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Dynamic explicit solution for higher-order crystal plasticity theories

INTERNATIONAL JOURNAL OF PLASTICITY 2014年 53卷 1-16页

作者： Bittencourt, Eduardo Univ Fed Rio Grande do Sul Dept Civil Engn BR-90035190 Porto Alegre RS Brazil

Dynamic terms are included in the balance equations that govern a higher-order crystal plasticity formulation. The resulting equations are integrated in time by the central-difference explicit method. The methodology avoids solution methods based on the inversion of the associated stiffness matrices. This is a great advantage of the proposed methodology, considering that these matrices tend to be highly ill-conditioned. As the solution becomes dependent on the time-step size used in the integration, a stability study is presented. Only a rate independent constitutive law is taken into account. As examples, a crystal layer and a composite material under simple shear and the wedge indentation of a single crystal are considered. Comparisons with an implicit quasi-static solution method show the robustness of the proposed methodology, but reveal an elevated computational cost related to it. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Dislocations Crystal plasticity Finite elements numerical algorithms Higher-order theories

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Efficient Heuristic Adaptive Quadrature on GPUs: Design and Evaluation

Efficient Heuristic Adaptive Quadrature on GPUs: Design and ...

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10th International Conference on Parallel Processing and Applied Mathematics (PPAM)

作者： Thuerck, Daniel Widmer, Sven Kuijper, Arjan Goesele, Michael Tech Univ Darmstadt Darmstadt Germany Tech Univ Darmstadt Grad Sch Computat Engn Darmstadt Germany Fraunhofer IGD Darmstadt Germany

ISBN: (纸本)9783642552243

numerical integration is a common sub-problem in many applications. It can be solved easily in CPU-based applications using adaptive quadrature such as the adaptive Simpson's rule. These algorithms rely, however, on error estimation yielding a significant computational overhead. In addition, they require recursive function evaluations, which are not well suited for parallel computation on graphics processing units (GPUs) due to warp divergence issues. In this paper, we introduce heuristic forward quadrature as an alternative that is not only more efficient than traditional methods, but also better suited for accelerated massively-parallel calculation on GPUs. Additionally, we will give an error estimate for our method and demonstrate performance results for 1D and 2D integral applications which show that the algorithm leverages quadrature for the efficient implementation on GPUs.

关键词： numerical integration GPGPU numerical algorithms Heuristics Interval estimation

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Optimal Control of Level Sets Dynamics

Optimal Control of Level Sets Dynamics

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American Control Conference

作者： Alessandri, Angelo Bagnerini, Patrizia Gaggero, Mauro Univ Genoa Dept Mech Engn I-16129 Genoa Italy

ISBN: (纸本)9781479932740

The problem of optimal tracking of level sets is investigated. More specifically, we propose a novel method to design a controller that is able to track a reference curve generated by a level set equation. Such a functional optimal control problem is nonstandard as it involves a moving domain over time, thus requiring the development of both an ad-hoc approximation scheme and an efficient numerical solver. We address the approximate solution of the resulting optimization problem by using the extended Ritz method, which has been recently applied to the solution of a number of optimal control problems in high dimensional setting. Such a method relies on the use a control law of fixed structure that depends on a number of parameters to be suitably chosen. Toward this end, we derive the adjoint equation for the optimal tracking problem. Such an equation allows one to compute the gradient of the cost function with respect to the vector of parameters of the control law. numerical results are reported to show the effectiveness and computational effort of the proposed approach for the purpose of tracking curves generated by the normal and mean curvature flow equations.

关键词： Approximation methods Equations Level set Mathematical model Optimization Simulation Vectors Distributed parameter systems Neural networks numerical algorithms

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Parametric algorithms for Global Optimization of Mixed-Integer Fractional Programming Problems in Process Engineering

Parametric Algorithms for Global Optimization of Mixed-Integ...

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American Control Conference

作者： Zhong, Zhixia You, Fengqi Northwestern Univ Dept Chem & Biol Engn Evanston IL 60208 USA

ISBN: (纸本)9781479932740

In this work, we proposed novel parametric algorithms for solving large-scale mixed-integer linear and nonlinear fractional programming problems, and illustrate their application in process systems engineering. By developing an equivalent parametric formulation of the general mixed-integer fractional program (MIFP), we propose four exact parametric algorithms based on the root-finding methods, including bisection method, Newton's method, secant method and false position method, respectively, for the global optimization of MIFPs. We also propose an inexact parametric algorithm that can potentially outperform the exact parametric algorithms for some types of MIFPs. Extensive computational studies are performed to demonstrate the efficiency of these parametric algorithms and to compare them with the general-purpose mixed-integer nonlinear programming methods. The applications of the proposed algorithms are illustrated through a case study on process scheduling. Computational results show that the proposed exact and inexact parametric algorithms are more computationally efficient than several general-purpose solvers for solving MIFPs.

关键词： Algorithm design and analysis Computational efficiency Linear programming Optimization Productivity Programming Testing Computational methods numerical algorithms Optimization algorithms

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Implementation of a Fan-Like Triangulation for the CPA Method to compute Lyapunov Functions

Implementation of a Fan-Like Triangulation for the CPA Metho...

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American Control Conference

作者： Giesl, Peter Hafstein, Sigurdur Univ Sussex Dept Math Brighton BN1 9RH E Sussex England

ISBN: (纸本)9781479932740

An integral part of the CPA method to compute Continuous and Piecewise Affine Lyapunov functions for nonlinear systems is the generation of a suitable triangulation. Recently, the CPA method was revised by using more advanced triangulations and it was proved that it can compute a CPA Lyapunov function for any nonlinear system possessing an exponentially stable equilibrium. This more advanced triangulation scheme includes a simplicial fan close to the equilibrium of the system, for which the Lyapunov function is computed. In this paper we prove a result that allows for a simpler, more general and more efficient generation of this simplicial fan and thus improves the implementation of the CPA method. Moreover, the simplicial fan subdivision at the origin is also of great importance in methods relying on a conic decomposition of the state-space.

关键词： Computers Educational institutions Hypercubes Lyapunov methods Nonlinear systems Tin Vectors Computational methods numerical algorithms

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Witness Computation for Solving Geometric Constraint Systems

Witness Computation for Solving Geometric Constraint Systems

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Science and Information Conference (SAI)

作者： Kubicki, Arnaud Michelucci, Dominique Foufou, Sebti Univ Burgundy Lab Elect Informat & Image Dijon France Qatar Univ Coll Engn Dept Comp Sci & Engn Doha Qatar

ISBN: (纸本)9780989319317

In geometric constraint solving, the constraints are represented with an equation system F (U, X) = 0, where X denotes the unknowns and U denotes a set of parameters. The target solution for X is noted X-T. A witness is a couple (U-W, X-W) such that F (U-W, X-W) = 0. The witness is not the target solution, but they share the same combinatorial features, even when the witness and the target lie on two distinct connected components of the solution set of F (U, X) = 0. Thus a witness enables the qualitative study of the system: the detection of over-and under-constrained systems, the decomposition into irreducible subsystems, the computation of subsystems boundaries. This paper investigates the witness computation in various configurations. The witness computation will be studied under several numerical methods: Newton iterations from random seeds either in R and C, the Broyden-Fletcher-Goldfarb-Shanno method, the Nelder-Mead simplex method. The robustness and performances of these methods will be analyzed and compared. The paper also presents the numerical probabilistic method from which the witness method was originated, and shows how the witness can be used for detecting dependent parameters within systems of geometric constraints.

关键词： Geometric constraint solving Witness computation numerical algorithms

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Arbitrary pole placement with the extended Kautsky-Nichols-van Dooren parametric form with minimum gain

Arbitrary pole placement with the extended Kautsky-Nichols-v...

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American Control Conference

作者： Schmid, Robert Thang Nguyen Ntogramatzidis, Lorenzo Univ Melbourne Dept Elect & Elect Engn Melbourne Vic 3010 Australia

ISBN: (纸本)9781479932740

We consider the classic problem of pole placement by state feedback. We revisit the well-known eigenstructure assignment algorithm of Kautsky, Nichols and van Dooren [1] and extend it to obtain a novel parametric form for the pole-placing feedback matrix that can deliver any set of desired closed-loop eigenvalues, with any desired multiplicities. This parametric formula is then employed to introduce an unconstrained nonlinear optimisation algorithm to obtain a feedback matrix that delivers the desired pole placement with minimum gain.

关键词： Eigenvalues and eigenfunctions Equations Nickel Optimization Silicon State feedback Vectors Linear systems numerical algorithms

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Model Reduction by Moment Matching for Linear Switched Systems

Model Reduction by Moment Matching for Linear Switched Syste...

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American Control Conference

作者： Bastug, Mert Petreczky, Mihaly Wisniewski, Rafael Leth, John Aalborg Univ Dept Elect Syst Automat & Control DK-9220 Aalborg Denmark

A moment-matching method for the model reduction of linear switched systems (LSSs) is developed. The method is based upon a partial realization theory of LSSs and it is similar to the Krylov subspace methods used for ... 详细信息

ISBN: (纸本)9781479932740

关键词： Approximation algorithms Approximation methods Computational modeling Markov processes Reduced order systems Switched systems Switches numerical algorithms Reduced order modeling

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Thermal Tune Method for AFM Oscillatory Resonant Imaging in Air and Liquid

Thermal Tune Method for AFM Oscillatory Resonant Imaging in ...

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American Control Conference

作者： Belikov, Sergey Alexander, John Wall, Craig Yermolenko, Ivan Magonov, Sergei Malovichko, Ivan NT MDT Dev Inc Tempe AZ 85284 USA

ISBN: (纸本)9781479932740

Continuous development of atomic force microscopy and its applications is not always supported by a rigorous theoretical treatment of the related phenomena. A proper understanding of the behavior of microscopic probes and their response to tip-sample force interactions are crucial for a microscope control, optimization of experimental procedures and rational data analysis in the frameworks of quantitative models. Several issues of the probe dynamics and instrument functionality are addressed with a rigorous theoretical analysis of the thermal tune method, which is presented in this paper. It covers theoretical derivation of the method, development of stable convergent algorithms, different averaging techniques, and implementation with high-speed acquisition or a heterodyne technique for low speed acquisition. The developed thermal tune procedure allows for precise determination of the probe resonant frequency, quality factor and spring constant. It was verified practically with AFM probes operating in different environments. It is also shown that this method is applicable for measurements of the microscope functional parameters such as optical deflection noise and inverse optical sensitivity.

关键词： Mathematical model Noise Probes Q-factor Resonant frequency Springs Thermal noise Mechatronics Nano systems numerical algorithms

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Towards the Formal Analysis of Microresonators based Photonic Systems

Towards the Formal Analysis of Microresonators based Photoni...

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Design, Automation and Test in Europe Conference and Exhibition (DATE)

作者： Siddique, Umair Tahar, Sofiene Concordia Univ Dept Elect & Comp Engn Montreal PQ H3G 1M8 Canada

ISBN: (纸本)9783981537024

Recent developments in the fabrication technology attracted the attention of optical engineers and physicists in the area of VLSI photonics. Due to the physical nature of light-wave systems and their usage in safety critical domains such as human surgeries and high budget space missions, it is indispensable to build high assurance systems. Traditionally, the analysis of such systems has been carried out by paper-and-pencil based proofs and numerical computations. However, these techniques cannot provide perfectly accurate results due to the risk of human error and inherent approximations of numerical algorithms. In order to overcome these limitations, we propose to use higher-order logic theorem proving to improve the analysis in the domain of integrated optics or VLSI photonics. In particular, this paper provides a higher-order logic formalization of optical microresonators which are the most fundamental building blocks of many photonic devices. In order to illustrate the practical utilization of our work, we present the formal analysis of 2-D microresonator lattice optical filters.

关键词： VLSI integrated optoelectronics micro-optomechanical devices microcavities micromechanical resonators optical filters 2D microresonator lattice optical filters VLSI photonics formal analysis high budget space missions higher-order logic formalization higher-order logic theorem human surgeries integrated optics light-wave systems numerical algorithms optical microresonators paper-and-pencil based proofs photonic devices photonic systems physical nature safety critical domains Adaptive optics Biomedical optical imaging High-speed optical techniques Microcavities Optical waveguides Photonics

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