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numerical INVESTIGATION OF THE DEFORMATION OF PLATES BY A LIQUID IN PRESS GUNS

STRENGTH OF MATERIALS 1979年第11期11卷 1293-1299页

作者： GALIEV, SU Institute of Strength Problems Academy of Sciences of the Ukrainian SSR Kiev

Conclusions Taking the possibility of cavitation into account is an obligatory condition in the dynamic calculation of plates contiguous to a liquid. Cavitation may cause an increase to a multiple in deflections. 2. In cases of underwater waves with amplitude A ≫ PK: a) decrease in wavelength with constant amplitude (or increased amplitude of the wave with constant length) leads in the calculation according to a model of a perfectly elastic liquid to an increase in the negative pressures, and in consequence, to increased differences in the results obtained with and without taking cavitation into account; b) decreased amplitude of the wave with constant length leads to increased time of growth of deflections, time of interaction of the cavitating liquid with the plate, and to increased differences in the results obtained with or without taking cavitation into account. 3. With decreasing volume of the liquid contiguous to the plate, the influence of cavitation decreases. 4. The numerical algorithms used in the work make it possible to investigate nonlinear processes in press guns. When cavitation is taken into account, it is possible to calculate successfully the case of impact of the shell at high speed, which is difficult to examine on the basis of the model of a perfectly elastic liquid because of the instability of the calculations.

关键词： Cavitation numerical Investigation Negative Pressure numerical algorithm Dynamic Calculation

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Library-based numerical reduction of the Hodgkin-Huxley neuron for network simulation

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JOURNAL OF COMPUTATIONAL NEUROSCIENCE 2009年第3期27卷 369-390页

作者： Sun, Yi Zhou, Douglas Rangan, Aaditya V. Cai, David New York Univ Courant Inst Math Sci New York NY 10012 USA

We present an efficient library-based numerical method for simulating the Hodgkin-Huxley (HH) neuronal networks. The key components in our numerical method involve (i) a pre-computed high resolution data library which contains typical neuronal trajectories (i.e., the time-courses of membrane potential and gating variables) during the interval of an action potential (spike), thus allowing us to avoid resolving the spikes in detail and to use large numerical time steps for evolving the HH neuron equations;(ii) an algorithm of spike-spike corrections within the groups of strongly coupled neurons to account for spike-spike interactions in a single large time step. By using the library method, we can evolve the HH networks using time steps one order of magnitude larger than the typical time steps used for resolving the trajectories without the library, while achieving comparable resolution in statistical quantifications of the network activity, such as average firing rate, interspike interval distribution, power spectra of voltage traces. Moreover, our large time steps using the library method can break the stability requirement of standard methods (such as Runge-Kutta (RK) methods) for the original dynamics. We compare our library-based method with RK methods, and find that our method can capture very well phase-locked, synchronous, and chaotic dynamics of HH neuronal networks. It is important to point out that, in essence, our library-based HH neuron solver can be viewed as a numerical reduction of the HH neuron to an integrate-and-fire (I&F) neuronal representation that does not sacrifice the gating dynamics (as normally done in the analytical reduction to an I&F neuron).

关键词： numerical algorithm Hodgkin-Huxley neuron Integrate-and-fire neurons Neuronal network Library method Chaos

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On numerical solution of dynamic problems in the theory of reinforced shells

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INTERNATIONAL APPLIED MECHANICS 2006年第5期42卷 536-540页

作者： Lugovoi, P. Z. Meish, V. F. Rybakin, B. P. Sekrieru, G. V. Natl Acad Sci Ukraine SP Timoshenko Inst Mech Kiev Ukraine Moldavian Acad Sci Inst Math & Comp Sci Kishinev Moldova

Dynamic problems for cylindrical shells reinforced with discrete ribs are examined. A numerical algorithm based on Richardson extrapolation is developed. Specific problems are solved, and the results are analyzed.

关键词： reinforced cylindrical shell Timoshenko model discrete ribs forced vibration numerical algorithm Richardson extrapolation

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Recent trends in numerical simulation of three-dimensional sheet forming processes

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART B-JOURNAL OF ENGINEERING MANUFACTURE 2003年第11期217卷 1553-1570页

作者： Yang, DY Kim, TJ Yoon, SJ Korea Adv Inst Sci & Technol Dept Mech Engn Taejon 305701 South Korea

The numerical method of analysis plays a key role in simulation of sheet metal forming processes for design innovation through virtual manufacturing. Recently, important advances in research and development of the sheet metal forming processes have been made by many scientists and engineers. This paper covers general issues in sheet metal forming but deals with the most challenging subjects including finite element (FE) techniques, springback, hydroforming and process design. Furthermore, the results of the proposed benchmark problems in NUMISHEET 2002 with both experiments and simulation results will be discussed.

关键词： sheet metal forming numerical algorithm springback hydroforming benchmark

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numerical STUDY OF THE DEPENDENCE OF THE CRITICAL FLUTTER SPEED AND TIME OF A PLATE ON RHEOLOGICAL PARAMETERS

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INTERNATIONAL APPLIED MECHANICS 2008年第6期44卷 676-682页

作者： Khudayarov, B. A. Tashkent Inst Irrigat & Ameliorat Tashkent Uzbekistan

The nonlinear flutter of some aircraft elements is modeled. A viscoelastic model is used. numerical algorithms for solving integro-differential equations are developed. The critical flutter speed and time for a viscoe... 详细信息

关键词： flutter viscoelastic plate numerical algorithm integro-differential equations critical speed critical time

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A Taylor series approach to the numerical analysis of the M/D/1/N queue

A Taylor series approach to the numerical analysis of the M/...

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International Conference on Computational Science (ICCS)

作者： Abbas, Karim Heidergott, Bernd Aissani, Djamil Vrije Univ Amsterdam Amsterdam Netherlands Univ Bejaia LAMOS Bejaia Algeria

This paper presents a functional approximation of the M/D/1/N built on a Taylor series approximation. numerical examples are carried out to illustrate the performance of our approach. (C) 2010 Published by Elsevier Ltd.

关键词： Taylor series numerical algorithm queueing

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Analytical and numerical Solutions of a Boundary Value Problem for Impulsive Differential Equations with Loadings

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LOBACHEVSKII JOURNAL OF MATHEMATICS 2023年第12期44卷 5276-5285页

作者： Kadirbayeva, Zh. M. Inst Math & Math Modeling Dept Differential Equat Alma Ata 050000 Kazakhstan Int Informat Technol Univ Dept Math & Comp Modeling Alma Ata 050040 Kazakhstan

The main interest of this paper is to propose a method in order to solve linear boundary value problem for impulsive differential equations with loadings. This method is called the Dzhumabaev parametrization method. The application of the this method leads the considering problem to a system of algebraic equations and Cauchy problems that are easy to solve. Some examples are introduced and the obtained results are compared with exact solution to illustrate the effectiveness and accuracy of the method.

关键词： impulsive differential equation loadings parametrization method numerical algorithm

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numerical performance of two formulations of truss topology optimization

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Acta Mechanica Sinica 1994年第4期10卷 326-335页

作者： Gengdong, Cheng Zheng, Jiang Dalian University of Technology Dalian 116024 China

The present paper studies topology optimization of truss structures in multiple loading cases and with stress constraints. It is pointed out in the paper that the special difficulty of adding bars and/or deleting bars from structure in the numerical algorithm of truss topology optimization is caused by the discontinuity of stress functions at the zero cross sectional area in the conventional formulation. In a new formulation, we replace the stress constraints by new constraints. The new constraints retain the same feasibility of the stress constraints, but are continuous in the closed interval up to zero cross sectional area. The new formulation enables us to solve topology optimization problem in the frame of the existing FEM software and mathematical programming techniques. Powell constrained variable metric method is applied to a number of examples of truss topology optimization. numerical performances of the two formulations are compared. It is shown that in the conventional formulation the iteration of numerical algorithm may be blocked by discontinuity of the stress constraint and often stops at a nonoptimum solution. And in the new formulation the bar adding and bar deleting is done rationally and a local optimum, even the global optimum can be obtained by iteration. © 1994 Chinese Society of Theoretical and Applied Mechanics.

关键词： numerical algorithm structural optimization topology optimization truss design

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numerical Computing With Modern Fortran

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丛书名： Other Titles in Applied Mathematics

2013年

作者： Richard J. Hanson Tim Hopkins

ISBN: (数字)9781611973129

ISBN: (纸本)9781611973112

The Fortran language standard has undergone significant upgrades in recent years (1990, 1995, 2003, and 2008). numerical Computing with Modern Fortran illustrates many of these improvements through practical solutions to a number of scientific and engineering problems. Readers will discover techniques for modernizing algorithms written in Fortran; examples of Fortran interoperating with C or C++ programs, plus using the IEEE floating-point standard for efficiency; illustrations of parallel Fortran programming using coarrays, MPI, and OpenMP; and a supplementary website with downloadable source codes discussed in the book. Audience: This book is intended for Fortran programmers seeking to update their programming skills using the language s latest features and for C and C++ programmers who want to understand key software aspects of numerical computing using modern Fortran. It is suitable for an upper-level undergraduate or early graduate course on advanced numerical scientific computing. Contents: Introduction; Chapter 1: The Modern Fortran Source; Chapter 2: Modules for Subprogram Libraries; Chapter 3: Generic Subprograms; Chapter 4: Sparse Matrices, Defined Operations, Overloaded Assignment; Chapter 5: Object-Oriented Programming for numerical Applications; Chapter 6: Recursion in Fortran; Chapter 7: Case Study: Toward a Modern QUADPACK Routine; Chapter 8: Case Study: Quadrature Routine qag2003; Chapter 9: IEEE Arithmetic Features and Exception Handling; Chapter 10: Interoperability with C; Chapter 11: Defined Operations for Sparse Matrix Solutions; Chapter 12: Case Study: Two Sparse Least-Squares System Examples; Chapter 13: Message Passing with MPI in Standard Fortran; Chapter 14: Coarrays in Standard Fortran; Chapter 15: OpenMP in Fortran; Chapter 16: Modifying Source to Remove Obsolescent or Deleted Features; Chapter 17: Software Testing; Chapter 18: Compilers; Chapter 19: Software Tools; Chapter 20: Fortran Book Code on SIAM Web Site; Bibliography; Index.

关键词： numerical application Fortran source code numerical algorithm scientific programming

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Fast numerical Multivariate Multipoint Evaluation 64

Fast Numerical Multivariate Multipoint Evaluation

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64th Annual IEEE Symposium on the Foundations of Computer Science (FOCS)

作者： Ghosh, Sumanta Harsha, Prahladh Herdade, Simao Kumar, Mrinal Saptharishi, Ramprasad CALTECH Pasadena CA USA Tata Inst Fundamental Res Mumbai Maharashtra India Yahoo Res San Francisco CA USA Tata Inst Fundamental Res Mumbai Maharashtra India

ISBN: (纸本)9798350318944

We design nearly-linear time numerical algorithms for the problem of multivariate multipoint evaluation over the fields of rational, real and complex numbers. We consider both exact and approximate versions of the algorithm. The input to the algorithms are (1) coefficients of an m-variate polynomial f with degree d in each variable, and (2) points a(1), ... , a(N) each of whose coordinate has absolute value bounded by one. Approximate version: Given additionally an accuracy parameter t, the algorithm computes rational numbers beta(1), ... , beta(N) such that vertical bar f(a(i)) - beta(i)vertical bar <= 1/2(t) for all i, and has a running time of ((Nm + d(m))t)(1+o(1)) for all m and all sufficiently large d. Exact version (when over rationals): Given additionally a bound s on the bit-complexity of all the rational numbers in the input and output, the algorithm computes the rational numbers f(a(1)), ... , f(a(N)), in time ((Nm + d(m))s)(1+o(1)) for all m and all sufficiently large d. Our results also naturally extend to the case when the input is over the field of real or complex numbers under an appropriate standard model of representation of field elements in such fields. Prior to this work, a nearly-linear time algorithm for multivariate multipoint evaluation (exact or approximate) over any infinite field appears to be known only for the case of univariate polynomials, and was discovered in a recent work of Moroz [Proc. 62nd FOCS, 2021]. In this work, we extend this result from the univariate to the multivariate setting. However, our algorithm is based on ideas that seem to be conceptually different from those of Moroz [Proc. 62nd FOCS, 2021] and crucially relies on a recent algorithm of Bhargava, Ghosh, Guo, Kumar & Umans [Proc. 63rd FOCS, 2022] for multivariate multipoint evaluation over finite fields, and known efficient algorithms for the problems of rational number reconstruction and fast Chinese remaindering in computational number theory.

关键词： Multivariate Multipoint Evaluation numerical algorithm Continued Fraction Chinese Remainder Theorem

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