• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.4
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• pp.301-308
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• 2013

In this paper, an accuracy analysis of parallel method based on non-overlapping domain decomposition method is carried out. In this approach, proposed by Tak et al.(2013), the decomposed subdomains do not overlap each other and the connection between adjacent subdomains is determined via simple connective finite element named interfacial element. This approach has two main advantages. The first is that a direct method such as gauss elimination is available even in a singular problem because the singular stiffness matrix from floating domain can be converted to invertible matrix by assembling the interfacial element. The second is that computational time and storage can be reduced in comparison with the traditional finite element tearing and interconnect(FETI) method. The accuracy of analysis using proposed method, on the other hand, is inclined to decrease at cross points on which more than three subdomains are interconnected. Thus, in this paper, an accuracy analysis for a novel non-overlapping domain decomposition method with a variety of subdomain numbers which are interconnected at cross point is carried out. The cause of accuracy degradation is also analyze and establishment of countermeasure is discussed.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.4
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• pp.369-378
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• 2010

The mixed finite element analysis is the most widely used method for saturated porous media. Generally, in this method, direct method and iterative method are proposed to obtain unknown variable, however, the iterative method is recommended because the method provide numerical stability and accuracy under the material properties for solid and fluid are different. In this paper, we introduce staggered method which has strong numerical stability, and FETI(Finite Element Tearing and Interconnecting) which is one of decomposition methods are applied into the method in order to obtain numerical efficiency. In which, Lagrange Multipliers and conjugated gradient method to solve decomposed domain are proposed, and then, the proposed method is verified numerical efficiency by point to point MPI(Message Passing Interface) library.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.2
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• pp.191-201
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• 2010

This paper presents a new global optimization algorithm based on the branch-and-bound principle using Bspline approximation techniques. It describes the algorithmic components and details on their implementation. The key components include the subdivision of a design space into mutually disjoint subspaces and the bound calculation of the subspaces, which are all established by a real-valued B-spline volume model. The proposed approach was demonstrated with various test problems to reveal computational performances such as the solution accuracy, number of function evaluations, running time, memory usage, and algorithm convergence. The results showed that the proposed algorithm is complete without using heuristics and has a good possibility for application in large-scale NP-hard optimization.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.5
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• pp.77-83
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• 1993

A modified Lanczos method combined with a substructure analysis technique was used for calculating natural frequencies and mode shapes of large structural systems. The method does not require generation and storage of stiffness and mass matrices of the entire structure. It only uses the stiffness and mass matrices of each substucture. No approximating assumptions are required other than the usual assumption of linear elastic system modelled by finite elements. Thus, natural frequencies and mode shapes for the finite element model employed are the same as those with or without the suhstructuring algorithm. To check the efficiency of the proposed method, first ten natural frequencies and the corresponding mode shapes of an open truss helicopter tail-boom structure are calculated by using it.

• Proceedings of the KIEE Conference
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• 2004.10a
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• pp.55-59
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• 2004

유한요소법을 이용하여 전자장을 해석할 경우 전류원이 전 영역에 비해 극히 작은 영역이면, 요소분할 과정에서 소스부분을 세분하여야 하므로 결국 미지수의 증가를 가져오게 된다. 또한, 선전류 문제의 경우 2차원 유한 요소 해석이 용이하지 않다. 이를 보안하기 위해 본 논문에서는 소스가 선전류이고 관심 영역이 선전류원으로부터 떨어져 있는 경우, 소스 영역은 해석해를 적용하여 유한요소법과 결합하는 방법을 제시하였다. 해석적인 해는 원통좌표계에서 반정에 대한 멱함수와 회전각도에 대한 삼각함수의 곱의 형태로 표현된다. 이때 두 종류의 적분 상수가 있는데, 이는 경계상의 포텐셜값과 유한요소법의 경계 적분항을 푸리에급수로 전개한 계수로 표현된다. 제안한 알고리즘의 검증을 위하여 해석해가 존재하는 모델을 설정하여 해석적인 방법, 기존의 유한요소 법 및 결합 방법에 의한 해를 비교 검증하였다.

• Proceedings of the Korea Electromagnetic Engineering Society Conference
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• 2002.11a
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• pp.375-379
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• 2002

본 논문에서는 수 만개이상의 미지수를 필요로 하는 복잡한 3차원 구조에서의 정전용량 추출을 위한 고속화 알고리즘(Fast mutilpole method)과 결합한 효과적인 적응 삼각요소 분할법(Adaptive triangular mesh refinement algorithm)을 제안하였다. 요소세분화과정은 초기요소로 전하의 분포를 구하고, 전하밀도가 높은 영역에서의 요소세분화를 수행하여 이루어진다. 제안된 방법을 이용하여 많은 미지수를 필요로 하는 IC packaging 구조에서의 정전용량을 추출하였다.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2011.04a
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• pp.773-777
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• 2011

본 논문에서는 국부적으로 비선형 거동을 보이는 고전적인 $J_2$ 소성흐름 이론에 근거한 탄소성 문제의 해를 효율적으로 구하기 위해 전체-국부 확장함수를 지닌 일반유한요소법을 제안한다. 제안된 기법은 비선형 거동을 보이는 영역을 포함하는 국부 문제의 비선형 해를 구하고 이를 일반유한요소법의 단위 오목 분할의 개념을 통해 전체 문제의 해 공간을 확장하는데 이용한다. 이는 적은 계산량으로 복잡한 탄소성문제의 정확한 해를 얻는 것을 가능하게 하며 기법의 강건성과 정확성을 입증하기 위한 수치해석 예제가 다루어진다.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.5A
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• pp.861-872
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• 2006

The element free Galerkin method is extended by the local partition of unity method to model the cohesive cracks in two dimensional continuum. The shape function of a particle whose domain of influence is completely cut by a crack is enriched by the step enrichment function. If the domain of influence contains a crack tip inside, it is enriched by a branch enrichment function which does not have the LEFM stress singularity. The discrete equations are obtained directly from the standard Galerkin method since the enrichment is only for the displacement field, which satisfies the local partition of unity. Because only particles whose domains of influence are influenced by a crack are enriched, the system matrix is still sparse so that the increase of the computational cost is minimized. The condition for crack growth in dynamic problems is obtained from the material instability; when the acoustic tensor loses the positive definiteness, a cohesive crack is inserted to the point so as to change the continuum to a discontiuum. The crack speed is naturally obtained from the criterion. It is found that this method is more accurate and converges faster than the classical meshless methods which are based on the visibility concept. In this paper, several well-known static and dynamic problems were solved to verify the method.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.19 no.4
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• pp.108-116
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• 2005

This paper presents finite element analyses solution in the travelling magnetic field problem. The travelling magnetic field problem is subject to convective-diffusion equation. Therefore, the solution derived from Galerkin-FEM with linear interpolation function may oscillate between the adjacent nodes. A simple model with Dirichlet, Neumann and Periodic boundary condition respectively, have been analyzed to investigate stabilities of solutions. It is concluded that the solution of Galerkin-FEM may oscillate according to boundary condition and element type, but that of Upwind-FFM is stable regardless boundary condition.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.6 no.4
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• pp.65-71
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• 1997

The automation of mesh generation in BEM is very important in numerical analysis field for the time and efficiency. In order to this problem, program and algorithm to achive the purpose of making input data and automation of mesh generation based in Expert System are developed in this study. This program has the function of rotating and zooming. The stress intensity factor which is a criteria of fracture mechanics is calculated and compared with other results to prove efficiency and availability of the program in result.