• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.2
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• pp.101-113
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• 2018

The dual singular function method(DSFM) is a numerical algorithm to get optimal solution including corner singularities for Poisson and Helmholtz equations. In this paper, we apply DSFM to solve heat equation which is a time dependent problem. Since the DSFM for heat equation is based on DSFM for Helmholtz equation, it also need to use Sherman-Morrison formula. This formula requires linear solver n + 1 times for elliptic problems on a domain including n reentrant corners. However, the DSFM for heat equation needs to pay only linear solver once per each time iteration to standard numerical method and perform optimal numerical accuracy for corner singularity problems. Because the Sherman-Morrison formula is rather complicated to apply computation, we introduce a simplified formula by reanalyzing the Sherman-Morrison method.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.5
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• pp.180-185
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• 2000

An interface V-notched crack problem can be formulated as a eigenvalue problem. there are the eigenvalues which give stress singularities at the V-notched crack tip. The RWCIM is a method of calculating the eigenvector coefficients associated with eigenvalues for a V-notched crack problem. Obtaining the stress intensity factors for an interface crack in dissimilar materials is examined by the RWCIM. The results of stress intensity factors for an interface crack are compared with those of the displacement extrapolation method by the BEM

• Proceedings of the Korean Society For Composite Materials Conference
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• 2003.04a
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• pp.83-86
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• 2003

동시경화조인트는 경화 시 복합재료로부터 흘러나오는 수지를 접착제로 사용하기 때문에 제조과정이 간편할 뿐 아니라 복합재료를 표면 처리할 필요가 없기 때문에 기존의 접착제에 의한 접합방법에 비해 장점을 지닌다. 최근 동시경화조인트에 관한 연구가 활발하게 진행되고 있으나 해석적인 방법을 통한 연구는 아직까지 미비하다. 실험적으로 연구된 결과를 보면 동시경화 조인트는 계면 모서리에서 파괴가 시작되어 계면을 따라 파괴가 진행된다. 그러므로 조인트의 계면 모서리에서의 응력집중계수에 관해 연구하는 것이 중요하다. 본 논문에서는 고유치 문제를 고려하여 복합재료와 강재료로 구성된 동시경화조인트의 계면 모서리에서 발생하는 응력 및 변위장을 결정하고, H-적분을 이용하여 응력집중계수를 구하는 방법을 제시하고자 한다.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2003.10a
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• pp.479-482
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• 2003

Edge, detected from image processing includes variety of information about original image's location and shape etc. So a lot of researches for detecting those edges have been continuing even now. And with the recent progress of wavelet theory which is presented as a new technique of signal processing fields, wavelet transform is being applied to many fields which analyzes singularities of image. For this reason, this paper detected original image's edge from the information such as local maximum, direction, and location of the wavelet transform data by using wavelet function which is independent of width of line.

• 한국전산유체공학회:학술대회논문집
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• 2006.05a
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• pp.163-166
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• 2006

We have introduced a new version of the 3-D lid-driven cavity problem that leads to more complicated fluid parcel trajectories and thus, enhanced mixing, but at the same time weakens corner singularities. We employed an advanced form of LES to solve this problem and presented preliminary results that show very complicated streamline structures on both large and small scales, despite a relatively low Reynolds number. Finally, we demonstrated moderate speedups via parallelization. Ongoing tests are expected to resolve the questions raised regarding possible sources of the rather poor parallel performance compared with that seen in earlier studies with the same code. Because it is expected that findings may be significant for parallel performance in general, we plan to emphasize this aspect in the oral presentation the Parrel (CFD 2006 Conference.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.1
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• pp.180-188
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• 1996

The stress singularity of a sharp wedge contacting a half plane can be avoided by changing the wedge shape. Shape optimization is accomplished with the geometric strain method (GSM), an optimality criterion method. Several numerical examples are provided for different materials in the wedge and half plane to avoid stress singularity neal the sharp corner of the wedge. Optimum wedge shapes are obtained and critical corner angles are compared with the angles from analytical contact mechanics. Numerical results are well matched to analytical and experimental results. It is shown that shape optimization by the geometric strain method is a useful tool to reshape the wedge and to avoid a stress singulatiry. The method applies to more general geometries where the singular behavior would be difficult to avoid by classical means.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.12
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• pp.1608-1615
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• 2004

CFD data compression methods based on Full-3D and Quasi-1D supercompact multiwavelets are presented. Supercompact wavelets method provide advantageous benefit that it allows higher order accurate representation with compact support. Therefore it avoids unnecessary interaction with remotely located data across singularities such as shock. Full-3D wavelets entails appropriate cross-derivative scaling function & wavelets, hence it can allow highly accurate multi-spatial data representation. Quasi-1D method adopt 1D multiresolution by alternating the directions rather than solving huge transformation matrix in Full-3D method. Hence efficient and relatively handy data processing can be conducted. Several numerical tests show swift data processing as well as high data compression ratio for CFD simulation data.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.1
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• pp.13-23
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• 2008

In [7, 8], they proposed a new singular function(NSF) method to compute singular solutions of Poisson equations on a polygonal domain with re-entrant angles. Singularities are eliminated and only the regular part of the solution that is in $H^2$ is computed. The stress intensity factor and the solution can be computed as a post processing step. This method was extended to the interface problem and Poisson equations with the mixed boundary condition. In this paper, we give NSF method for the Helmholtz equations ${\Delta}u+Ku=f$ with homogeneous Dirichlet boundary condition. Examples with a singular point are given with numerical results.

• Journal of electromagnetic engineering and science
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• v.7 no.2
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• pp.59-63
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• 2007

This paper suggests a novel method to efficiently calculate the spatial-domain Green's functions of 2D electromagnetic problems Briefly speaking, this method combines spectral and spatial domain calculation schemes and prevents the Green's functions from poor convergence due to the singularities that complicate the process of the Method of Moment(MoM) applications For the validation of this proposed method, fields will be evaluated along the spatial distance including zero distance for 2D free-space and periodic homogeneous geometry The numerical results show the validity of the prosed method and correspondng physics.

• 한국지구물리탐사학회:학술대회논문집
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• 2007.06a
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• pp.124-129
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• 2007

For seismic imaging and inversion, the inverted image depends on how we define the objective function. ${\ell}^1$-norm is more robust than ${\ell}^2$-norm. However, it is difficult to apply the Newton-type algorithm directly because the partial derivative for ${\ell^1$-norm has a singularity. In our paper, to overcome the difficulties of singularities, Huber function given by hybrid ${\ell}^1/{\ell}^2$-norm is used. We tested the robustness of our new object function with several noisy data set. Numerical results show that the new objective function is more robust to band limited spiky noise than the conventional object function.