• 대한수학회지
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• 제43권2호
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• pp.399-411
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• 2006

Let L be a subspace lattice on a Hilbert space H and X and Y be operators acting on a Hilbert space H. Let P be the projection onto $\frac\;{R(X)}$, where RX is the range of X. If PE = EP for each $E\;\in\;L$, then there exists an operator A in AlgL such that AX = Y if and only if $$sup\{{\parallel}E^{\bot}Yf{\parallel}/{\parallel}E^{\bot}Xf{\parallel}\;:\;f{\in}H,\; E{\in}L}=K\;<\;\infty$$ Moreover, if the necessary condition holds, then we may choose an operator A such that AX = Y and ${\parallel}A{\parallel} = K.$ Let x and y be vectors in H and let $P_x$ be the projection onto the singlely generated space by x. If $P_xE = EP_x$ for each $E\inL$, then the assertion that there exists an operator A in AlgL such that Ax = y is equivalent to the condition $$K_0\;:\;=\;sup\{{\parallel}E^{\bot}y{\parallel}/{\parallel}E^{\bot}x\;:\;E{\in}L}=<\;\infty$$ Moreover, we may choose an operator A such that ${\parallel}A{\parallel} = K_0$ whose norm is $K_0$ under this case.

• 유체기계공업학회:학술대회논문집
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• 유체기계공업학회 2006년 제4회 한국유체공학학술대회 논문집
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• pp.33-36
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• 2006

As the computing environment is rapidly improved, the interests of CFD are gradually focused on large-scale computation over complex geometry. Keeping pace with the trend, essential computational tools to obtain solutions of complex aerospace flow analysis and design problems are examined. An accurate and efficient flow analysis and design codes for large-scale aerospace problem are presented in this work. With regard to original numerical schemes for flow analysis, high-fidelity flux schemes such as RoeM, AUSMPW+ and higher order interpolation schemes such as MLP (Multi-dimensional Limiting Process) are presented. Concerning the grid representation method, a general-purpose basis code which can handle multi-block system and overset grid system simultaneously is constructed. In respect to design optimization, the importance of turbulent sensitivity is investigated. And design tools to predict highly turbulent flows and its sensitivity accurately by fully differentiating turbulent transport equations are presented. Especially, a new sensitivity analysis treatment and geometric representation method to resolve the basic flow characteristics are presented. Exploiting these tools, the capability of the proposed approach to handle complex aerospace simulation and design problems is tested by computing several flow analysis and design problems.

• Journal of applied mathematics & informatics
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• 제33권3_4호
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• pp.417-424
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• 2015

In this paper the following is proved: Let L be a subspace lattice on a Hilbert space H and X and Y be operators acting on a Hilbert space H. If XE = EX for each E ${\in}$ L, then there exists an operator A in AlgL such that AX = Y if and only if sup $\left{\frac{\parallel{XEf}\parallel}{\parallel{YEf}\parallel}\;:\;f{\in}H,\;E{\in}L\right}$ = K < $\infty$ and YE=EYE. Let x and y be non-zero vectors in H. Let P_x be the orthogonal pro-jection on sp(x). If EP_x = P_xE for each E $\in$ L, then the following are equivalent. (1) There exists an operator A in AlgL such that Ax = y. (2) < f, Ey > y =< f, Ey > Ey for each E ${\in}$ L and f ${\in}$ H.

• 대한기계학회논문집A
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• 제24권3호
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• pp.803-809
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• 2000

For the effective analysis of an engineering problem, meshless methods which require only positioning finite points without the element meshing recently have been proposed and being studied extensively. Meshless methods have difficulty in imposing essential boundary conditions directly, because non-interpolate shape functions originated from an approximation process are used. So some techniques, which are Lagrange multiplier method, modified variational principles and coupling with finite elements and so on, were introduced in order to impose essential boundary conditions. In spite of these methods, imposition of essential boundary conditions have still many problems like as non-positive definiteness, inaccuracy and negation of meshless characteristics. In this paper, we propose a new method which modifies shape function. Through numerical tests, convergence, accuracy and validity of this method are compared with the standard EFGM which uses Lagrange multiplier method or modified variational principles. According to this study, the proposed method shows the comparable accuracy and efficiency.

• Journal of Electrical Engineering and Technology
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• 제3권4호
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• pp.576-583
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• 2008

In this study, we attempt to design a real-time autonomic nervous system(ANS) evaluation system usable during exercise using heart instantaneous frequency(HIF). Although heart rate variability(HRV) is considered to be a representative signal widely used ANS evaluation system, the R-peak detection process must be included to obtain an HRV signal, which involves a high sampling frequency and interpolation process. In particular, it cannot accurately evaluate the ANS using HRV signals during exercise because it is difficult to detect the R-peak of electrocardiogram(ECG) signals with exposure to many noises during exercise. Therefore, in this study, we develop the ground for a system that can analyze an ANS in real-time by using the HIF signal circumventing the problem of the HRV signal during exercise. First, we compare the HRV and HIF signals in order to prove that the HIF signal is more efficient for ANS analysis than HRV signals during exercise. Further, we performed real-time ANS analysis using HIF and confirmed that the exerciser's ANS variation experiences massive surges at points of acceleration and deceleration of the treadmill(similar to HRV).

• 대한토목학회논문집
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• 제11권3호
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• pp.1-10
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• 1991

본 논문에서는 개선된 감절점(degenerated) 쉘 유한요소의 복합적충을 갖는 쉘구조에의 적용성을 고찰하였다. 본 논문의 개선된 쉘 요소는 shear locking 해결에 우수한 결과를 보인 가정된 전단변형도를 대치사용하고, membrane locking 현상을 제거하기 위해 평면내 변형도의 구성시 감차적분을 행하며, 쉘요소 자체의 거동을 보완하기 위해 비적합변위형을 선택적으로 추가하였다. 본 요소는 shear/membrane locking이 발생하지 않으며, 전달가능한 거짓 영에너지모드도 나타나지 않는다. 유한변형을 고려한 기하학적 비선형 방정식을 total Lagrangian 수식화를 시용하여 정형화 하였고, 비선형 수치해석은 Newton-Raphson 반복법으로 반복 계산한다. 여러 예제해석을 통하여 본 개선된 쉘 유한요소의 유용성과 정확도를 고찰하였다.

• 한국복합재료학회:학술대회논문집
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• 한국복합재료학회 2003년도 춘계학술발표대회 논문집
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• pp.184-187
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• 2003

Complete prediction of second order permeability tensor for three dimensional circular braided preform is critical to understand the resin transfer molding process of composites. The permeability can be predicted by considering resin flow through the multi-axial fiber structure. In this study, permeability tensor for a 3-D circular braided preform is calculated by solving a boundary problem of a periodic unit cell. Flow field through the unit cell is obtained by using a 3-D finite volume method (FVM) and Darcy's law is utilized to obtain permeability tensor. Flow analysis for two cases that a fiber tow is regarded as impermeable solid and permeable porous medium is carried out respectively. It is found that the flow within the intra-tow region of the braided preform is negligible if inter-tow porosity is relatively high but the flow through the tow must be considered when the porosity is low. To avoid checkerboard pressure field and improve the efficiency of numerical computation, a new interpolation function for velocity variation is proposed on the basis of analytic solutions. Permeability of the braided preform is measured through a radial flow experiment and compared with the permeability predicted numerically.

• 대한기계학회논문집A
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• 제29권9호
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• pp.1243-1252
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• 2005

A current trend of design methodologies is to make engineers objectify or automate the decision-making process. Numerical optimization is an example of such technologies. However, in numerical optimization, the uncertainties are uncontrollable to efficiently objectify or automate the process. To better manage these uncertainties, the Taguchi method, reliability-based optimization and robust optimization are being used. To obtain the target performance with the maximum robustness is the main functional requirement of a mechanical system. In this research, a design procedure for global robust optimization is developed based on the kriging and global optimization approaches. The DACE modeling, known as the one of Kriging interpolation, is introduced to obtain the surrogate approximation model of the function. Robustness is determined by the DACE model to reduce real function calculations. The simulated annealing algorithm of global optimization methods is adopted to determine the global robust design of a surrogated model. As the postprocess, the first order second-moment approximation method is applied to refine the robust optimum. The mathematical problems and the MEMS design problem are investigated to show the validity of the proposed method.

• 한국항공우주학회지
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• 제34권7호
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• pp.1-11
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• 2006

본 논문에서는 불연속면이 포함된 다차원 유동에서 흔히 발생하는 수치적 진동현상을 막기 위해 기존의 TVD 제한자를 분석함으로써 새로운 형태의 다차원 제한 함수를 유도하였다. MLP 기법은 유도된 다차원 제한 함수를 기반으로 하며, 다차원 불연속면에서의 수치 진동을 효과적으로 제거하고 동시에 3차 이상의 공간 정확도 내삽기법과 함께 사용할 수 있다는 장점을 갖는다. 또한, 정상 유동의 경우 수치 진동이 제거됨으로써 수렴성이 향상됨을 확인할 수 있었고, 실제 코드에 적용하는 방법도 간단하다. MLP 기법을 적용함으로써 불연속 유동 뿐 만 아니라 연속 유동에서도 정확성, 효율성, 강건성 면에서 향상된 결과를 얻을 수 있음을 여러 가지 수치 실험을 통하여 확인하였다.

• Kyungpook Mathematical Journal
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• 제48권4호
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• pp.665-684
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• 2008

Runge-Kutta-Nystr$\"{o}$m (RKN) methods provide a popular way to solve the initial value problem (IVP) for a system of ordinary differential equations (ODEs). Users of software are typically asked to specify a tolerance ${\delta}$, that indicates in somewhat vague sense, the level of accuracy required. It is clearly important to understand the precise effect of changing ${\delta}$, and to derive the strongest possible results about the behaviour of the global error that will not have regular behaviour unless an appropriate stepsize selection formula and standard error control policy are used. Faced with this situation sufficient conditions on an algorithm that guarantee such behaviour for the global error to be asympotatically linear in ${\delta}$ as ${\delta}{\rightarrow}0$, that were first derived by Stetter. Here we extend the analysis to cover a certain class of ODEs with low-order derivative discontinuities, and the class of ODEs with constant delays. We show that standard error control techniques will be successful if discontinuities are handled correctly and delay terms are calculated with sufficient accurate interpolants. It is perhaps surprising that several delay ODE algorithms that have been proposed do not use sufficiently accurate interpolants to guarantee asymptotic proportionality. Our theoretical results are illustrated numerically.