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VIth International Conference on Mathematical Methods in Electromagnetic Theory (MMET 96)

作者： Sirenko, Y Yashina, N Inst of Radiophysics and Electronics of the Natl Acad of Sciences of Ukraine Kharkov Ukraine

ISBN: (纸本)9660200269

The main subject of present communication is the review of modern methods and algorithms for numerical analyses of transient processes in open compact, waveguide and periodic resonators. The number of considered problems is rather big one and that is the reason to reformulate several authentic results orienting them towards less complicated scalar problems: 2d scattering bodies;all ″metal″ boundaries are supposed to be perfectly conducting;filling and wave propagation medium are supposed to be non magnetic, non absorbing, non dispersive;field is supposed to be E-polarized. Computation of scattering characteristics of elementary discontinuities is of special importance in this approach. We have developed specialized algorithms, using formally correct numerical subroutines in key steps of solution constructing, including analytical regularization of operator equations of the first kind.

关键词： boundary value problem transient process numerical algorithm

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numerical Technologies for Investigating Optimal Control Problems with Free Right-Hand End of Trajectories 6th

Numerical Technologies for Investigating Optimal Control Pro...

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6th International Conference on Computer Science, Applied Mathematics and Applications (ICCSAMA)

作者： Zarodnyuk, Tatiana Gornov, Alexander Anikin, Anton Sorokovikov, Pavel Matrosov Inst Syst Dynam & Control Theory SB RAS Irkutsk Russia

ISBN: (纸本)9783030383640;9783030383633

The paper considers numerical approaches for solving optimal control problems with free trajectories at the end of the time interval. A modification of the algorithm of the conjugate gradient for studying the controlled dynamic problem is presented. The proposed technique has been tested by using the test optimal control problems. We describe the results of solving an applied problem of nanophysics. It is considered two cells of a quantum computer which are based on four tunnel-coupled semiconductor quantum dots. The multistage series of computations for investigation of system dependence from changes of the model parameters values are carried out and allowed to demonstrate the effectiveness of the proposed approach.

关键词： numerical algorithm Optimal control Applied problem

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A time integral formulation and algorithm for structural dynamics with nonlinear stiffness

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Acta Mechanica Sinica 2006年第5期22卷 479-485页

作者： Kaiping Yu Jie Zhao Department of Astronautical Science and Mechanics Harbin Institute of Technology Harbin 150001 China

A newly-developed numerical algorithm, which is called the new Generalized-α （G-α） method, is presented for solving structural dynamics problems with nonlinear stiffness. The traditional G-α method has undesired overshoot properties as for a class of α-method. In the present work, seven independent parameters are introduced into the single-step three-stage algorithmic formulations and the nonlinear internal force at every time interval is approximated by means of the generalized trapezoidal rule, and then the algorithm is implemented based on the finite difference theory. An analysis on the stability, accuracy, energy and overshoot properties of the proposed scheme is performed in the nonlinear regime. The values or the ranges of values of the seven independent parameters are determined in the analysis process. The computational results obtained by the new algorithm show that the displacement accuracy is of order two, and the acceleration can also be improved to a second order accuracy by a suitable choice of parameters. Obviously, the present algorithm is zero- stable, and the energy conservation or energy decay can be realized in the high-frequency range, which can be regarded as stable in an energy sense. The algorithmic overshoot can be completely avoided by using the new algorithm without any constraints with respect to the damping force and initial conditions.

关键词： Nonlinear structural dynamics numerical algorithm Stability Overshoot

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A Novel Fractional Plastic Damage Model for Quasi-brittle Materials

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Acta Mechanica Solida Sinica 2021年第5期34卷 706-717页

作者： Peng-Fei Qu Qi-Zhi Zhu Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering Hohai UniversityNanjing210098China College of Civil and Transportation Engineering Hohai UniversityNanjing210098China

In this work,a novel constitutive model is developed within the framework of fractional plasticity to delineate the coupling between inelastic deformation and damage of quasi-brittle *** with the common challenge of determining plastic flow direction,we resort herein to the Riemann–Liouville definition of fractional derivatives,instead of introducing an additional plastic *** pre-peak hardening behavior is described using an exponential function,while the post-peak softening response is viewed as the consequence of material *** describing damage evolution,a damage criterion is constructed in terms of plastic volume dilation related to micro-crack *** is conducive to supply a new insight for describing the complex influence of the non-orthogonality of plastic flow on damage *** numerical applications,a semi-implicit return mapping algorithm is *** predictive performance of the model is evaluated by comparing numerical simulations with experimental data under various loading paths.

关键词： Quasi-brittle materials Fractional plasticity Damage Dilatancy numerical algorithm

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A differential algorithm for the Lyapunov spectrum

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PHYSICA D-NONLINEAR PHENOMENA 2011年第16期240卷 1221-1227页

作者： Stachowiak, Tomasz Szydlowski, Marek Jagiellonian Univ Astron Observ PL-30244 Krakow Poland Copernicus Ctr Interdisciplinary Studies PL-30387 Krakow Poland Jagiellonian Univ Marc Kac Complex Syst Res Ctr PL-30059 Krakow Poland

We present a new algorithm for computing the Lyapunov exponents spectrum based on a matrix differential equation. The approach belongs to the so-called continuous type, where the rate of expansion of perturbations is obtained for all times, and the exponents are reached as the limit at infinity. It does not involve exponentially divergent quantities so there is no need of rescaling or realigning of the solution. We show the algorithm's advantages and drawbacks using mainly the example of a particle moving between two contracting walls. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Lyapunov exponents numerical algorithm Highly oscillatory systems

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Extreme values of solution of Caputo-Hadamard uncertain fractional differential equation and applications

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2024年第6期47卷 4105-4121页

作者： Liu, Hanjie Zhu, Yuanguo He, Liu Nanjing Univ Sci & Technol Sch Math & Stat Nanjing Peoples R China

Uncertain fractional differential equation (UFDE) is a useful tool for studying complex systems in uncertain environments. The mathematical characteristics of solution of an UFDE are also widely used in various fields. In this paper, we give the extreme value theorems of solution of Caputo-Hadamard UFDE and applications. A numerical algorithm for obtaining the inverse uncertainty distributions (IUDs) for extreme values of solution of Caputo-Hadamard UFDE is presented;the stability and feasibility of the proposed algorithm are validated by numerical experiments. As an application of extreme value theorems in uncertain financial market, the pricing formulas of the American option based on the new uncertain stock model are given. Besides, the algorithms for computing the price of the American option without explicit pricing formulas based on the Simpson's rule are designed. Finally, the price fluctuation of the American option is illustrated by numerical experiments.

关键词： American option extreme value theorems numerical algorithm Simpson's rule uncertain fractional differential equation

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In-situ alignment calibration of attitude and ultra short baseline sensors for precision underwater positioning

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OCEAN ENGINEERING 2008年第14-15期35卷 1448-1462页

作者： Chen, Hsin-Hung Natl Sun Yat Sen Univ Asian Pacific Ocean Res Ctr Inst Appl Marine Phys & Undersea Technol Kaohsiung 804 Taiwan

Positioning accuracy of an ultra short baseline (USBL) tracking system is significantly reduced with the increase of alignment errors in the installation of sensors. Although techniques for sensor alignment calibration have been developed, they are either complex or lacking in rigor. This study proposes an algorithm to estimate the angular misalignments of a USBL transceiver relative to attitude sensors. The numerical algorithm is based on the positioning errors caused by heading, pitch, and roll misalignments, respectively, when running a circular survey around a seabed transponder. The positioning errors introduced by the angular misalignments outline an iterative scheme of estimating the roll alignment error first, next the heading alignment error, and then finally the pitch alignment error. This makes possible the efficient estimation of all angular misalignments with a high degree of accuracy. With the consideration of measurement error and executing a non-centered and non-perfect circle around the true transponder position, numerical simulations are performed to validate the effectiveness of the proposed algorithm. The simulation results show that the proposed algorithm is robust to the effects of measurement error, non-centered circles, and non-perfect circles. Moreover, the estimates converge fairly quickly, and can be achieved with good accuracy in only a few iterations. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： Ultra short baseline Transponder Sensor alignment numerical algorithm Misalignment calibration Positioning

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Discrete techniques for 3-D digital images and patterns under transformation

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IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS 1998年第6期28卷 883-894页

作者： Li, ZC Natl Sun Yat Sen Univ Dept Math Appl Kaohsiung 80424 Taiwan

Three-dimensional (3-D) digital images and patterns under transformations are facilitated by the splitting- shooting method (SSM) and the splitting- integration method (SIM), The combination (CSIM) of using both SSM and SIM and two combinations (CIIM) of using SIM only are proposed for a cycle conversion T-1T, where T is a nonlinear transformation, and T-1 is its inverse transformation. This paper focuses on exploitation of accuracy of obtained image greyness. In our discrete algorithms, letting a 3-D pixel be split into N-3 subpixels, the convergence rates, O(1/N), O(1/N-2), and O(1/N-3);of sequential error can be achieved by the three combinations respectively. High convergence rates indicate less CPU time needed. Both error bounds and computation of pixel greyness have shown the significance of the proposed new algorithms.

关键词： digital pattern image transformation inverse transformation numerical algorithm three-dimensional image

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algorithms for Stochastically Rounded Elementary Arithmetic Operations in IEEE 754 Floating-Point Arithmetic

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IEEE TRANSACTIONS ON EMERGING TOPICS IN COMPUTING 2021年第3期9卷 1451-1466页

作者： Fasi, Massimiliano Mikaitis, Mantas Orebro Univ Sch Sci & Technol S-70182 Orebro Sweden Univ Manchester Dept Math Manchester M13 9PL Lancs England

We present algorithms for performing the five elementary arithmetic operations (+, -, x, divided by, and root) in floating point arithmetic with stochastic rounding, and demonstrate the value of these algorithms by discussing various applications where stochastic rounding is beneficial. The algorithms require that the hardware be compliant with the IEEE 754 floating-point standard and that a floating-point pseudorandom number generator be available. The goal of these techniques is to emulate stochastic rounding when the underlying hardware does not support this rounding mode, as is the case for most existing CPUs and GPUs. By simulating stochastic rounding in software, one has the possibility to explore the behavior of this rounding mode and develop new algorithms even without having access to hardware implementing stochastic rounding- once such hardware becomes available, it suffices to replace the proposed algorithms by calls to the corresponding hardware routines. When stochastically rounding double precision operations, the algorithms we propose are between 7.3 and 19 times faster than the implementations that use the GNU MPFR library to simulate extended precision. We test our algorithms on various tasks, including summation algorithms and solvers for ordinary differential equations, where stochastic rounding is expected to bring advantages.

关键词： Stochastic processes Hardware Standards Tools Software Libraries Monte Carlo methods Floating-point arithmetic error-free transformation stochastic rounding numerical analysis numerical algorithm IEEE 754

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A new computational algorithm for the calculation of maximum wind energy penetration in autonomous electrical generation systems

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APPLIED ENERGY 2009年第7-8期86卷 1011-1023页

作者： Kaldellis, J. K. Kavadias, K. A. Filios, A. E. TEI Piraeus Lab Soft Energy Applicat & Environm Protect Athens 12201 Greece Sch Pedag & Technol Educ Fluid Mech & Turbomachines Lab N Heraklio Attica 14121 Greece

The entirety of Aegean Sea Islands, including Crete. is characterized during the last decade by a considerable annual increase of the electrical power demand exceeding the 5% in annual basis. This continuous amplifying electricity consumption is hardly fulfilled by several outmoded internal combustion engines usually at a very high operational cost. On the other hand most of the islands possess high wind potential that may substantially contribute in order to meet the corresponding load demand. However, in this case some wind energy absorption problems related with the collaboration between wind parks and the local electricity production system cannot be neglected. In this context, the present study is devoted to realistically estimating the maximum wind energy absorption in autonomous electrical island networks. For this purpose a new reliable and integrated numerical algorithm is developed, using the available information of the corresponding electricity generation system, in order to calculate the maximum acceptable wind power contribution in the system. under the normal restrictions that the system manager imposes. The proposed algorithm is successfully compared with existing historical data as well as with the results of a recent investigation based almost exclusively on the existing wind parks energy production. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： numerical algorithm Electricity production Thermal power stations Wind energy Penetration constraints Maximum wind energy absorption Autonomous island networks

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