) with low-complexity ones (the low-order model, LO). The primary goal of HOLO algorithms is to achieve nonlinear convergence between HO and LO components while minimizing memory footprint and managing the computational complexity in a practical manner. Key to the HOLO approach is the use of the LO representations to address temporal stiffness, effectively accelerating the convergence of the HO/LO coupled system. The HOLO approach is broadly underpinned by the concept of nonlinear elimination, which enables segregation of the HO and LO components in ways that can effectively use heterogeneous architectures. The accuracy and efficiency benefits of HOLO algorithms are demonstrated with specific applications to radiation transport, gas dynamics, plasmas (both Eulerian and Lagrangian formulations), and ocean modeling. Across this broad application spectrum, HOLO algorithms achieve significant accuracy improvements at a fraction of the cost compared to conventional approaches. It follows that HOLO algorithms hold significant potential for high-fidelity system scale multiscale simulations leveraging exascale computing. (C) 2016 Elsevier Inc. All rights reserved.

关键词： High-order/low-order HOLO multiscale algorithms Implicit timestepping Communication avoiding algorithms

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Erratum: A multiscale Domain Decomposition Algorithm for Boundary Value Problems for Eikonal Equations

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multiscale Modeling & Simulation 2019年第4期17卷 1301-1302页

作者： Lindsay Martin Yen-Hsi R. Tsai

This note is an erratum to the article [L. Martin and Y.-H. R. Tsai, multiscale Model. Simul., 17 (2019), pp. 620--649]. We correct the complexity and speed-up of the proposed algorithm given in section 4.3.

This note is an erratum to the article [L. Martin and Y.-H. R. Tsai, multiscale Model. Simul., 17 (2019), pp. 620--649]. We correct the complexity and speed-up of the proposed algorithm given in section 4.3.

关键词： Eikonal equation parallel algorithms domain decomposition multiscale algorithms 65N22 65N55 65N12 35F30 65Y05

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A multiscale sub-linear time Fourier algorithm for noisy data

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APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 2016年第3期40卷 553-574页

作者： Christlieb, Andrew Lawlor, David Wang, Yang Michigan State Univ Dept Math E Lansing MI 48824 USA Stat & Appl Math Sci Inst 19 TW Alexander DrPOB 14006 Res Triangle Pk NC 27709 USA Duke Univ Dept Math Box 90320 Durham NC 27708 USA

We extend the recent sparse Fourier transform algorithm of [1] to the noisy setting, in which a signal of bandwidth N is given as a superposition of k << N frequencies and additive random noise. We present two such extensions, the second of which exhibits a form of error-correction in its frequency estimation not unlike that of the beta-encoders in analog-to-digital conversion [2]. On k-sparse signals corrupted with additive complex Gaussian noise, the algorithm runs in time O(k log(k) log(N/k)) on average, provided the noise is not overwhelming. The error-correction property allows the algorithm to outperform FFTW [3], a highly optimized software package for computing the full discrete Fourier transform, over a wide range of sparsity and noise values. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Fast Fourier algorithms multiscale algorithms Fourier analysis

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On some multiscale algorithms for sector modeling in multiphase flow in porous media

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Mathematical Models and Computer Simulations 2011年第3期3卷 365-374页

作者： Pergament, A. Kh. Semiletov, V.A. Tomin, P. Yu. Keldysh Institute of Applied Mathematics Russian Academy of Sciences Moscow Russian Federation Moscow State University Moscow Russian Federation Moscow Institute of Physics and Technology Moscow Russian Federation

A multiscale algorithm for a multiphase filtration problem is proposed. Filtration fluxes on a fine grid are determined from the solution of the pressure equation on a coarse grid. Further, the domain is decomposed into subdomains with an acceptable number of cells and the full second boundary condition filtration problem is solved using the fluxes. The support operator method has been improved for a complex structure cell for solution of the pressure equation on a coarse grid. This method is a high resolution one: a divergence operator has the approximation of the second order, while fluxes have the approximation of the first order. At the same time, the method allows revealing the solution’s properties related to a fine grid structure. © 2011, Pleiades Publishing, Ltd.

关键词： approximation on nonorthogonal grids multiphase flows multiscale algorithms

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multiscale approach for the network compression-friendly ordering

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JOURNAL OF DISCRETE algorithms 2011年第2期9卷 190-202页

作者： Safro, Ilya Temkin, Boris Argonne Natl Lab Math & Comp Sci Div Argonne IL 60439 USA

present a fast multiscale approach for the network minimum logarithmic arrangement problem. This type of arrangement plays an important role in the network compression and fast node/ link access operations. The algorithm is of linear complexity and exhibits good scalability, which makes it practical and attractive for use in large-scale instances. Its effectiveness is demonstrated on a large set of real-life networks. These networks with corresponding best-known minimization results are suggested as an open benchmark for the research community to evaluate new methods for this problem. (C) 2010 Elsevier B.V. All rights reserved.

关键词： multiscale algorithms Minimum logarithmic arrangement Network compression

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Mathematical test models for superparametrization in anisotropic turbulence

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PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA 2009年第14期106卷 5470-5474页

作者： Majda, Andrew J. Grote, Marcus J. NYU Courant Inst Math Sci Dept Math & Climate Atmosphere Ocean Sci New York NY 10012 USA Univ Basel Dept Math CH-4052 Basel Switzerland

The complexity of anisotropic turbulent processes over a wide range of spatiotemporal scales in engineering turbulence and climate atmosphere ocean science requires novel computational strategies with the current and next generations of supercomputers. In these applications the smaller-scale fluctuations do not statistically equilibrate as assumed in traditional closure modeling and intermittently send significant energy to the large-scale fluctuations. Superparametrization is a novel class of seamless multi-scale algorithms that reduce computational labor by imposing an artificial scale gap between the energetic smaller-scale fluctuations and the large-scale fluctuations. The main result here is the systematic development of simple test models that are mathematically tractable yet capture key features of anisotropic turbulence in applications involving statistically intermittent fluctuations without local statistical equilibration, with moderate scale separation and significant impact on the large-scale dynamics. The properties of the simplest scalar test model are developed here and utilized to test the statistical performance of superparametrization algorithms with an imposed spectral gap in a system with an energetic -5/3 turbulent spectrum for the fluctuations.

关键词： intermittency moderate-scale separation multiscale algorithms

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Scale-splitting error in complex automata models for reaction-diffusion systems

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8th International Conference on Computational Science

作者： Caiazzo, Alfonso Falcone, Jean Luc Chopard, Bastien Hoekstra, Alfons G. Univ Amsterdam Sect Computat Sci NL-1012 WX Amsterdam Netherlands Univ Geneva CUI Dept CH-1211 Geneva 4 Switzerland

ISBN: (纸本)9783540693864

Complex Automata (CxA) have been recently proposed as a paradigm for the simulation of multiscale systems. A CxA model is constructed decomposing a multiscale process into single scale sub-models, each simulated using a Cellular Automata algorithm, interacting across the scales via appropriate coupling templates. Focusing on a reaction-diffusion system, we introduce a mathematical framework for CxA modeling. We aim at the identification of error sources in the modeling stages, investigating in particular how the errors depend upon scale separation. Theoretical error estimates will be presented and numerically validated on a simple benchmark, based on a periodic reaction-diffusion problem solved via multistep lattice Boltzmann method.

关键词： complex Automata multiscale algorithms reaction-diffusion lattice Boltzmann method

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Kalman filtering in pairwise Markov trees

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SIGNAL PROCESSING 2006年第5期86卷 1049-1054页

作者： Desbouvries, F Lecomte, J Pieczynski, W CITI GET INT Dept F-91011 Evry France CNRS UMR 5157 F-91011 Evry France

An important problem in multiresolution analysis of signals or images consists in estimating hidden random variables x = {x(s)}(s is an element of S) from observed ones y = {y(s)}(s is an element of S). This is done classically in the context of hidden Markov trees (HMT). HMT have been extended recently to the more general context of pairwise Markov trees (PMT). In this note, we propose an adaptive filtering algorithm which is an extension to PMT of the Kalman filter (KF). (C) 2005 Elsevier B.V. All rights reserved.

关键词： hidden Markov trees pairwise Markov trees multiresolution signal and image analysis multiscale algorithms Kalman filtering

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