• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.3
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• pp.211-236
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• 2019

This paper is devoted to the study and investigation of the Runge-Kutta discontinuous Galerkin method for a system of differential equations consisting of two hyperbolic conservation laws. The numerical coupling flux which is used at a given interface (x = 0) is the upwind flux. Moreover, in the linear case, we derive optimal convergence rates in the $L_2$-norm, showing an error estimate of order ${\mathcal{O}}(h^{k+1})$ in domains where the exact solution is smooth; here h is the mesh width and k is the degree of the (orthogonal Legendre) polynomial functions spanning the finite element subspace. The underlying temporal discretization scheme in time is the third-order total variation diminishing Runge-Kutta scheme. We justify the advantages of the Runge-Kutta discontinuous Galerkin method in a series of numerical examples.

• Structural Engineering and Mechanics
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• v.83 no.1
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• pp.67-77
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• 2022

In this study, frictionless continuous and discontinuous contact problems of a magneto-electro-elastic layer in the presence of the body force were discussed. The layer was indented by a rigid cylindrical insulating punch and supported by a rigid substrate without bond. Applying the Fourier integral transform technique, the general expressions of the problem were derived in the presence of body force. Thanks to the boundary conditions, the singular integral equations were obtained for both the continuous and the discontinuous contact cases. Gauss-Chebyshev integration formulas were used to transform the singular integral equations into a set of nonlinear equations. Contact width under the punch, initial separation distance, critical load, separation regions and contact stress under the punch and between the layer, and substrate were given as a result.

• Structural Engineering and Mechanics
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• v.85 no.2
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• pp.207-216
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• 2023

Three time-discontinuous Galerkin quadrature element methods (TDGQEMs) are developed for structural dynamic problems. The weak-form time-discontinuous Galerkin (TDG) statements, which are capable of capturing possible displacement and/or velocity discontinuities, are employed to formulate the three types of quadrature elements, i.e., single-field, single-field/least-squares and two-field. Gauss-Lobatto quadrature rule and the differential quadrature analog are used to turn the weak-form TDG statements into a system of algebraic equations. The stability, accuracy and numerical dissipation and dispersion properties of the formulated elements are examined. It is found that all the elements are unconditionally stable, the order of accuracy is equal to two times the element order minus one or two times the element order, and the high-order elements possess desired high numerical dissipation in the high-frequency domain and low numerical dissipation and dispersion in the low-frequency domain. Three fundamental numerical examples are investigated to demonstrate the effectiveness and high accuracy of the elements, as compared with the commonly used time integration schemes.

• 대한방사선방어학회:학술대회논문집
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• 2010.04a
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• pp.96-97
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• 2010

• Journal of Korean Tunnelling and Underground Space Association
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• v.10 no.4
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• pp.421-430
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• 2008

In discontinuous rock masses, hydraulic-mechanical coupled analyses are required since groundwater flow in joints have a great influence on the stability of a subsea tunnel. In this study, a sensitivity analysis was performed based on coupled analysis to verify the routine which can estimate the safety factor of a tunnel in discontinuous rock mass. To this end, 324 cases of numerical calculations were performed with a commercial program, UDEC-2D. As a result, it was confirmed that the proposed routine for coupled analysis in discontinuous rock mass could give a reasonable result for the estimation of safety factor of a tunnel. Therefore, it is expected that the safety factor estimation method used in this study can be effectively applied for the stability estimation of a subsea tunnel in discontinuous rock masses.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.419-425
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• 1997

Consider a d-dimensional domain D that has finite Lebesque measure and a Dirichlet form which has discontinuous coefficient. Then the stationary Markov process corresponding to the given Dirichlet form is a semimartingale under suitable condition for D and the coefficient.

• East Asian mathematical journal
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• v.24 no.2
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• pp.169-176
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• 2008

The aim of this paper is to prove a common fixed point theorem in normed linear spaces for noncompatible, discontinuous mappings without assuming completeness of the space. We also give an application of our theorem to best approximation theory.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2009.06a
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• pp.297-298
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• 2009

• 한국전산유체공학회:학술대회논문집
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• 2006.05a
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• pp.188-189
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• 2006

• Proceedings of the KIPE Conference
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• 1998.07a
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• pp.113-115
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• 1998

This paper present a buck-boost PWM inverter and its application for residential system. The PWM power inverter is realized by driving a inverter constructed with a high frequency buck-boost chopper in the discontinuous conduction mode (DCM)