• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.4
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• pp.244-262
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• 2022

In this paper, we analyze the hybridizable discontinuous Galerkin (HDG) method for second-order elliptic equations with nonlinear coefficients, which are used in many fields. We present the HDG method that uses a mixed formulation based on numerical trace and flux. Under assumptions on the nonlinear coefficient and H²-regularity for a dual problem, we prove that the discrete systems are well-posed and the numerical solutions have the optimal order of convergence as a mesh parameter. Also, we provide a matrix formulation that can be calculated using an iterative technique for numerical experiments. Finally, we present representative numerical examples in 2D to verify the validity of the proof of Theorem 3.10.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.419-431
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• 2023

In this paper, we propose an iterative method for a symmetric interior penalty Galerkin method for heterogeneous elliptic problems. The iterative method consists mainly of two parts based on a non-overlapping domain decomposition approach. One is an intermediate preconditioner constructed by understanding the properties of the discontinuous finite element functions and the other is a preconditioning related to the dual-primal finite element tearing and interconnecting (FETI-DP) methodology. Numerical results for the proposed method are presented, which demonstrate the performance of the iterative method in terms of various parameters associated with the elliptic model problem, the finite element discretization, and non-overlapping subdomain decomposition.

• Journal of Information Technology Applications and Management
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• v.28 no.5
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• pp.61-70
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• 2021

With the proliferation of smartphones and 5G networks, mobile social network service (SNS) has become an indispensable part of people's daily lives. However, with the use of SNS, fatigue and withdrawal behavior gradually emerged. Based on The Transactional Theory of Stress and Coping (TTSC), we explored the mechanism of SNS overload on users' discontinuous intention under the framework of "stressor-strain-outcome". And we also investigated the moderating effects of gender in this process. We hope that through our research, we can help SNS users to reduce unnecessary fatigue, and provide better suggestions for platform designers to adjust product design to improve user experience.

• Steel and Composite Structures
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• v.52 no.5
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• pp.595-608
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• 2024

This study presents a static analysis of thin shallow cylindrical and spherical panels, as well as plates (which are a special case of shells), under Levy-type mixed boundary conditions and various loading conditions. The study utilizes the boundary discontinuous double Fourier series method, where displacements are expressed as trigonometric functions, to analyze the system of partial differential equations. The panels are subjected to a simply supported type 3 (SS3) boundary condition on two opposite edges, while the remaining two edges are subjected to clamped type 3 (C3) boundary conditions. The study presents comprehensive tabular and graphical results that demonstrate the effects of curvature on the deflections and moments of thin shallow shells made from symmetric and antisymmetric cross-ply laminated composites, as well as isotropic steel materials. The proposed model is validated through comparison with existing literature, and the convergence characteristics are demonstrated. The changing trends of displacements and moments are explained in detail by investigating the effect of various parameters, such as stacking lamination, material types, curvature, and loading conditions.

• The Journal of Engineering Geology
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• v.15 no.3
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• pp.257-268
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• 2005

In situ rock mass is generally heterogeneous and discontinuous, with varying degrees of strength along the planes of weakness. The planes of weakness such as joints, faults, cracks and bedding planes, control the strength and deformation characteristics of the rock mass. Subsequently, the stability of underground opening depends upon the spatial distribution of discontinuities and their mechanical properties in relation with geometrical shape of openins as well as the mechanical properties of intact rock materials. Understanding the behaviour of a discontinuous rock mass remains a key issue for improving excavation design in hiかy stressed environments. Although recent advances in rock mechanics have provided guidelines for the design of underground opening in isotropic rock mass, prediction and control of deformation in discontinuous rock masses are still unclear. In this study, parametric study was performed to investigate the plastic zone size, stress distribution and deformation behavior around underground opening in a discontinuous rock mass using a continuum joint model. The solutions were obtained by an elasto-plastic finite difference analysis, employing the Mohr-Coulomb failure criteria. Non-associated flow rule and perfectly plastic material behavior are also assumed.

• Journal of Korean Society of Environmental Engineers
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• v.22 no.12
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• pp.2187-2195
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• 2000

A water treatment system using membrane separation technology can provide stable effluent quality and its maintenance is relatively easy comparing to the conventional water treatment system. In addition, the membrane filtration system is very compact such that it can replace existing water treatment processes of coagulation/sedimentation/filtration by only one process. However, a major problem associated with membrane filtration is flux decline with operating time due to concentration polarization and fouling, so a systematic study on evaluation of long-term filtration performance is necessary. A membrane filtration system using tubular type ultrafiltration membranes with MWCO of 30.000 Da was constructed for this study and it had been operated in a feed-and-discontinuous bleed mode. Flux was stabilized after operation of 1.500 hours and maintaining above 25 LMH until 4.000 hours. Contaminants causing SS and turbidity were almost completely removed while the $UV_{260}$ and DOC removals were 55% and 49%, respectively. A simple mass balance equation was developed to predict maximum concentrations of SS, turbidity, $UV_{260}$ and DOC in a operation cycle. For SS and turbidity the measured max, concentrations in each cycle agree well with the predicted values while the measured max, concentrations of $UV_{260}$ and DOC were 59% and 37% of the predicted values, respectively.

• Proceedings of the Korean Statistical Society Conference
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• 2002.11a
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• pp.103-108
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• 2002

We consider an estimation of discontinuous variance function in nonparametric heteroscedastic random design regression model. We first propose estimators of a change point and jump size in variance function and then construct an estimator of entire variance function. We examine the rates of convergence of these estimators and give results on their asymptotics. Numerical work reveals that the effectiveness of change point analysis in variance function estimation is quite significant.

• Proceedings of the Korea Concrete Institute Conference
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• 1998.04a
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• pp.353-358
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• 1998

The strain localization is a discontinuous phenomenon that addresses the formation of jumps of the field variables across a singularity surface. It has become widely accepted that the localization may occur as the result of discontinuous bifurcation which corresponds to the loss of ellipticity of the governing differential equations for elasto-plastic continua. In this paper, condition for strain localization in concrete based on bifurcation theory is studied and localization tensor analysis algorithm is employed to determine the directions of localization of deformations in concrete. By applying a plasticity model of concrete into the algorithm, localization analysis is performed concrete under uniaxial tension, pure shear and uniaxial compression.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.127.4-127
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• 2001

Inspection and shape measurement of three-dimensional objects are widely needed in industries for quality monitoring and control. A number of visual or optical technologies have been successfully applied to measure three dimensional surfaces. Especially, the shape measurement using an interferometric principle becomes a successful methodology. However, those conventional interferometric methods to measure surface profile have an inherent shortcoming, namely 2∏ ambiguity problem. The problem inevitably happens when the object to be measured has discontinuous shape due to the repetition of interferometric signal with phase period of 2∏. Therefore, in this paper, we choose as a shape measuring method, ...

• East Asian mathematical journal
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• v.31 no.5
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• pp.685-693
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• 2015

In this paper, we introduce fully discrete mixed discontinuous Galerkin approximations for parabolic problems. And we analyze the error estimates in $l^{\infty}(L^2)$ norm for the primary variable and the error estimates in the energy norm for the primary variable and the flux variable.