• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제4권2호
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• pp.111-133
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• 2000

A Legendre spectral tau approximation scheme for solving the two-dimensional stationary incompressible Stokes equations is considered. Based on the vorticity-stream function formulation and variational forms, boundary value and normal derivative of vorticity are computed. A factorization technique for matrix stems based on the Schur decomposition is derived. Several numerical experiments are performed.

• Smart Structures and Systems
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• 제31권2호
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• pp.155-169
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• 2023

The quasi-static component of the moving vehicle-induced dynamic response is promising in damage detection as it is sensitive to bridge damage but insensitive to environmental changes. However, accurate extraction of quasi-static component from the dynamic response is challenging especially when the vehicle velocity is high. This paper proposes an adaptive quasi-static component extraction method based on the modified variational mode decomposition (VMD) algorithm. Firstly the analytical solutions of the frequency components caused by road surface roughness, high-frequency dynamic components controlled by bridge natural frequency and quasi-static components in the vehicle-induced bridge response are derived. Then a modified VMD algorithm based on particle swarm algorithm (PSO) and mutual information entropy (MIE) criterion is proposed to adaptively extract the quasi-static components from the vehicle-induced bridge dynamic response. Numerical simulations and real bridge tests are conducted to demonstrate the feasibility of the proposed extraction method. The results indicate that the improved VMD algorithm could extract the quasi-static component of the vehicle-induced bridge dynamic response with high accuracy in the presence of the road surface roughness and measurement noise.

• 동력기계공학회지
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• 제19권3호
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• pp.55-62
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• 2015

This paper discusses a new model for investigating the micro-mechanical behavior of beam-like structures composed of various elastic moduli and complex geometries varying through the cross-sectional directions and also periodically-repeated along the axial directions. The original three-dimensional problem is first formulated in an unified and compact intrinsic form using the concept of decomposition of the rotation tensor. Taking advantage of two smallness of the cross-sectional dimension-to-length parameter and the micro-to-macro heterogeneity and performing homogenization along dimensional reduction simultaneously, the variational asymptotic method is used to rigorously construct an effective zeroth-order beam model, which is similar a generalized Timoshenko one (the first-order shear deformation model) capable of capturing the transverse shear deformations, but still carries out the zeroth-order approximation which can maximize simplicity and promote efficiency. Two examples available in literature are used to demonstrate the consistence and efficiency of this new model, especially for the structures, in which the effects of transverse shear deformations are significant.

• 대한기계학회논문집A
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• 제32권10호
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• pp.836-843
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• 2008

An efficient domain/boundary decomposition method is applied for heat transfer problems with non-linear thermal radiation boundaries. The whole domain of solids or structures is considered as set of subdomains, an interface, and radiation interfaces. In a variational formulation, simple penalty functions are introduced to connect an interface or radiation interfaces with neighboring subdomains that satisfy continuity conditions. As a result, non-linear finite element computations due to the thermal radiation boundaries can be localized within a few subdomains or radiation interfaces. Therefore, by setting up suitable solution algorithms for the governing finite element equations, the computational efficiency can be improved considerably. Through a set of numerical examples, these distinguishing characteristics of the present method are investigated in detail.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 가을 학술발표회 논문집
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• pp.575-582
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• 2002

A new coupling method of Element-Free Galerkin Method(EFGM) and Boundary Element Method(BEM) using the domain decomposition method is presented in this paper. This proposed methodology is that the problem domain is decomposed into sub-domains being modeled by the EFGM and BEM respectively and the respective EFGM and BEM domains share a partially overlapped region over an entire domain. Then, the each sub-domain is separately computed and the variables on common region are iteratively updated until converging. It is an important note that in the developed coupling method, there is no need to combine the coefficient matrices of EFGM and BEM sub-domains, in contrast with the other conventional coupling methods. In the first part of this paper, a theory of EFGM and BEM is summarized, and then a brief introduction of domain decomposition method is described. Then, a new coupling method is presented. Also, patch test and Some numerical examples are studied to verify stability, accuracy and efficiency of the proposed method, in which numerical performance of the method is compared with that of conventional method such as EFGM-BEM variational coupling method, EFGM and BEM.

• 한국태양에너지학회 논문집
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• 제36권3호
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• pp.9-16
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• 2016

This paper discusses a refined model for investigating the micro-mechanical behavior of beam-like structures, which are composed of various elastic moduli and complex geometries varying through the cross-section directions and are also periodically-repeated and heterogeneous along the axial direction. Following the previous work (Lee and Yu, 2011), the original three-dimensional static problem is first formulated in a unified and compact form using the concept of decomposition of the rotation tensor. Taking advantage of the smallness of the cross-sectional dimension-to-length parameter and the micro-to-macro heterogeneity, while also performing homogenization along the dimensional reduction simultaneously, the variational asymptotic method is rigorously used to construct a total energy function, which is asymptotically correct up to the second order. Furthermore, through the transformation procedure based on the pure kinematic relations and the linearized equilibrium equations, a generalized Timoshenko model is systematically established. For the purpose of dealing with realistic and complex geometries and constituent materials at the microscopic level, this present approach is incorporated into a commercial analysis package. A few examples available in literature are used to demonstrate the consistency and efficiency of this proposed model, especially for the structures, in which the effects of transverse shear deformations are significant.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.165-177
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• 2013

In this paper, we apply Homotopy perturbation transform method (HPTM) for solving singular fourth order parabolic partial differential equations with variable coefficients. This method is the combination of the Laplace transform method and Homotopy perturbation method. The nonlinear terms can be easily handled by the use of He's polynomials. The aim of using the Laplace transform is to overcome the deficiency that is mainly caused by unsatisfied conditions in other semi-analytical methods such as Homotopy perturbation method (HPM), Variational iteration method (VIM) and Adomain Decomposition method (ADM). The proposed scheme finds the solutions without any discretization or restrictive assumptions and avoids the round-off errors. The comparison shows a precise agreement between the results and introduces this method as an applicable one which it needs fewer computations and is much easier and more convenient than others, so it can be widely used in engineering too.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권1호
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• pp.43-56
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• 2010

The representative numerical algorithms to solve the time dependent Navier-Stokes equations are projection type methods. Lots of projection schemes have been developed to find more accurate solutions. But most of projection methods [4, 11] suffer from inconsistency and requesting unknown datum. E and Liu in [5] constructed the gauge method which splits the velocity $u=a+{\nabla}{\phi}$ to make consistent and to replace requesting of the unknown values to known datum of non-physical variables a and ${\phi}$. The errors are evaluated in [9]. But gauge method is not still obvious to find out suitable combination of discrete finite element spaces and to compute boundary derivative of the gauge variable ${\phi}$. In this paper, we define 4 gauge algorithms via combining both 2 decomposition operators and 2 boundary conditions. And we derive variational derivative on boundary and analyze numerical results of 4 gauge algorithms in various discrete spaces combinations to search right discrete space relation.

• 방송공학회논문지
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• 제24권5호
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• pp.791-801
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• 2019

전기화재의 원인중의 하나는 직렬 아크이다. 최근까지 아크 신호를 검출하기 위해 다양한 기법들이 진행되고 있다. 시간 신호에 푸리에 변환, 웨이블릿, 또는 통계적 특징 등을 활용하여 아크 검출을 하는 방법들이 소개되었지만, 다양한 불규칙 아크 파형 때문에, 실제 환경에서는 아크 성능이 저하되는 문제가 있다. 따라서, 기존의 부족한 특징 데이터를 증가시켜, 성능을 개선하는 것이 요구된다. 본 논문에서는 입력신호를 변분 모드 분할을 통해 원신호를 분할한 후 통계적 특징을 추출한다. 변분 모드 분할으로부터 추출한 통계적 특징의 성능이 원신호로부터 얻은 특징보다 개선된 성능을 얻는다. 아크 분류기로 인공 신경망을 이용하고, 14,000개의 학습 데이터에 적용한 결과 VMD의 사용이 약 4%의 아크 검출 성능을 높혔다.

• 대한수학회논문집
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• 제20권3호
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• pp.563-578
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• 2005

In [Z. Cai and B. C. Shin, SIAM J. Numer. Anal. 40 (2002), 307-318], we developed the discrete first-order system least squares method for the second-order elliptic boundary value problem by directly approximating $H(div){\cap}H(curl)-type$ space based on the Helmholtz decomposition. Under general assumptions, error estimates were established in the $L^2\;and\;H^1$ norms for the vector and scalar variables, respectively. Such error estimates are optimal with respect to the required regularity of the solution. In this paper, we study solution methods for solving the system of linear equations arising from the discretization of variational formulation which possesses discrete biharmonic term and focus on numerical results including the performances of multigrid preconditioners and the finite element accuracy.