• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제23권3호
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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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• 제83권1호
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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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• 제85권2호
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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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• 대한방사선방어학회 2010년도 춘계 학술발표회 및 심포지엄
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• pp.96-97
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• 2010

• 한국터널지하공간학회 논문집
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• 제10권4호
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• pp.421-430
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• 2008

불연속면이 발달한 암반 내에서 해저터널을 건설할 경우 절리내의 지하수 흐름이 터널거동에 커다란 영향을 미치므로 안정성 평가 시 수리-역학적 연계해석이 필요하다. 이에 본 연구에서는 불연속체의 연계해석 시 터널의 안전율을 산정하는 루틴의 검증을 위해 민감도 분석을 수행하였다. 이를 위해 암반블록과 절리의 상호작용을 해석할 수 있는 UDEC-2D 프로그램을 이용하였으며 총 324가지의 경우에 대하여 수치해석을 수행하였다. 결과적으로 불연속체 연계해석을 위해 제안된 안전율 산정 루틴이 타당한 결과를 줌을 확인하였다. 따라서, 본 연구에서 사용된 안전율 산정 방법이 불연속 암반 내에 시공되는 해저터널의 안정성 평가 시 효과적으로 사용될 수 있을 것으로 기대된다.

• 대한수학회논문집
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• 제12권2호
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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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• 제24권2호
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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.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2009년도 춘계학술대회 논문집
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• pp.297-298
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• 2009

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2006년도 PARALLEL CFD 2006
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• pp.188-189
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• 2006

• 전력전자학회:학술대회논문집
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• 전력전자학회 1998년도 전력전자학술대회 논문집
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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)