In this paper, a numerical method for computing the relaxation modulus of a linearly viscoelastic material is presented. The method is valid for relaxation tests where a constant strain rate is followed by a constant ...
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In this paper, a numerical method for computing the relaxation modulus of a linearly viscoelastic material is presented. The method is valid for relaxation tests where a constant strain rate is followed by a constant strain. The method is similar to the procedure suggested by Zapas and Phillips. Unlike Zapas-Phillips approach, this new method can be also applied for times shorter than t (1)/2, where t (1) denotes time when the maximum strain is achieved. Therefore this method is very suitable for materials that experiences fast relaxation. The method is verified with numerical simulations. Results from the simulations are compared with analytical solution and Zapas-Phillips method. Results indicate that the presented approach is suitable for estimating the relaxation modulus.
A novel, simple iterative algorithm is used to calculate the temperature distribution in a finite medium for the case of non-Fourier (hyperbolic) heat conduction. In this algorithm the temperature is calculated explic...
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A novel, simple iterative algorithm is used to calculate the temperature distribution in a finite medium for the case of non-Fourier (hyperbolic) heat conduction. In this algorithm the temperature is calculated explicitly in one simple calculation that is repeated for each time step as the heat wave propagates through the medium with constant speed. When the wave reaches a boundary of the medium, it bounces back and moves in the opposite direction. All simple initial and boundary conditions can be modelled. An example of using the algorithm for the case of a finite, thermally insulated medium is given, and the results are compared with an exact analytical solution.
The mathematical model of the Baltic Sea dynamics developed at the Institute of numerical Mathematics of RAS is considered. The problem of variational assimilation of average daily data for the sea surface temperature...
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The mathematical model of the Baltic Sea dynamics developed at the Institute of numerical Mathematics of RAS is considered. The problem of variational assimilation of average daily data for the sea surface temperature (SST) is formulated and studied with the use of covariance matrices of observation data errors. Based on variational assimilation of satellite observation data, we propose an algorithm for solving the inverse problem of the heat flux reconstruction on the sea surface. The results of numerical experiments on reconstruction of the heat flux function are presented for the problem of variational assimilation of observation SST data.
Aiming at the shortcomings of the analytical algorithm and numerical algorithm for calculating the eddy current losses in the solid rotor of high speed squirrel cage induction motor, this study proposes a semi-analyti...
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Aiming at the shortcomings of the analytical algorithm and numerical algorithm for calculating the eddy current losses in the solid rotor of high speed squirrel cage induction motor, this study proposes a semi-analytical algorithm. Based on the magnetic field of the rotor surface and Maxwell's equations, the analytical formula of this algorithm is derived. According to the law of energy conservation, the losses in rotor and rotor bars are calculated, respectively, so that the eddy current losses in the solid rotor are calculated indirectly. Taking a high speed squirrel cage induction motor as an example, the eddy current losses in the solid rotor are calculated by the semi-analytical method. The calculation result is verified by the two-dimensional transient finite-element method, and the calculation result meets the basic requirements of engineering practice.
Gauss-Newton method is mainly designed and exploited to solve the nonlinear least squares problems of static overdetermined systems with order-2 precision. When the system comes to the future time-variant situation, t...
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Gauss-Newton method is mainly designed and exploited to solve the nonlinear least squares problems of static overdetermined systems with order-2 precision. When the system comes to the future time-variant situation, the disadvantages of the Gauss-Newton method in effectiveness and precision need to be overcome. On the basis of Zhang neurodynamics, the first Zhang neurodynamics model and the second Zhang neurodynamics model are constructed and discussed to obtain the nonlinear least squares solution of the time-variant overdetermined system in the future time-variant situation. Then, we propose a novel eleven-instant Zhang time discretization formula whose convergenceness and truncation errors of order-6 are proved through rigorous mathematical derivation. The proposed eleven-instant Zhang time discretization formula is thus utilized to discretize the constructed first Zhang neurodynamics model and second Zhang neurodynamics model, respectively. Consequently, a novel discrete-time eleven-instant first Zhang neurodynamics-based algorithm and a novel discrete-time eleven-instant second Zhang neurodynamics-based algorithm are proposed and generalized to obtain the predictive nonlinear least squares solution of the time-variant overdetermined system in the future time-variant situation. Furthermore, the precisions of the proposed discrete-time eleven-instant first Zhang neurodynamics-based and second Zhang neurodynamics-based algorithms are proved to be of order-6 through mathematical derivation. Moreover, this work reveals the facts that the Gauss-Newton method is actually the simplified version of the discrete-time two-instant first Zhang neurodynamics-based algorithm and the discrete-time two-instant second Zhang neurodynamics-based algorithm, respectively. Finally, five challenging numerical experiments, including the problem-solving of the critical force of a crane in a complicated environment, are carried out. The experimental results further substantiate the appli
In this article, our damped-heat wave (DHW) algorithm for the calculation of temperature distribution in a homogeneous finite medium is compared with Fourier's algorithm for transmission of heat between discrete b...
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In this article, our damped-heat wave (DHW) algorithm for the calculation of temperature distribution in a homogeneous finite medium is compared with Fourier's algorithm for transmission of heat between discrete bodies.
We have extended our previous 2D method [Gerya, T.V., Yuen, D.A., 2003. Characteristics-based marker-in-cell method with conservative finite-differences schemes for modeling geological flows with strongly variable tra...
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We have extended our previous 2D method [Gerya, T.V., Yuen, D.A., 2003. Characteristics-based marker-in-cell method with conservative finite-differences schemes for modeling geological flows with strongly variable transport properties. Phys. Earth Planet. Interiors 140, 295-320], which is a combination of conservative finite-differences with marker-in-cell techniques to include the effects of visco-elasto-plastic rheology, self-gravitation and a self-consistently derived evolving curvilinear planetary surface. This code is called 12ELVIS and can solve a new class of computationally challenging problems in geodynamics, such as shear localization with large strains, crustal intrusion emplacement of magmas, bending of realistic visco-elasto-plastic plates and core-formation by vigorous shell tectonics activities related to a global Rayleigh-Taylor instability of a metal layer formed around silicate-rich lower density (primordial) core during planetary accretion. We discuss in detail the computational strategy required the rheological constraints to be satisfied at each time step and spatial location. We show analytical benchmarks and examples drawn from comparing between numerical and analogue experiments in structural geology, subducting slab bending with a visco-elasto-plastic rheology and equilibrium spherical configurations from self-gravitation. We have also tested possibilities of future applications by addressing 3D geometries based on multigrid method and including inertial effects in the momentum equation with tracers in order to simulate meteoritic impact events and eventually earthquake instabilities. (c) 2007 Elsevier B.V. All rights reserved.
We present a hybrid imaging method for a challenging traveltime tomography problem which includes both unknown medium and unknown scatterers in a bounded domain. The goal is to recover both the medium and the boundary...
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We present a hybrid imaging method for a challenging traveltime tomography problem which includes both unknown medium and unknown scatterers in a bounded domain. The goal is to recover both the medium and the boundary of the scatterers from the scattering relation data on the domain boundary. Our method is composed of three steps: (1) preprocess the data to classify them into three different categories of measurements corresponding to nonbroken rays, broken-once rays, and others, respectively, (2) use the the nonbroken ray data and an effective data-driven layer stripping strategy-an optimization based iterative imaging method-to recover the medium velocity outside the convex hull of the scatterers, and (3) use selected broken-once ray data to recover the boundary of the scatterers-a direct imaging method. By numerical tests, we show that our hybrid method can recover both the unknown medium and the not-too-concave scatterers efficiently and robustly.
This paper analyses the mechanism of tensor projection transformation in depth and introduces a high-efficiency original algorithm developed in a quantum computing language for forward and backward projection between ...
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This paper analyses the mechanism of tensor projection transformation in depth and introduces a high-efficiency original algorithm developed in a quantum computing language for forward and backward projection between multidimensional tensors and one-dimensional vectors. Additionally, the author compares this algorithm with similar methods from both the Python scientific computing package and other relative development kits in method calls and source code to demonstrate the innovation of the tensor projection algorithm. On this basis, the classical convolution operation program commonly used in machine learning has been parallelized and improved, the analysis algorithm of the Beidou communication satellite view area has been parallelized and improved, and the actual operating efficiency has been greatly improved. After verification, the tensor projection transformation successfully solves the problem of location index mapping of the entity units among different dimensions, can provide a means for optimizing the traditional model of traversal algorithm, and can have significant reference value in eigenspace transformation against a tensor field.
numerical algorithms are formulated for the prediction of seiche modes (eigen frequencies and mode shapes) in elongated natural basins. Confirmation is provided by an analytical solution for a basin with a linear vari...
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numerical algorithms are formulated for the prediction of seiche modes (eigen frequencies and mode shapes) in elongated natural basins. Confirmation is provided by an analytical solution for a basin with a linear variation in surface width and a parabolic variation in cross-section. Spatial variations in geometry are shown to have a significant influence on modal frequencies and especially modal shapes. In particular, local modal amplitudes axe significantly enhanced by extensive regions of shallower water. Applications are given to the Caspian Sea and the Adriatic Sea.
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