• 대한수학회보
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• 제50권4호
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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.

• 대한수학회논문집
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• 제18권4호
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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.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 2003년도 춘계 학술발표회논문집
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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

• 한국안전학회지
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• 제23권3호
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• pp.87-92
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• 2008

시간에 불연속성인 유한요소법이 열전도 방정식에 적용하였다. 근사값은 고정된 시간에 공간변수에는 연속이며 그러나 각 시간 구간에서는 시간변수에 불연속을 허용하였다. 이 유한요소법은 지금까지 많이 알려진 재래식 유한요소해석에 보다 해의 수렴속도가 빠르고 해를 쉽게 얻을 수 있으며 지반이 동결된 동상지반과 같이 복잡한 공학문제와 같은 동적 경계치 문제에 쉽게 접근할 수 있었다. 다차원 문제에도 적용이 가능하며 본 연구에서는 일차원, 이차원 열전도 문제에 적용하였다. 결과 치를 해석해와 비교 검토하였다.

• 한국통신학회논문지
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• 제17권5호
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• pp.460-471
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• 1992

본 논문에서는 최근에 주로 사용되는 디지털 PLL중 Tri-State 방식과 sample-Hold 방식을 사용한 PLL루프의 시간 불연속 동작을 묘사하기 위한 새로운 모델을 설정하여 비선형 PLL의 안정도 해석을 Z영역에서 하였으며 과도응답을 구하기 위한 상태방정식을 유도하였다. 종래에는 디지털 PLL의 시간 불연속 동작을 시간 연속 동작으로 근사화 시켜 선형적 해석을 하므로써 실제로는 시간 불연속 동작을 하는 디지털 PLL의 불안정한 영역을 정확히 찾아내지 못하였으나 새로운 모델에 의한 Z영역에서의 해석에서는 시간연속 해석에서 발견할 수 없었던 불안정 영역을 밝혀냄으로써 디지털 PLL의 최적 설계가 가능하도록 루프계수의 한계를 구하였다.

• JSTS:Journal of Semiconductor Technology and Science
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• 제9권1호
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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.

• 대한수학회논문집
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• 제18권3호
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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.

• 한국전산유체공학회지
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• 제12권3호
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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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• 한국전산유체공학회 2008년도 학술대회
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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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• 한국전산유체공학회 2008년 추계학술대회논문집
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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.