• 대한수학회지
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• 제50권1호
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• pp.81-93
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• 2013

We consider a distributed optimal flux control problem: finding the potential of which gradient approximates the target vector field under an elliptic constraint. Introducing the Lagrange multiplier and a change of variables the Euler-Lagrange equation turns into a coupled equation of an elliptic equation and a reaction diffusion equation. The change of variables reduces iteration steps dramatically when the Gauss-Seidel iteration is considered as a solution method. For the elliptic equation solver we consider the Cell Boundary Element (CBE) method, which is the finite element type flux preserving methods.

• 한국추진공학회:학술대회논문집
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• 한국추진공학회 2006년도 제26회 춘계학술대회논문집
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• pp.253-256
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• 2006

액체로켓의 연소실내 분무연소 현상을 해석하기 위해 비연소 반응의 연료와 산화제 액적의 분무유동을 해석하였다. 분무연소 모델로 DSF 모델과 Euler-Lagrange 방법을 사용하였다. 액적과 가스상 그리고 증발한 기체상의 커플효과는 PSIC 모델을 사용하여 계산하였으며 수치 해석 방법으로 SIMPLER 알고리즘과 QUICK Scheme을 사용하였다. 해석결과 연소실내 속도와 온도 분포를 알 수 있었고, 연료와 산화제의 몰분율 또한 알 수 있었다.

• Structural Engineering and Mechanics
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• 제23권3호
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• pp.263-278
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• 2006

This work presents a time-truncation scheme, based on the Lagrange interpolation polynomial, for the solution of the two-dimensional scalar wave problem by the time-domain boundary element method. The aim is to reduce the number of stored matrices, due to the convolution integral performed from the initial time to the current time, and to keep a compromise between computational economy and efficiency and the numerical accuracy. In order to verify the accuracy of the proposed formulation, three examples are presented and discussed at the end of the article.

• Steel and Composite Structures
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• 제35권6호
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• pp.753-763
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• 2020

In this article, the influence of fuzzified uncertain composite elastic properties on non-linear deformation behaviour of the composite structure is investigated under external mechanical loadings (uniform and sinusoidal distributed loading) including the different end boundaries. In this regard, the composite model has been derived considering the fuzzified elastic properties (through a triangular fuzzy function, α cut) and the large geometrical distortion (Green-Lagrange strain) in the framework of the higher-order mid-plane kinematics. The results are obtained using the fuzzified nonlinear finite element model via in-house developed computer code (MATLAB). Initially, the model accuracy has been established and explored later to show the dominating elastic parameter affect the deflection due to the inclusion of fuzzified properties by solving a set of new numerical examples.

• 한국연소학회:학술대회논문집
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• 한국연소학회 1999년도 제19회 KOSCO SYMPOSIUM 논문집
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• pp.71-79
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• 1999

Numerical analysis on the characteristics of nitrogen oxides (NOx) formation in turbulent nonpremixed hydrogen-air flames was carried out. Lagrange IEM model and Assumed PDF model were applied to consider turbulence-chemistry interaction known to affect the production of NOx. Partial equilibrium assumption was used to predict nonequilibrium effect to which one-half power dependence between EINOx normalized by flame residence time and global strain rate is attributed. As a result. such one-half power dependence could be reproduced only by reaction model including $HO_{2}$and $H_{2}O_{2}$, which means its dependence on Damkohler number; nonequilibrium effect. This dependence was shown better in the region of higher global strain. Besides, the improvement of turbulence model is required to predict mean flow properties quantitatively in the radial direction.

• 대한수학회지
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• 제38권1호
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• pp.1-23
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• 2001

This paper is concerned with an optimal shape control problem for the stationary Navier-Stokes system. A two-dimensional channel flow of an incompressible, viscous fluid is examined to determine the shape of a bump on a part of the boundary that minimizes the viscous drag. by introducing an artificial compressibility term to relax the incompressibility constraints, we take the penalty method. The existence of optima solutions for the penalized problem will be shown. Next, by employing Lagrange multipliers method and the material derivatives, we derive the shape gradient for the minimization problem of the shape functional which represents the viscous drag.

• 대한수학회논문집
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• 제20권1호
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• pp.145-159
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• 2005

In this paper we consider the problem of testing statistical hypotheses for unknown parameters in nonlinear regression models and propose three asymptotically equivalent tests based on regression quantiles estimators, which are Wald test, Lagrange Multiplier test and Likelihood Ratio test. We also derive the asymptotic distributions of the three test statistics both under the null hypotheses and under a sequence of local alternatives and verify that the asymptotic relative efficiency of the proposed test statistics with classical test based on least squares depends on the error distributions of the regression models. We give some examples to illustrate that the test based on the regression quantiles estimators performs better than the test based on the least squares estimators of the least absolute deviation estimators when the disturbance has asymmetric and heavy-tailed distribution.

• 대한수학회지
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• 제46권3호
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• pp.551-560
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• 2009

A theorem of Robert Blumenthal is used here in order to obtain a sufficient condition for a function between two Finsler manifolds to be a fibre bundle map. Our study is connected with two possible constructions: 1) a Finslerian generalization of usually Kaluza-Klein theories which use Riemannian metrics, the well-known particular case of Finsler metrics, 2) a Finslerian version of reduction process from geometric mechanics. Due to a condition in the Blumenthal's result the completeness of Euler-Lagrange vector fields of Finslerian type is discussed in detail and two situations yielding completeness are given: one concerning the energy and a second related to Finslerian fundamental function. The connection of our last framework, namely a regular Lagrangian having the energy as a proper (in topological sense) function, with the celebrated $Poincar{\acute{e}}$ Recurrence Theorem is pointed out.

• Journal of Astronomy and Space Sciences
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• 제20권4호
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• pp.313-318
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• 2003

A communications satellite system placed in three-Lagrange points, $L_3$, $L_4$ and $L_5$, of the restricted three-body problem in Earth-Moon system is proposed in this paper. LEO satellite constellation has been another choice of communications system. The proposed system which is alternatives of limited geostationary orbit resources, has some weak points such as long distance from the Earth, relatively expensive launch cost, long delay time, more required power, and so on. It has good points like less efforts (fuel) for station keeping, less eclipses, etc. This system has limitations for applications to provide commercial services but it is still some attractive points.

• International Journal of Aeronautical and Space Sciences
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• 제15권2호
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• pp.183-189
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• 2014

Pseudo-spectral method typically converges at an exponential rate. However, it requires a special set of fixed collocation points (CPs) to get highly accurate formulas for partial integration and differentiation. In this study, computational nodes for defining the discrete variables of states and controls are built independently of the CPs. The state and control variables at each CP, which are required to transcribe an NOCP into the corresponding NLP, are interpolated, using those variables allocated at each node. Additionally, Lagrange interpolation and spline interpolation are investigated, to provide a guideline for selecting a favorable interpolation method. The proposed techniques are applied to the solution of an NOCP using equally spaced nodes, and the computed results are compared to those using the standard PS approach, to validate the usefulness of the proposed methods.