• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.23-40
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• 1998

Mixed finite element method is developed to approxi-mate the solution of the initial-boundary value problem for a strongly nonlinear second-order hyperbolic equation in divergence form. Exis-tence and uniqueness of the approximation are proved and optimal-order $L\infty$-in-time $L^2$-in-space a priori error estimates are derived for both the scalar and vector functions approximated by the method.

• Ocean Science Journal
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• v.40 no.4
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• pp.201-208
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• 2005

An accurate particle tracking method for a finite difference method model is developed using a constant acceleration method. Being assumed constant temporal and spatial gradients, the new method permits temporal-spatial variability of particle velocity. Test results in a solid rotating flow show that the new method has second-order accuracy. The performance of the new method is compared with that of other methods; the first-order Euler forward method, and the second-order Euler predictor-corrector method. The new method is the most efficient method among the three. It is more accurate and efficient than the other two.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.2 no.1
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• pp.51-62
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• 2008

This paper proposes a second-order implicit constraint enforcement method which yields enhanced controllability compared to a first-order implicit constraints enforcement method. Although the proposed method requires solving a linear system twice, it yields superior accuracy from the constraints error perspective and guarantees the precise and natural movement of objects, in contrast to the first-order method. Thus, the proposed method is the most suitable for exact prediction simulations. This paper describes the numerical formulation of second-order implicit constraints enforcement. To prove its superiority, the proposed method is compared with the firstorder method using a simple two-link simulation. In this paper, there is a reasonable discussion about the comparison of constraints error and the analysis of dynamic behavior using kinetic energy and potential energy.

• Computational Structural Engineering
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• v.7 no.3
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• pp.115-122
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• 1994

Design sensitivity analysis of the second order perturbed eigenproblems for random structural system is presented. Dynamic response of random system including uncertainties for the design variable is calculated with the first order and second order perturbation method to original governing equation. In optimal design methods, there is fundamental requirement for design gradients. A method for calculating the sensitivity coefficients is developed using the direct differentiation method for the governing equation and first order and second order perturbed equation.

• Journal of the Korean Society for Nondestructive Testing
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• v.33 no.3
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• pp.257-263
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• 2013

Acoustic nonlinearity of surface waves is an effective method to evaluate the micro damage on the surface of materials. In this method, the $A_1$ (magnitude of the fundamental wave) and $A_2$ (magnitude of the second-order harmonic wave) are measured for evaluation of acoustic nonlinearity. However, if there is another source of second-order harmonic wave other than the material itself, the linear relationship between $A_1{^2}$ and $A_2$ will not be guaranteed. Therefore, the second-order harmonic generation by another source should be fully suppressed. In this paper, we investigated the initial second-order harmonic generation in narrowband surface waves by multi-line laser beams. The spatial profile of laser beam was considered in the cases of Gaussian and square-like. The temporal profile was assumed to be Gaussian. In case of Gaussian spatial profile, the generation of the initial second-order harmonic wave was inevitable. However, when the spatial profile was square-like, the generation of the initial second-order harmonic wave was able to be fully suppressed at specific duty ratio. These results mean that the multi-line laser beams of square-like profile with a proper duty ratio are useful to evaluate the acoustic nonlinearity of the generated surface waves.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.1
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• pp.110-119
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• 1995

The lateral resolution in an ultrasound imaging system is one of the most important factors for quality of the image and is determined by the beam focusing. For the better lateral resolution SDF(Sampled Delay Focusing) capable of digital focusing was proposed. The second-order sampling, one of band-width sampling methods, is suggested as being the best suitable for SDF because it allows total digital processing and is simple and economical. By proving that it introduces too much error, this article shows the second-order sampling is not appropriate for sampling of the wide-band signal generally used in ultrasound imaging systems. Also, this article suggests new sampling methods that maintain the advantages and reduce the unavoidable errors of the second-order sampling method. From computer simulation it is expected that the proposed methods reduce the errors of the second-order sampling method and can be used in real applications.

• International Journal of Ocean System Engineering
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• v.1 no.3
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• pp.155-164
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• 2011

The second-order motion characteristics of a semi-submersible are investigated in regular waves. A higher-order boundary element method in a frequency domain and a finite element method in a time-domain were applied to the numerical analysis of the nonlinear hydrodynamic force and motion characteristics of semi-submersibles in view point of potential flow. Various aspects of nonlinear effects on the heave and roll of a semi-submersible were numerically investigated and some selected cases were compared with the model test data.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.8
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• pp.1822-1831
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• 1995

A general formulation of the design optimization problem with the random parameters is presented here. The formulation is based on the stochastic finite element second-order perturbation method ; it takes into full account of the stress and displacement constraints together with the rates of change of the random variables. A method of direct differentiation for calculating the sensitivity coefficients in regard to the governing equation and the second-order perturbed equation is derived. A gradient-based nonlinear programming technique is used to solve the problem. The numerical results are specifically noted, where the stiffness parameter and external load are treated as random variables.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1253-1268
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• 2006

We develop the upper and lower solutions method for the four point problem relative to second order differential equations in order to obtain the existence of solution.

• Ocean Systems Engineering
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• v.1 no.4
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• pp.317-336
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• 2011

A time domain finite element based method is employed to analyze wave radiation by multiple cylinders. The nonlinear free surface and body surface boundary conditions are satisfied based on the perturbation method up to the second order. The first- and second-order velocity potential problems at each time step are solved through a finite element method (FEM). The matrix equation of the FEM is solved through an iteration and the initial solution is obtained from the result at the previous time step. The three-dimensional (3D) mesh required is generated based on a two-dimensional (2D) hybrid mesh on a horizontal plane and its extension in the vertical direction. The hybrid mesh is generated by combining an unstructured grid away from cylinders and two structured grids near the cylinder and the artificial boundary, respectively. The fluid velocity on the free surface and the cylinder surface are calculated by using a differential method. Results for various configurations including two-cylinder and four-cylinder cases are provided to show the mutual influence due to cylinders on the first and second waves and forces.