• 대한수학회보
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• 제53권2호
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• pp.423-440
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• 2016

The bubble stabilization technique of Chebyshev-Legendre high-order element methods for one dimensional advection-diffusion equation is analyzed for the proposed scheme by Canuto and Puppo in [8]. We also analyze the finite element lower-order preconditioner for the proposed stabilized linear system. Further, the numerical results are provided to support the developed theories for the convergence and preconditioning.

• 한국전자파학회논문지
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• 제10권4호
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• pp.550-563
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• 1999

본 논문은 시변 맥스웰 방정식에 기초한 웨이브릿-갤러킨 설계를 제안하였다. 두 개의 모멘트 함수가 0 이 되는 Daubechies 웨이브릿 함수를 기저함수로 전개하고 Yee가 제안한 Leap-frog 접근법을 적용하였다. D Daubechies 웨이브릿의 변위된 보간 특성을 이용하여 적분이나 매체 연산자에 대한 부가적인 행렬이 필요없 는 방정식을 유도하였다 안정화 조건을 유도하고 분산특성을 분석한 후 유한차분 시간영역법과 다해상도 시 간영역법의 결과와 비교하였고. 분산특성의 분석을 통해 기저함수의 정규성(Regularity)과 받침폭(Support width) 사이의 균형을 확인했다. 기저함수가 단 2개의 0이 되는 웨이브릿 모멘트 함수를 가지지만. 이는 수치 해석 상에서 무시할 수 있는 분산 오류를 수반하였고, 컴팩트 받침(Compact support)에 의해 노드 당 적은 수의 계수만이 고려되었다. 제안된 설계의 저장계수의 효율, 실행 시간의 감소와 정확도를 균일 공진기와 비 균일 공진기의 공진주파수 해석을 통해 검증하였다.

• 한국통신학회논문지
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• 제31권3A호
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• pp.321-327
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• 2006

본 논문은 접지된 유전체 평면 위에 균일한 저항율을 갖는 저항띠 격자구조로 임의의 방향으로 입사되는 H-분극 전자파산란 문제를 모멘트 법으로 해석하였다. 기존의 논문에서는 전류밀도의 분포에 따라 기저함수를 다양한 직교다항식으로 변경하여 I-분극의 경우만 수치해석 하였다. 반면에, 본 연구에서는 각 저항띠의 양끝에서 유도 전류밀도가 0 이 되도록 cosine 함수와 sine 함수로 구성된 다항식의 급수로 나타내었다. 산란 전자계는 주기적인 구조에 대응시킬 수 있는 Floquet 모드함수의 급수로 전재하였으며, 미지의 계수를 구하기 위하여 경계조건을 적용하였다. 또한, Fourier-Galerkin 모멘트 법을 적용함으로서 접지된 유전체 위에 여러 가지 저항율을 갖는 저항띠에 대하여 기하광학적인 정규화 된 반사전력에 관한 스트립 폭 및 주기, 입사각의 영향을 수치해석 하였다.

• 문화기술의 융합
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• 제9권3호
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• pp.721-726
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• 2023

본 논문에서는 접지된 2중 유전체층 사이의 도체띠 격자구조에 의한 TM(tranverse magnetic) 전자파 산란 문제를 전자파 수치해석방법으로 알려진 FGMM(fourier galerkin moment method)과 PMM(point matching method)을 적용하여 해석하였다. 경계조건들은 미지의 계수를 구하기 위하여 이용하였다. 접지된 2중 유전층의 비유전율과 두께는 동일한 값에 대해서만 취급하였으며, 유전체층의 두께와 비유전율의 값이 증가하면 전반적으로 반사전력은 증가하였으며, 반사전력의 최소값들이 스트립 폭이 증가하는 방향으로 이동하였다. 본 논문의 제안된 구조에 대해 FGMM과 PMM의 수치해석 방법을 적용한 수치결과들은 매우 잘 일치하였다.

• 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.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2000년도 봄 학술발표회논문집
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• pp.324-331
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• 2000

In this study, a new algorithm analyzing dynamic crack propagation problem by the coupling technique of Meshfree Method and Finite Element Method is proposed. The coupling procedure of two methods is presented with a short description of Meshfree Method especially, Element-free Galerkin (EFG) method. The elastodynamic fracture theory is presented, and a numerical implementation procedure for dynamic fracture analysis by Meshfree Method is also discussed. A couple of dynamic crack propagation problems illustrate the performance of the propsed technique. The accuracy of numerical solutions by the developed algorithm are compared with those of analytical solutions and experimental ones.

• 호남수학학술지
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• 제38권1호
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• pp.47-57
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• 2016

In the discrete formulation of the bubble stabilized Legendre Galerkin methods, the system of equations includes the artificial viscosity term as the parameter. We investigate the estimation of this parameter to get the least-squares solution which minimizes the sum of the squares of errors at each node points. Some numerical results are reported.

• Steel and Composite Structures
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• 제19권1호
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• pp.1-19
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• 2015

The buckling analysis is presented for non-homogeneous (NH) orthotropic truncated conical shells subjected to combined loading of axial compression and external pressure. The governing equations have been obtained for the non-homogeneous orthotropic truncated conical shell, the material properties of which vary continuously in the thickness direction. By applying Superposition and Galerkin methods to the governing equations, the expressions for critical loads (axial, lateral, hydrostatic and combined) of non-homogeneous orthotropic truncated conical shells with simply supported boundary conditions are obtained. The results are verified by comparing the obtained values with those in the existing literature. Finally, the effects of non-homogeneity, material orthotropy, cone semi-vertex angle and other geometrical parameters on the values of the critical combined load have been studied.

• Geomechanics and Engineering
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• 제9권4호
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• pp.465-481
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• 2015

Three-dimensional simulation of flow through dam foundation is performed using finite element (Seep3D model) and artificial neural network (ANN) models. The governing and discretized equation for seepage is obtained using the Galerkin method in heterogeneous and anisotropic porous media. The ANN is a feedforward four layer network employing the sigmoid function as an activator and the back-propagation algorithm for the network learning, using the water level elevations of the upstream and downstream of the dam, as input variables and the piezometric heads as the target outputs. The obtained results are compared with the piezometric data of Shahid Abbaspour's Dam. Both calculated data show a good agreement with available measurements that demonstrate the effectiveness and accuracy of purposed methods.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 춘계학술대회논문집
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• pp.424-429
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• 2005

In this paper, the response characteristics of one to one resonance on the rectangular cantilever beam in which basic harmonic excitations are applied by nonlinear coupled differential integral equations are studied. This equations have 3-dimensional non-linearity of nonlinear inertia and nonlinear curvature. Galerkin and multi scale methods are used for theoretical approach to one to one internal resonance. Nonlinear response characteristics of 1st, 2nd, 3rd modes are measured from the experiment for basic harmonic excitation. From the experimental result, geometrical terms of nonlinearity display light spring effect and these terms play an important role in the response characteristics of low frequency modes. Dynamic behaviors in the out of plane are also studied.