• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1079-1086
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• 2013

This paper is devoted to solving one dimensional backward stochastic differential equations (BSDEs). We prove the existence of the solutions to BSDEs if the generator satisfies the general growth and discontinuous conditions.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.767-779
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• 2003

We consider a model of population dynamics whose mortality function is unbounded. We approximate the solution of the model using a discontinuous Galerkin finite element for the age variable and a backward Euler for the time variable. We present several numerical examples. It is experimentally shown that the scheme converges at the rate of $h^{3/2}$ in the case of piecewise linear polynomial space.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2003.03a
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• pp.50-58
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• 2003

We have developed a locally variable time-step scheme matching with discontinuous grids in the flute-difference method for the efficient simulation of seismic wave propagation. The first-order velocity-stress formulations are used to obtain the spatial derivatives using finite-difference operators on a staggered grid. A three-times coarser grid in the high-velocity region compared with the grid in the low-velocity region is used to avoid spatial oversampling. Temporal steps corresponding to the spatial sampling ratio between both regions are determined based on proper stability criteria. The wavefield in the margin of the region with smaller time-step are linearly interpolated in time using the values calculated in the region with larger one. The accuracy of the proposed scheme is tested through comparisons with analytic solutions and conventional finite-difference scheme with constant grid spacing and time step. The use of the locally variable time-step scheme with discontinuous grids results in remarkable saving of the computation time and memory requirement with dependency of the efficiency on the simulation model. This implies that ground motion for a realistic velocity structures including near-surface sediments can be modeled to high frequency (several Hz) without requiring severe computer memory

• Journal of the Korean Society of Safety
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• v.23 no.3
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• pp.87-92
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• 2008

A finite element method which is discontinuous in time is developed for the solution of the classical parabolic model of heat conduction problems. The approximations are continuous with respect to the space variables for each fixed time, but they admit discontinuities with respect to the time variable at each time step. The method is superior to other well-known approaches to these problems in that it allows a wider range of moving boundary value problems to be dealt with, such as are encountered in complex engineering operations like ground freezing. The method is applied to one-dimensional and two-dimensional heat conduction problems in this paper, although it could be extended to more higher dimensional problems. Several example problems are discussed and illustrated, and comparisons are made with analytical approaches where these can also be used.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.17 no.5
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• pp.460-471
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• 1992

By setting a new model to describe the time-discontinuous operation of PLL loop which used tri-state and sample-hold method, the stability analysis of nonlinear PLL has been performed in z-domain and the state equations for the transient response has been introduced. Until now, the lin-ear analysis by approximation of time-discontinuous to time-continuous operation had not found then stable region of time-discontinuous digital PLL exactly. However, the analysis In z-domain by the new model has been found the unstable region where the time-continuous analysis had have not. 1'herefore the limit of loop coefficient has been computed to design digital PLL optimally.

• JSTS:Journal of Semiconductor Technology and Science
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• v.9 no.1
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• pp.8-13
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• 2009

In this paper, discontinuous interconnect lines are modeled as a cascaded line composed of many uniform interconnect lines. The system functions of respective uniform interconnect lines are determined, followed by its time domain response. Since the time domain response expression is a transcendental form, the waveform expression is reconfigured as an approximated linear expression. The proposed model has less than 2% error in the delay estimation.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.569-580
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• 2003

The Lotka-McKendrick equation which describes the evolution of a single population under the phenomenological conditions is developed from the well-known Malthus’model. In this paper, we introduce the Lotka-McKendrick equation for the description of the dynamics of a population. We apply a discontinuous Galerkin finite element method in age-time domain to approximate the solution of the system. We provide some numerical results. It is experimentally shown that, when the mortality function is bounded, the scheme converges at the rate of $h^2$ in the case of piecewise linear polynomial space. It is also shown that the scheme converges at the rate of $h^{3/2}$ when the mortality function is unbounded.

• Journal of computational fluids engineering
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• v.12 no.3
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• pp.29-40
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• 2007

An implicit discontinuous Galerkin method for the two-dimensional Euler equations was developed on unstructured triangular meshes. The method can achieve high-order spatial accuracy by using hierachical basis functions based on Legendre polynomials. Numerical tests were conducted to estimate the convergence order of numerical solutions to the Ringleb flow and the supersonic vortex flow for which analytic solutions are available. Also, the flows around a 2-D circular cylinder and an NACA0012 airfoil were numerically simulated. The numerical results showed that the implicit discontinuous Galerkin methods couples with a high-order representation of curved solid boundaries can be an efficient method to obtain very accurate numerical solutions on unstructured meshes.

• 한국전산유체공학회:학술대회논문집
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• 2008.03a
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• pp.57-70
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• 2008

A high-order accurate Euler flow solver based on a discontinuous Galerkin finite-element method has been developed for the numerical simulations of blade-vortex interaction phenomena on unstructured meshes. A free vortex in freestream was investigated to assess the vortex-preserving property and the accuracy of the present flow solver. Blade-vortex interaction problems in subsonic and transonic freestreams were simulated by adopting a multi-level solution-adaptive dynamic mesh refinement/coarsening technique. The results were compared with those of other numerical and experimental methods. It was shown that the present discontinuous Galerkin flow solver can preserve the vortex structure for significantly longer vortex convection time and can accurately capture the complex unsteady blade-vortex interaction flows, including generation and propagation of acoustic waves.

• 한국전산유체공학회:학술대회논문집
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• 2008.10a
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• pp.57-70
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• 2008

A high-order accurate Euler flow solver based on a discontinuous Galerkin finite-element method has been developed for the numerical simulations of blade-vortex interaction phenomena on unstructured meshes. A free vortex in freestream was investigated to assess the vortex-preserving property and the accuracy of the present flow solver. Blade-vortex interaction problems in subsonic and transonic freestreams were simulated by adopting a multi-level solution-adaptive dynamic mesh refinement/coarsening technique. The results were compared with those of other numerical and experimental methods. It was shown that the present discontinuous Galerkin flow solver can preserve the vortex structure for significantly longer vortex convection time and can accurately capture the complex unsteady blade-vortex interaction flows, including generation and propagation of acoustic waves.