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Effective algorithm for two-dimensional frictional system involving arbitrary impacting boundaries

INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES 2020年第0期167卷 105232-000页

作者： Wang, Xiaosun Zhao, Deng Wu, Shijing Li, Xiaofeng Yuan, Hao Li, Qiaoquan Wuhan Univ Sch Power & Mech Engn Wuhan 430072 Peoples R China

Impacting and friction are always encountered in the mechanical system and make the system experience nonlinearities in both force-position and force-velocity characteristics. In this paper, we propose one effective numerical algorithm for a two-dimensional frictional system involving the impacting by employing the closed form solution to yield the slip responses and extend the closed form solutions for curve length to predict the impacting location and time with high accuracy. By performing the accuracy analysis and robustness analysis through several representative scenarios, we reveal that, (1) the impacting dynamic responses can be predicted through our new algorithm with high accuracy, (2) the accumulative errors of dynamic responses are insensitive to the complex boundary, (3) the new algorithm can keep better robustness when involving repeated impacting.

关键词： numerical algorithm Accuracy analysis Robust analysis Impacting Two-dimensional frictional system

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Application of Residual Power Series Method for the Solution of Time-fractional Schrodinger Equations in One-dimensional Space

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FUNDAMENTA INFORMATICAE 2019年第2期166卷 87-110页

作者： Abu Arqub, Omar Univ Jordan Fac Sci Dept Math Amman 11942 Jordan

The object of this article is to present the computational solution of the time-fractional Schrodinger equation subject to given constraint condition based on the generalized Taylor series formula in the Caputo sense. The algorithm methodology is based on construct a multiple fractional power series solution in the form of a rabidly convergent series with minimum size of calculations using symbolic computation software. The proposed technique is fully compatible with the complexity of this problem and obtained results are highly encouraging. Efficacious computational experiments are provided to guarantee the procedure and to illustrate the theoretical statements of the present algorithm in order to show its potentiality, generality, and superiority for solving such fractional equation. Graphical results and numerical comparisons are presented and discussed quantitatively to illustrate the solution.

关键词： Fractional Schrodinger equation Multiple fractional power series Residual power series method numerical algorithm Symbolic computations

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Detection of the singularities of a complex function by numerical approximations of its Laurent coefficients

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numerical algorithmS 2018年第4期77卷 955-982页

作者： Rizzardi, Mariarosaria Univ Napoli Parthenope Ctr Direz Napoli DiST Dipartimento Sci & Tecnol Is C4 I-80143 Naples Italy

For several applications, it is important to know the location of the singularities of a complex function: just for example, the rightmost singularity of a Laplace Transform is related to the exponential order of its inverse function. We discuss a numerical method to approximate, within an input accuracy tolerance, a finite sequence of Laurent coefficients of a function by means of the Discrete Fourier Transform (DFT) of its samples along an input circle. The circle may also enclose some singularities, since the method works with the Laurent expansion. The DFT is computed by the FFT algorithm so that, from a computational point of view, the efficiency is guaranteed. The function samples may be obtained by solving a numerical problem such as, for example, a differential problem. We derive, as consequences of the method, some new outcomes able to detect those singularities which are close to the circle and to discover if the singularities are all external or internal to the circle so that the Laurent expansion reduces to its regular or singular part, respectively. Other singularities may be located by means of a repeated application of the method, as well as an analytic continuation. Some examples and results, obtained by a first implementation, are reported.

关键词： numerical algorithm Software suite Interactive software Complex singularities Laurent coefficients Analytic continuation

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The Benchmark Problems for the Assessment of numerical algorithms on Fractional-Order Differential Equations 29

The Benchmark Problems for the Assessment of Numerical Algor...

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29th Chinese Control And Decision Conference (CCDC)

作者： Bai, Lu Xue, Dingyu Northeastern Univ Sch Informat Sci & Engn Shenyang 110004 Liaoning Peoples R China Shenyang Univ Sch Informat Engn Shenyang 110044 Liaoning Peoples R China

ISBN: (纸本)9781509046577

There are many numerical algorithms for solving the fractional-order differential equations (FODEs). The numerical algorithms are very different, and it is difficult to compare their performances. To solve this problem, some different FODEs with the known analytical solution are designed and proposed, they could be used as the benchmark problems for testing the numerical algorithms. A Simulink block diagram scheme is proposed for solving these benchmark problems, and the computing errors and the running times are reported. These benchmark problems and the solutions are constituted as a framework, and the numerical algorithms for solving the FODEs could be compared in the same framework. The comparing result could assess which algorithm is better to a concrete FODE.

关键词： Fractional-order differential equation Benchmark problem numerical algorithm Simulink block diagram

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Discrete State Event-Driven Approach for High-Power Converter Simulations 11

Discrete State Event-Driven Approach for High-Power Converte...

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11th Annual IEEE Energy Conversion Congress and Exposition (ECCE)

作者： Shi, Bochen Zhao, Zhengming Zhu, Yicheng Yu, Zhujun Ju, Jiahe Yuan, Liqiang Chen, Kainan Tsinghua Univ Dept Elect Engn State Key Lab Control & Simulat Power Syst & Gene Beijing Peoples R China

ISBN: (纸本)9781728103952

Demands for high-power converters are increasing rapidly. Nevertheless, due to their complex structures and multi-time-scale features, accurate and efficient simulation of such systems has long been a huge obstacle. Aiming at improving the unacceptably slow simulation speed of high-power converters, this paper improves Discrete State Event-Driven (DSED) approach by implementing a decoupling method. Taking a 10kV 1MW electric energy router as an example, this paper evaluates the effectiveness of DSED with the proposed decoupling method in high-power applications. In the studied case, compared with commercially available tool for power electronics simulation, PLECS (R), DSED can achieve an up to 1000-fold improvement in simulation speed under the same accuracy: PLECS (R) takes 6 hours while DSED only takes 18 seconds. DSED provides a powerful simulation tool for analysis, design and control of high-power converters.

关键词： event-driven simulation numerical algorithm circuit partitioning high-power converter electric energy router solid-state transformer

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Computation of Initial Transformation for Implicit Double Step in the Periodic QZ algorithm 23

Computation of Initial Transformation for Implicit Double St...

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23rd International Conference on System Theory, Control and Computing (ICSTCC)

作者： Sima, Vasile Natl Inst Res & Dev Informat Bucharest Romania

ISBN: (纸本)9781728106991

The periodic QZ algorithm (pQZ) is required in many applications, including periodic linear systems, cyclic matrices and matrix pencils, and some structured eigenproblems. The implicit double pQZ step is the essential part of this algorithm, since it determines its convergence rate. The pQZ step acts on a formal matrix product already reduced to the Hessenberg-triangular form. Each pQZ step starts with an initial transformation aimed to make the first column of the identity matrix and of the Wilkinson double-shift polynomial parallel. This transformation is found in an implicit manner, without evaluating the formal matrix product and the polynomial. This paper presents in detail the computation of the initial transformation in the periodic QZ step, and summarizes the benefits obtained using a new such approach for solving skew-Hamiltonian/Hamiltonian eigenproblems. The previous convergence failures are avoided and the number of iterations necessary to converge can be significantly reduced.

关键词： linear multivariable system periodic system numerical algorithm software stability

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numerical Simulation of Vibration of Composite Pipelines Conveying Pulsating Fluid

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INTERNATIONAL JOURNAL OF APPLIED MECHANICS 2019年第9期11卷

作者： Khudayarov, B. A. Komilova, Kh M. Turaev, F. Zh Tashkent Inst Irrigat & Agr Mechanizat Engineers Dept Higher Math Tashkent 100000 Uzbekistan

Vibration problems of pipelines made of composite materials conveying pulsating flow of gas and fluid are investigated in the paper. A dynamic model of motion of pipelines conveying pulsating fluid flow supported by a Hetenyi's base is developed taking into account the viscosity properties of the structure material, axial forces, internal pressure and Winkler's viscoelastic base. To describe the processes of viscoelastic material strain, the Boltzmann-Volterra integral model with weakly singular hereditary kernels is used. Using the Bubnov-Galerkin method, the problem is reduced to the study of a system of ordinary integro-differential equations (IDE). A computational algorithm is developed based on the elimination of the features of IDE with weakly singular kernels, followed by the use of quadrature formulas. The effect of rheological parameters of the pipeline material, flow rate and base parameters on the vibration of a viscoelastic pipeline conveying pulsating fluid is analyzed. The convergence analysis of the approximate solution of the Bubnov-Galerkin method is carried out. It was revealed that the viscosity parameters of the material and the pipeline base lead to a significant change in the critical flow rate. It was stated that an increase in excitation coefficient of pulsating flow and the parameter of internal pressure leads to a decrease in the critical flow rate. It is shown that an increase in the singularity parameter, the Winkler base parameter, the rigidity parameter of the continuous base layer and the Reynolds number increases the critical flow rate.

关键词： Mathematical model viscoelasticity pipeline numerical algorithm vibration fluid

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algorithm Study for Supersonic Steam Injection Process Simulation of The Pressurizer Relief Tank 10

Algorithm Study for Supersonic Steam Injection Process Simul...

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10th IEEE International Conference on Software Engineering and Service Science (ICSESS)

作者： Wang, Yi Guo, Xiao-Wei Li, Chao Chcn, Lijuan Zhao, Ran Yang, Canqun Natl Univ Def Technol Coll Comp Changsha 410073 Peoples R China

ISBN: (纸本)9781728109459

Simulating the steam Injection process of pressurized decompression tanks is a challenging engineering problem due to the large amount of computational resource requirements and its complex physical model. This study is a necessary algorithmic study to perform a 3D numerical simulation from the PRT (Pressurizer Relief Tank) to the transient dumping process in a chamber containing a tank. Parallel simulation was performed by the open source CFD tool OpenFOAM based on the numerical algorithm we discussed. The results show that the simulation results are in accordance with the basic physical laws, and the results reflect the pressure and temperature of the entire pressure relief tank in detail, which can provide guidance for the safe design of the reactor coolant system.

关键词： pressurizer relief tank steam Injection process OpenFOAM numerical algorithm

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A New Saint-Venant Solver for SWMM 11th

A New Saint-Venant Solver for SWMM

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11th International Conference on Urban Drainage Modelling (UDM)

作者： Hodges, Ben R. Liu, Frank Rowney, A. Charles Univ Texas Austin Ctr Infrastruct Modeling & Management Austin TX 78712 USA IBM Res Austin TX USA

ISBN: (纸本)9783319998671;9783319998664

The next generation of the public domain Storm Water Management Model (SWMM) code needs to be able to effectively use parallelization of 1000 + threads for high-resolution simulation of large urban drainage systems. We propose a new explicit solution technique using a "no-neighbour" finite-volume algorithm. A no-neighbour algorithm is strictly limited in the design of its time/space discretization stencil to limit the communication bandwidth issues that typically cause codes to lose efficiency when applied over large numbers of parallel threads. Returning SWMM to an explicit solver creates a number of challenges for implementing the solution technique, but also raises some new possibilities for how the model can be used. In this work, we briefly describe the proposed algorithm and examine its performance in simulating a steep urban stream.

关键词： numerical algorithm Multi-threading parallel Saint-Venant equations

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numerical method and convergence order for second-order impulsive differential equations

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ADVANCES IN DIFFERENCE EQUATIONS 2019年第1期2019卷 260-260页

作者： Mei, Liangcai Sun, Hongbo Lin, Yingzhen Beijing Inst Technol Zhuhai Campus Zhuhai Peoples R China

This paper is devoted to the numerical scheme for the impulsive differential equations. The main idea of this method is, for the first time, to establish a broken reproducing kernel space that can be used in pulse models. Then the uniform convergence of the numerical solution is proved, and the time consuming Schmidt orthogonalization process is avoided. The proposed method is proved to be stable and have the second-order convergence. The algorithm is proved to be feasible and effective through some numerical examples.

关键词： Impulsive differential equations Broken reproducing kernel space Convergence order numerical algorithm

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