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numerical solution of eigenvalue problems for Hamiltonian systems

Advances in Computational Mathematics 1994年第2期2卷 155-184页

作者： Marletta, Marco Department of Mathematics and Computer Science University of Leicester Leicester LE1 7RH University Road United Kingdom

This paper discusses the numerical solution of eigenvalue problems for Hamiltonian systems of ordinary differential equations. Two new codes are presented which incorporate the algorithms described here;to the best of the author's knowledge, these are the first codes capable of solving numerically such general eigenvalue problems. One of these implements a new new method of solving a differential equation whose solution is a unitary matrix. Both codes are fully documented and are written in Pfort-verified Fortran 77, and will be available in netlib/aicm/sl11f and netlib/aicm/sl12f. © 1994 J.C. Baltzer AG, Science Publishers.

关键词： AMS(MOS) subject classification: 65L15 eigenvalue problems Hamiltonian systems mathematical software numerical algorithms

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An improved two-terminal numerical algorithm for fault location estimation considering shunt capacitance

An improved two-terminal numerical algorithm for fault locat...

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General Meeting of the Power-Engineering-Society

作者： Kim, H. H. Lee, C. J. Radojevic, Z. M. Park, J. B. Shin, J. R. Konkuk Univ Dept Elect Engn Seoul 143701 South Korea

ISBN: (纸本)9781424404926

This paper presents a new two-terminal numerical algorithm for fault location estimation using the synchronized phasor in time-domain. The proposed algorithm is also based on the synchronized voltage and current phasor measured from the PMUs(Phasor Measurement Units) installed at both ends of the transmission lines. In this paper the algorithm is given with-out shunt capacitance and with shunt capacitance using, Pi -model and estimated using DFT(Discrete Fourier Transform) and the LES(Least Error Squares Method). The algorithm uses a very short data window and classification for real-time transmission line protection. To test the validity, of the proposed algorithm, the Electro-Magnetic Transient Program(EMTP) and MATLAB is used.

关键词： numerical algorithms fault location time-domain with-out/with shunt capacitance protection

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Theoretical formulation and numerical implementation of electromagnetic and thermomechanical loading processes in solids

Theoretical formulation and numerical implementation of elec...

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作者： Thomas, Jesse D. University of Michigan

学位级别：Ph.D.

The electromagnetic-thermal-mechanical process of electromagnetic forming (EMF) is a high velocity manufacturing technique that uses electromagnetic (Lorentz) body forces to shape sheet metal parts. One of the several advantages of this technique is the considerable ductility increase observed in several metals, particularly aluminum. In this research two important aspects of this process are addressed: the influence of the sheet metal's constitutive response on ductility and the consistent formulation of the fully coupled electromagnetic-mechanical problem. The first part of the work addresses the necking localization of a metal sheet during an electromagnetic process. A "weak band" model is used to predict the onset of necking of a thin sheet under plane stress and in-plane electric currents, an idealization of the local conditions in unconstrained electromagnetic loading. This work finds that EMF increases ductility over quasistatic techniques, due to the material's strain-rate sensitivity, and details how the material constitutive response and process characteristics affect ductility. The general theory is subsequently applied to freely expanding electromagnetically loaded aluminum tubes. Necking strains are measured in tubes of various geometries that are loaded by different forming coils and electric currents. The experimental results show reasonable agreement with the corresponding theoretical forming limit predictions, which indicate a two to three fold increase in the forming limits with respect to the quasistatic case. The second part of the work pertains to predictive modeling of EMF processes. Recent works do not consistently account for the coupling between electromagnetic fields and finite deformations. Typically, separate solutions to the electromagnetic and finite strain mechanical problems are combined in lock-step. The present work employs a fully coupled Lagrangian (reference configuration) least-action variational principle. This principle forms

关键词： Electromagnetic-thermal-Mechanical Processes Continuum Mechanics High Strain Rate Ductility numerical algorithms Variational Calculus Thesis

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DeepStability: A Study of Unstable numerical Methods and Their Solutions in Deep Learning 22

DeepStability: A Study of Unstable Numerical Methods and The...

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ACM/IEEE 44th International Conference on Software Engineering (ICSE)

作者： Kloberdanz, Eliska Kloberdanz, Kyle G. Le, Wei Iowa State Univ Dept Comp Sci Ames IA 50011 USA Cape Privacy Ames IA USA

ISBN: (纸本)9781450392211

Deep learning (DL) has become an integral part of solutions to various important problems, which is why ensuring the quality of DL systems is essential. One of the challenges of achieving reliability and robustness of DL software is to ensure that algorithm implementations are numerically stable. DL algorithms require a large amount and a wide variety of numerical computations. A naive implementation of numerical computation can lead to errors that may result in incorrect or inaccurate learning and results. A numerical algorithm or a mathematical formula can have several implementations that are mathematically equivalent, but have different numerical stability properties. Designing numerically stable algorithm implementations is challenging, because it requires an interdisciplinary knowledge of software engineering, DL, and numerical analysis. In this paper, we study two mature DL libraries PyTorch and Tensorflow with the goal of identifying unstable numerical methods and their solutions. Specifically, we investigate which DL algorithms are numerically unstable and conduct an in-depth analysis of the root cause, manifestation, and patches to numerical instabilities. Based on these findings, we launch DeepStability, the first database of numerical stability issues and solutions in DL. Our findings and DeepStability provide future references to developers and tool builders to prevent, detect, localize and fix numerically unstable algorithm implementations. To demonstrate that, using DeepStability we have located numerical stability issues in Tensorflow, and submitted a fix which has been accepted and merged in.

关键词： numerical stability deep learning numerical algorithms

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Dynamic interaction between pantograph and rigid overhead lines using a coupled FEM - multibody procedure

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MECHANISM AND MACHINE THEORY 2016年 97卷 100-111页

作者： Bautista, A. Montesinos, J. Pintado, P. Univ Castilla La Mancha Dept Mech Engn ETSI Ind E-13071 Ciudad Real Spain Electrificac & Estudios Ferroviarios Albacete 02008 Spain

Most studies on the interaction between pantograph and overhead contact systems refer to the conventional catenary composed of contact and messenger wires and droppers, whereas the literature related to the interaction with rigid overhead conductor rails is limited. This paper presents an algorithm capable of simulating the interaction between a catenary represented as a Finite Element Model and a pantograph modeled as a multibody linkage. The algorithm will be proven to be accurate and efficient. The procedure has been used to simulate the interaction in different scenarios as a tool to optimize the design of the infrastructure as well as the configuration of the pantograph. The piece of software produced can consider interaction of one or two pantographs with one or two overhead lines in transition sections. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Rigid overhead conductor rail Pantograph FEM Multibody Dynamic interaction numerical algorithms

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INSTABILITIES OF FLOWS OVER BODIES AT LARGE INCIDENCE

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AIAA JOURNAL 1992年第1期30卷 94-100页

作者： DEGANI, D NASA Ames Research Center Moffett Field California 94035

The phenomena of the flow about an ogive-cylinder placed at incidence to an oncoming stream were numerically investigated for angles of attack of 60 and 80 deg. It was found that the flow around the cylindrical part of the body became unsteady, and vortex shedding was observed. For the 80-deg case, the corresponding Strouhal frequency was about 0.2, which is in agreement with the average value of the Strouhal frequency for flow around a two-dimensional cylinder. For both angles of attack, a small temporal disturbance of finite duration was sufficient to trigger the unsteadiness, which evolved to a finite amplitude fluctuation in the wake. Therefore, it seems possible that the origin of flow unsteadiness and vortex shedding in the wake is an absolute-type instability of the originally steady flow. When a permanent disturbance was also added near the tip of the body in the case of 60-deg angle of attack, a pair of steady, asymmetric vortices emerged from the vicinity of the body nose. These vortices could be the result of a convective-type instability of the originally symmetric now. It appears that both types of instability may coexist.

关键词： Strouhal Number Angle of Attack Freestream Mach Number Two Dimensional Flow Pressure Coefficient Shear Layers Conservation Equations numerical Simulation numerical algorithms Aerospace Sciences

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Serrated flow in NaI:Tl scintillator crystals

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Journal of Materials Science & Technology 2023年第22期153卷 120-127页

作者： Jamieson Brechtl Xie Xie Rui Feng Gongyao Wang Charles Melcher Mariya Zhuravleva Peter K.Liaw The Bredesen Center for Interdisciplinary Research and Graduate Education The University of TennesseeKnoxvilleTN 37996USA Department of Materials Science and Engineering The University of TennesseeKnoxvilleTN 37996USA Scintillation Materials Research Center The University of TennesseeKnoxvilleTN 37996USA

The serrated-flow behavior is an important phenomenon that unveils material-deformation mechanisms,as reported for various kinds of *** doped with Tl(NaI:Tl)is unique among scintillation ma-terials in that the structure contains glide planes that are linked to serration *** the present work,single crystals of NaI:Tl were subjected to room-temperature compression experiments at different strain *** serrated flow was observed,and complexity and multifractal analyses were performed to analyze the serration *** findings revealed that the strain rate had a pronounced effect on the complexity and multifractality of the serrated flow,similar to what has been found in other alloy *** results also indicate that there may be a strong link between the complexity of the serrated flow behavior and the heterogeneity of the underlying *** is expected that the present work could be a step toward a better understanding of the deformation behavior and forgeability of NaI:Tl single crystals.

关键词： Dislocations Ceramic material Mechanical testing numerical algorithms Scintillator

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A NOTE ON EXPLOITING STRUCTURE WHEN USING SLACK VARIABLES

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MATHEMATICAL PROGRAMMING 1994年第1期67卷 89-97页

作者： CONN, AR GOULD, N TOINT, PL CERFACS F-31057 TOULOUSEFRANCE FAC UNIV NOTRE DAME PAIX DEPT MATHB-5000 NAMURBELGIUM

We show how to exploit the structure inherent in the linear algebra for constrained nonlinear optimization problems when inequality constraints have been converted to equations by adding slack variables and the proble... 详细信息

关键词： LARGE-SCALE PROBLEMS NONLINEAR OPTIMIZATION numerical algorithms SLACK VARIABLES AUGMENTED LAGRANGIAN

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Nonlinear programming without a penalty function or a filter

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MATHEMATICAL PROGRAMMING 2010年第1期122卷 155-196页

作者： Gould, N. I. M. Toint, Ph. L. FUNDP Univ Namur Dept Math B-5000 Namur Belgium Univ Oxford Comp Lab Oxford OX1 3QD England

A new method is introduced for solving equality constrained nonlinear optimization problems. This method does not use a penalty function, nor a filter, and yet can be proved to be globally convergent to first-order stationary points. It uses different trust-regions to cope with the nonlinearities of the objective function and the constraints, and allows inexact SQP steps that do not lie exactly in the nullspace of the local Jacobian. Preliminary numerical experiments on CUTEr problems indicate that the method performs well.

关键词： Nonlinear optimization Equality constraints numerical algorithms Global convergence

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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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