• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.61-82
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• 2000

In this paper two so-called regularized Green's functions are introduced to derive the optimal maximum norm error estimates for the unknown function and the adjoint vector-valued function for mixed finite element methods of Laplacian operator. One contribution of the paper is a demonstration of how the boundedness of $L^1$-norm estimate for the second Green's function ${\lambda}_2$ and the optimal maximum norm error estimate for the adjoint vector-valued function are proved. These results are seemed to be to be new in the literature of the mixed finite element methods.

• 한국전자파학회논문지
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• 제19권3호
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• pp.281-293
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• 2008

평면형 구조에서 공간 영역 그린 함수를 구하기 위해서는 무한 Sommerfeld 적분을 계산하여야 한다. 무한 적분을 짧은 시간에 계산하기 위한 실수축 적분 방법(real axis integration method)은 주파수와 거리에 대해 넓은 범위에 걸쳐 매우 정확한 방법이지만 관측점의 수지 성분 z가 변하게 되면, 근사의 과정을 반복해야 하는 비효율성과 z가 커질수록 파수 영역 함수의 변화가 심해져 정확한 근사가 어렵다는 단점이 있다. 본 논문에서는 폐루프 적분 경로를 이용하여 파수 영역 함수를 근사화 함으로써 일반적인 마이크로스트립 구조에서 기존의 결과에 비해 정확한 closed-form 그린 함수를 구하는 방법을 제시하였다.

• Earthquakes and Structures
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• 제9권2호
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• pp.305-320
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• 2015

The present paper is devoted to study SH-wave propagation in heterogeneous layer laying over an inhomogeneous isotropic elastic half-space. The dispersion relation for propagation of said waves is derived with Green's function method and Fourier transform. As a special case when the upper layer and lower half-space are homogeneous, our derived equation is in agreement with the general equation of Love wave. Numerically, it is observed that the velocity of SH-wave increases with the increase of inhomogeneity parameter.

• 한국에너지공학회:학술대회논문집
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• 한국에너지공학회 2000년도 추계 학술발표회 논문집
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• pp.115-120
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• 2000

The analysis of flux distribution under stead-state in large power reactors with assymetry reactivity insertions requires the use of three-dimensional diffusion calculations. For the purpose, consistently formulated modern nodal methods based on higher order interface techniques have become popular tools for flux distributions in large commercial nuclear reactors. Among the earlier developments, the nodal Green's function method obtains its nodal interface equation from the transverse-integrated integral diffusion equation using a finite-medium Green's function. In this method, the outgoing current from a node surface is formulated as a response of the incoming currents and the spatially integrated neutron source within the same node. The well-known nodal expansion method is also based on an interface partial current formulation. Nodal methods high-level interface variables, i.e., interface net current and flux, may be more computationally efficient than the nodal Green's function method because they have one fewer unknown per interface. The Analytic Nodal Method(ANM), which can be classified as an interface net current technique and, was faster in solving some standard benchmark problems than the other two methods.(omitted)

• ETRI Journal
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• 제46권2호
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• pp.333-346
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• 2024

Various techniques for noninvasively focus microwave energy on lesions have been proposed for thermotherapy. To focus the microwave energy on the lesion, a focusing parameter, which is referred to as the magnitude and phase of microwaves radiated from an external array antenna, is very important. Although the finite-difference time-domain (FDTD)-based time-reversal (TR) focusing algorithm is widely used, it has a long processing time if the focusing target position changes or if optimization is needed. We propose a technique to obtain multistatic data (MSD) based on Green's function and use it to derive the focusing parameters. Computer simulations were used to evaluate the electric fields inside the object using the FDTD method and Green's function as well as to compare the focusing parameters using FDTD- and MSD-based TR focusing algorithms. Regardless of the use of Green's function, the processing time of MSD-based TR focusing algorithms reduces to approximately 1/2 or 1/590 compared with the FDTD-based algorithm. In addition, we optimize the focusing parameters to eliminate hotspots, which are unnecessary focusing positions, by adding phase-reversed electric fields and confirm hotspot suppression through simulations.

• 대한조선학회논문집
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• 제31권4호
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• pp.73-81
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• 1994

선박 내항성능의 3차원적 해석을 위하여 3차원 판넬 방법을 이용한 쏘오스 분포법과 쏘오스-다이폴 분포법이 널리 이용되어 왔다. 그러나, 이 방법들을 이용하는 경우에는 내부 유동에 의한 자유표면의 공진현상에 의해 특이파수(irregular frequency)라고 불리는 파주파수에서 동유체력 계산에 큰 오차가 발생하게 되며 이런 현상을 제거하는 것은 정확한 내항성능 해석에 필수적이라 할 수 있다. 본 논문에서는 전진동요하는 선박의 운동 해석을 위하여 Wu등이 유도한 전진하면서 동요하는 Green 함수를 이용하였다. Green함수의 계산을 위하여는 어뎁티브(adaptive) 적분방법과 스트레칭(stretching) 변환 및 정류위상(stationary phase) 적분 방법을 사용하였으며 선체의 표면과 선체 내부 수선면에 특이점을 분포한 적분방정식을 도출하였다. 또한 2차원 문제를 다룬 Ohmatsu의 제안에 따라 내부 수선면에서 법선속도가 0이라는 조건을 이용하여 동요하는 문제의 불규칙파수 현상을 제거할 수 있었다. 계산은 Series 60($C_B=0.7$)에 대하여 수행되었으며 부가질량 계수, 감쇠 계수 및 파랑강제력에 대하여 기존의 연구 결과 및 실험 결과와 비교하였다.

• 대한전자공학회논문지TC
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• 제37권11호
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• pp.23-31
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• 2000

평면형 구조에서 공간영역 그린함수를 구하기 위해서는 무한 Sommerfeld 적분을 계산하여야 한다. 무한 적분을 짧은 시간에 계산하기 위한 복소 영상법(complex image method)과 2단계 근사화법(two-level method)은 전원점과 관측점 사이의 거리가 가까운 경우에는 정확하지만, 거리가 멀어지면 오차가 커지게 된 다. 본 논문에서는 실수축 상의 적분경로에서 파수영역 그린함수를 근사화 함으로써 코플래너 도파로 구조에서 기존의 결과에 비해 정확한 closed-form 그린함수를 구하는 방법을 제시하였다.

• Nuclear Engineering and Technology
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• 제46권1호
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• pp.101-108
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• 2014

About 40% of reactors in the world are being operated beyond design life or are approaching the end of their life cycle. During long-term operation, various degradation mechanisms occur. Fatigue caused by alternating operational stresses in terms of temperature or pressure change is an important damage mechanism in continued operation of nuclear power plants. To monitor the fatigue damage of components, Fatigue Monitoring System (FMS) has been installed. Most FMSs have used Green's Function Approach (GFA) to calculate the thermal stresses rapidly. However, if temperature-dependent material properties are used in a detailed FEM, there is a maximum peak stress discrepancy between a conventional GFA and a detailed FEM because constant material properties are used in a conventional method. Therefore, if a conventional method is used in the fatigue evaluation, thermal stresses for various operating cycles may be calculated incorrectly and it may lead to an unreliable estimation. So, in this paper, the modified GFA which can consider temperature-dependent material properties is proposed by using an artificial neural network and weight factor. To verify the proposed method, thermal stresses by the new method are compared with those by FEM. Finally, pros and cons of the new method as well as technical findings from the assessment are discussed.

• International Journal of Naval Architecture and Ocean Engineering
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• 제13권1호
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• pp.50-56
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• 2021

An accurate evaluation of three-dimensional (3D) Time-Domain Green Function (TDGF) in infinite water depth is essential for ship's hydrodynamic analysis. Various numerical algorithms based on the TDGF properties are considered, including the ascending series expansion at small time parameter, the asymptotic expansion at large time parameter and the Taylor series expansion combines with ordinary differential equation for the time domain analysis. An efficient method (referred as "Present Method") for a better accuracy evaluation of TDGF has been proposed. The numerical results generated from precise integration method and analytical solution of Shan et al. (2019) revealed that the "Present method" provides a better solution in the computational domain. The comparison of the heave hydrodynamic coefficients in solving the radiation problem of a hemisphere at zero speed between the "Present method" and the analytical solutions proposed by Hulme (1982) showed that the difference of result is small, less than 3%.

• International Journal of Naval Architecture and Ocean Engineering
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• 제13권1호
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• pp.260-277
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• 2021

The appropriate radiation conditions of ship motion problem with advancing speed in frequency domain are investigated from a theoretical and practical point of view. From extensive numerical experiments that have been conducted for evaluation of the relevant radiation conditions, a hybrid radiation technique is proposed in which the Sommerfeld radiation condition and the free surface damping are mixed. Based on the comparison with the results of the translating and pulsating Green function method, the optimal damping factor of the hybrid radiation technique is selected, and the observed limitations of the proposed hybrid radiation technique are discussed, along with its accuracy obtained from the numerical solutions. Comparative studies of the forward-speed seakeeping prediction methods available confirm that the results of applying the hybrid radiation technique are relatively similar to those obtained from the translating and pulsating Green function method. This confirmation is made in comparisons with the results of solely applying either the free surface damping, or the Sommerfeld radiation condition. By applying the proposed hybrid radiation technique, the wave patterns, hydrodynamic coefficients, and motion responses of the Wigley III hull are finally calculated, and compared with those of model tests. It is found that, in comparison with the model test results, the three-dimensional Rankine source method adopting the proposed hybrid radiation technique is more robust in terms of accuracy and numerical stability, as well as in obtaining the forward speed seakeeping solution.