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Finding the minimal root of an equation with the multiextremal and nondifferentiable left-hand part

numerical algorithms 2001年第1-4期28卷 255-272页

作者： Molinaro, A Sergeyev, YD Univ Calabria Dipartimento Elettron Informat & Sistemist I-87036 Arcavacata Di Rende CS Italy Univ Calabria DEIS CNR ISI I-87036 Cosenza Italy Nizhnii Novgorod State Univ Nizhnii Novgorod Russia

A problem very often arising in applications is presented: finding the minimal root of an equation with the objective function being multiextremal and nondifferentiable. Applications from the field of electronic measurements are given. Three methods based on global optimization ideas are introduced for solving this problem. The first one uses an a priori estimate of the global Lipschitz constant. The second method adaptively estimates the global Lipschitz constant. The third algorithm adaptively estimates local Lipschitz constants during the search. All the methods either find the minimal root or determine the global minimizers (in the case when the equation under consideration has no roots). Sufficient convergence conditions of the new methods to the desired solution are established. numerical results including wide experiments with test functions, stability study, and a real-life applied problem are also presented.

关键词： minimal root numerical algorithms global optimization electrical engineering

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Review of attitude representations used for aircraft kinematics

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JOURNAL OF AIRCRAFT 2001年第4期38卷 718-737页

作者： Phillips, WF Hailey, CE Gebert, GA Utah State Univ Dept Mech & Aerosp Engn Logan UT 84322 USA Sverdrup Technol Inc Eglin AFB FL 32542 USA

A detailed survey is presented of the literature on attitude representation dating from the early work of Euler and Hamilton to recent publications in fields such as navigation and control. The scope is limited to the development of the aircraft kinematic transformation equations in terms of four different attitude representations, including the well-known Enter angles, the Euler-axis rotation parameters, the direction cosines, and the Euler-Rodrigues quaternion. The emphasis is directed at the application of the quaternion formulation to aircraft kinematics. Results are presented that reinforce observations that the quaternion formulation, typically implemented to eliminate singularities associated with the Enter angle formulation, is far superior to the other commonly used formulations based on computational efficiency alone. A development of quaternion constraints necessary to independently constrain roll, pitch, yaw, bank angle, elevation angle, and/or azimuth angle is presented. For verification of simulation codes, a general closed-form solution to the quaternion formulation, for the case of constant rotation, is also presented. Additionally, a discussion is provided of numerical integration methods and numerical errors for the quaternion formulation. This discussion is especially important for simulations that may still utilize a common error reduction scheme originally developed for analog computers.

关键词： Aircraft Kinematics Quaternions Angular Motion Aerodynamic Moments Earth numerical Integration Pilot Airspeed Integration Algorithm numerical algorithms

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numerical algorithms and issues concerning the discrete-time optimal projection equations for systems with white parameters

Numerical algorithms and issues concerning the discrete-time...

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UKACC International Conference on Control 98

作者： De Koning, WL Van Willigenburg, LG Delft Univ Technol Fac Tech Math & Informat NL-2628 CD Delft Netherlands

ISBN: (纸本)085296708X

The discrete-time optimal projection equations for systems with white parameters are strengthened. For the class of minimal ms (mean square) stabilizing compensators the strengthened discrete-time optimal projection equations are proved to be equivalent to first-order necessary optimality conditions for optimal reduced-order dynamic compensation of systems with white parameters. The conventional discrete-time optimal projection equations are proved to be weaker. As a result solutions of the conventional discrete-time optimal projection equations may not correspond to optimal reduced-order compensators. To compute optimal reduced-order compensators two numerical algorithms are proposed. One is a homotopy algorithm and one is based on iteration of the strengthened discrete-time optimal projection equations. The latter algorithm is a generalization of the algorithm that solves the full-order problem, which in turn is a generalization of the algorithm that solves the two Riccati equations of full-order LQG control through iteration. Therefore the efficiency of these three types of algorithms is comparable. It is demonstrated that, despite the strengthening of the optimal projection equations, the optimal reduced-order compensation problem, in general, may posses multiple extrema.

关键词： multiplicative white noise white stochastic parameters reduced-order control numerical algorithms optimal projection equations

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Diffraction effects, scattering effects, analytical problems, numerical algorithms and program packages 5

Diffraction effects, scattering effects, analytical problems...

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5th Congress on Modern Optics

作者： Sreckovic, M Ostojic, S Mircevski, J Bundaleski, N Univ Belgrade Fac Elect Engn YU-11001 Belgrade Yugoslavia

ISBN: (纸本)0819430382

Diffraction problems in analytical treatments and numeric have been constant topics for a very long time and there are a lot of different analytical expressions as well as numerical algorithms. The modern approaches are concentrated in the area of particle sizing, fibber optical sizing and loss evaluation in laser physics and techniques. Some problems between the fibber optics dimensioning and particles of cylindrical shape dimensioning are chosen and based on literature;some ameliorations in numerical approaches are made. The evolved expressions can be used for different laser wavelengths, different dimensions of disturbance objects tin scattering and diffraction phenomena) as well as different indices of refractions where the particles tin a very general way) are stratified. Some existing programs for scattering are discussed and the new computer architecture is presented here.

关键词： diffraction scattering laser computer simulation Bessel functions numerical algorithms

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numerical Solution of a General Quadratic Algebraic Matrix Riccati Equation via Probability-1 Homotopy algorithms 1

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IFAC Proceedings Volumes 2000年第24期33卷 75-80页

作者： Vassilios A. Tsachouridis Department of Engineering University of Leicester Leicester LE1 7RH UK

The design of an algorithm for the numerical solution of a generalized quadratic algebraic matrix Riccati equation is presented. The approach is based on probability-1 homotopy methods. The algorithm is illustrated wi... 详细信息

关键词： numerical algorithms numerical methods Riccati equations

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numerical solution of acoustic propagation problems using linearized Euler equations

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AIAA JOURNAL 2000年第1期38卷 22-29页

作者： Bailly, C Juvé, D Ecole Cent Lyon Lab Mecan Fluides & Acoust CNRS UMR 5509 F-69131 Ecully France

Some numerical solutions of acoustic propagation problems using linearized Euler equations are studied. The two-dimensional Euler equations are linearized around a known stationary mean flow. The computed solution is obtained by using is dispersion-relation-preserving scheme in space, combined with a fourth-order Runge-Kutta algorithm in time. This numerical integration leads to very good results in terms of accuracy, stability, and low storage. The implementation of source terms in these equations is studied very carefully in various configurations, inasmuch as the final goal is to improve and to validate the stochastic noise generation and radiation model. In this approach, the turbulent velocity field is modeled by a sum of random Fourier modes through a source term in the linearized Euler equations to predict the noise from subsonic flows. The radiation of a point source in a subsonic and a supersonic uniform mean flow is investigated. The numerical estimates are shown to be in excellent agreement with the analytical solutions. Then, the emphasis is on the ability of the method to describe correctly the multipolar structure of aeroacoustic sources. The radiation of dipolar and guadrupolar extended sources is, thus, studied. Next, a typical problem in jet noise is considered with the propagation of acoustic waves in a sheared mean flow. The numerical solution compares favorably with ray tracing. Finally, a nonlinear formulation of Euler's equations is solved to limit the growth of instability waves excited by the acoustic source terms.

关键词： Acoustic Propagation Continuity Equation Jet Noise numerical Integration Courant Friedrichs Lewy Bessel Functions numerical algorithms Aerodynamic Noise Shear Layers Mach Cones

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numerical algorithm delivery mechanisms

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MATHEMATICS AND COMPUTERS IN SIMULATION 2000年第4-5期54卷 259-268页

作者： Trefethen, AE Ford, B Numer Algorithms Grp Oxford OX2 8DR England

We consider the changing face of computing and the evolving interface of numerical algorithms from subroutines to: spreadsheets, high-level scripting languages, visual programming, Web browsers. Through examples we consider the movement from the subroutine language interface to sophisticated computational environments and trace how NAG libraries and products have evolved along this path. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.

关键词： numerical algorithms NAG libraries software

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numerical investigation of instability and transition in an obstructed channel flow

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AIAA JOURNAL 2000年第7期38卷 1173-1178页

作者： Yang, KS Inha Univ Dept Engn Mech Nam Ku Inchon 402751 South Korea

Instability and transition in an obstructed channel how are investigated using direct numerical simulation. The flow geometry under consideration is a plane channel with two-dimensional thin obstacles (baffles) mounted symmetrically in the vertical direction and periodically in the streamwise direction. The flow is steady and symmetric at low Reynolds numbers. Above a certain Reynolds number, the flow undergoes a Hopf bifurcation, leading to a solution periodic in time. At high Reynolds numbers the unsteady flow exhibits a space-time symmetry-breaking bifurcation. A secondary instability is also observed at high Reynolds numbers, which is believed to be responsible for a subsequent chaotic breakdown of the flow. To study the secondary instability, we take the periodic solution, which results from the Hopf bifurcation, as the basic flow to be disturbed with small-amplitude random noise. Depending on the Reynolds number the basic Row becomes unstable to three-dimensional disturbances, which results in a chaotic how The numerical results obtained are consistent with experimental findings currently available.

关键词： Reynolds Numbers Direct numerical Simulation Channel Flow Laminar Turbulent Transition Navier Stokes Solver Bifurcation Theory Tollmien Schlichting waves Hydrodynamic Instability Navier Stokes Equations numerical algorithms

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Strain rate sensitivity in superelasticity

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INTERNATIONAL JOURNAL OF PLASTICITY 2000年第10-11期16卷 1269-1288页

作者： Entemeyer, D Patoor, E Eberhardt, A Berveiller, M Univ Metz ENIM ENSAM MetzLab Phys & Mecan Mat Inst Super Genie Mecan & ProdUMR CNRS 7554 F-57045 Metz France

This paper. deals with the influence of martensitic transformation latent heat on the superelastic behaviour modelling. Exothermic and endothermic effects are responsible for a strong evolution on the temperature field inside the material that modifies its mechanical response. This is responsible for a strain late effect that is taken into account by introducing a coupling equation between the production rate of martensite and the temperature change, into a micro macro modelling of the superthermoelastic behaviour with the assumption that the temperature field remains uniform but different to the test temperature imposed. numerical simulations so obtained show a good agreement with experimental results performed on Cu-based superelastic alloys. (C) 2000 Published by Elsevier Science Ltd.

关键词： phase transformation constitutive behaviour polycrystalline material mechanical testing numerical algorithms

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Rate-independent crystalline and polycrystalline plasticity, application to FCC materials

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INTERNATIONAL JOURNAL OF PLASTICITY 2000年第2期16卷 179-198页

作者： Knockaert, R Chastel, Y Massoni, E Ecole Mines Paris CEMEF F-06904 Sophia Antipolis France

This paper deals with the simulation of the mechanical response and texture evolution of cubic crystals and polycrystals for a rate-independent elastic-plastic constitutive law. No viscous effects are considered. An algorithm is introduced to treat the difficult case of multi-surface plasticity. This algorithm allows the computation of the mechanical response of a single crystal. The corresponding yield surface is made of the intersection of several hyper-planes in the stress space. The problem of the multiplicity of the slip systems is solved thanks to a pseudo-inversion method. Self and latent hardening are taken into account. In order to compute the response of a polycrystal, a Taylor homogenization scheme is used. The stress-strain response of single crystals and polycrystals is computed for various loading cases. The texture evolution predicted for compression, plane strain compression and simple shear are compared with the results given by a visco-plastic polycrystalline model. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： crystal plasticity polycrystalline material elastic-plastic material numerical algorithms

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