• Proceedings of the Korea Information Processing Society Conference
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• 2010.11a
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• pp.1839-1842
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• 2010

등각사상은 함수론의 기본적인 문제로 2차원 Laplace방정식이 나타나는 열전도, 정전(靜電) potential, 유체의 문제에 이용되는 등 공학이나 물리학에서 그 응용분야가 넓다. 수치등각사상의 목적은 보다 빠르고, 보다 정확하며, 보다 적용범위가 넓은 계산법을 연구하는데 있다. 단위원 내부로부터 Jordan 영역 내부로의 등각사상을 구하는 문제는 비선형 방정식인 Theodorsen 방정식을 푸는 것으로 귀결된다. Theodorsen 방정식에 관해서는 여러 가지 수치해법이 제안되어 있는데 본 논문에서는 그 중 SOR 법인 Niethammer와 Newton법인 Vertgeim의 방법을 다루어 비교, 분석하였다. 이 2가지 방법을 실제 계산기상에 실현시켜 수치실험을 하여 그 유효성을 비교, 분석한 결과 난이도가 낮은 문제에서는 Niethammer의 방법이 난이도가 높은 문제에서는 Vertgeim이 제안한 방법이 유효함을 알게 되었다.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2009.10a
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• pp.821-824
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• 2009

Conformal mapping is useful to solve problems in physics, engineering and so on. This paper is to discuss the numerical conformal mapping from the unit disk onto Jordan region, which can be solved by Theodorsen equation. Wegmann's method has been known as the most efficient one for the Theodorsen equation. However, we found divergence through numerical experiments by the iterative method of Wegmann. The divergence occurs especially when some degree of difficulty is high. We analyze the cause of divergence and propose an improved method by applying a low frequency pass filter to Wegmann's method. By this proposed method we can get a stable convergence for all the problems which was unstable with the Wegmann's method.

• The KIPS Transactions:PartA
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• v.14A no.1 s.105
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• pp.73-76
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• 2007

The determination of the conformal maps from the unit disk onto a Jordan region has been completed by solving the Theodorsen equation which is an nonlinear equation for the boundary correspondence function. Wegmann's method has been well known for the efficient mothed among the many suggestions for the Theodorsen equation. We proposed an improved method for convergence by applying a low-frequency pass filter to the Wegmann's method and theoretically proved convergence of improved iteration[1, 2]. And we proposed an effective method which makes it possible to estimate an error even if the real value is nut acquired[3]. In this paper, we propose an automatic algorithm for numerical conformal mapping bared on this error analysis in our early study. By this algorithm numerical conformal mapping is determined automatically according to the given domain of problem and the required accuracy. The discrete numbers and parameters of the low-frequency filter were acquired only by experience. This algorithm, however, is able to determine the discrete numbers and parameters of the low-frequency filter automatically in accordance with the given region This results from analyzing the function, which may decide the shape of the given domain under the assumption that the degree of the problem depends of the transformation of a given domain, as seen in the Fourier Transform. This proposed algorithm is also ploved by numerical experience.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.27 no.2
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• pp.281-288
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• 2009

In the paper, we try to develop the methodology for updating road networks of large-scale digital maps by using construction drawing data. For the purpose, it is pre-requite step to merge road networks detached in CAD drawing data. As such, tie points are identified in neighboring drawings and used for solving the parameters of 2D conformal transformation between drawings. Then, the merged road network in CAD data is transformed to the coordinate system of digital maps. In the process, IPs in the drawings are considered as control information and 2D affine transformation is selected for coordinate transformation. Through the experiments with real dataset, we can identify that the developed method is valid and generally applicable.

• The KIPS Transactions:PartA
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• v.8A no.4
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• pp.503-508
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• 2001

Conformal mapping is useful to solve problems in heat conduction, electrostatic potential and fluid flow involving Laplace's equation in two independent variables. Determinations of conformal maps from the unit disk onto a Jordan region eventually requires solving the Theodorsen equation which is in general nonlinear with respect to the boundary correspondence function. H bner's method which has been well known for the efficient method among the many suggestions for the Theodorsen equation, was improved in early study[1, 2]. In this paper Wegmann's method is treated that is more efficient in computation cost rather than H bner's. But we found that a question which is divergent in some difficult problems by numerical experiment of Wegmann's iteration. We analyze theoretically the cause of divergence and propose an improved method by applying a low frequency filter to the Wegmann's method. Numerical experiments by our improved method show convergence for all divergent problems by Wegmann's method.

• Proceedings of the Korea Information Processing Society Conference
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• 2002.11a
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• pp.419-422
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• 2002

저자는 등각사상을 추하기 위한 기존의 여러 Theodorsen 방정식의 해법 중 가장 유효한 해법으로 알려져 있는 Wegmann의 방법을 다룬바 있다. Wegmann의 방법으로 수치실험을 한 결과 난이도가 높다고 예상되는 문제에 있어 수렴했다가 발산을 하는 불안정현상이 나타났으며 수렴하지 않는 불안정현상의 원인을 분석하여 저주파필터를 적용한 새로운 반복법을 제안하여 Wegmann 방법으로는 발산하는 모든 문제에 있어서 수렴하는 수치실험 결과를 얻었다[1]. 본 논문에서는 저주파필터를 적용한 해법에 의해 수치적으로 수렴한 결과를 이론적으로 증명한다.

• Proceedings of the Korea Information Processing Society Conference
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• 2004.05a
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• pp.989-992
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• 2004

수학적 모델을 컴퓨터 상에 실현시키는데 있어 보다 효율적인 알고리즘을 구현하고 개발하는 것이 수치해석 연구의 궁극적인 목표이다. 일반적으로 수치해석을 사용할 때 컴퓨터 상에서 구한 계산 결과, 즉 근사 값과 수학적으로 구한 값인 참값은 정확하게 같지 않다. 따라서 근사 값이 얼마나 참값에 가까운가에 따라 알고리즘의 효율성을 평가하는 오차평가는 수치해석의 가장 중요한 과제라 할 수 있다. 대부분의 경우 오차평가에 있어 오차의 한계를 이용하지만 주어진 문제의 참값을 모르기 때문에 정확한 오차평가를 할 수 없다. 본 논문에서는 수치등각사상을 구하기 위한 해법중 하나인 Wegmann해법에 있어 몇 가지 수학적 이론에 근거하여 참값을 모르더라도 오차평가를 할 수 있는 방법을 제안하고 수치실험을 통해 그 유효성을 입증한다.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.10
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• pp.1702-1711
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• 1997

A numerical study for the number of terms of a power series stress function and the effect of hybrid element size on stress analysis around a hole in loaded orthotropic composites is presented. The hybrid method coupling experimental and/or theoretical inputs and complex variable formulations involving conformal mappings and analytical continuity is used to calculate tangential stress on the boundary of the hole in uniaxially loaded, finite width glass epoxy tensile plate. The tests are done by rarying the number of terms, element size and nodal locations on the external boundary of the hybrid region. The numerical results indicate that the hybrid method is accurate and powerful in both experimental and numerical stress analysis.

• Proceedings of the Korea Information Processing Society Conference
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• 2005.05a
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• pp.1053-1056
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• 2005

단위원의 내부로부터 Jordan 영역으로의 등각사상을 구하는 것은 일반적으로 경계대응함수에 관한 Theodorsen 방정식을 푸는 것으로 귀결된다. 저자는 이 비선형 방정식의 수치적 해법 중 가장 효율적인 방법으로 알려진 Wegmann의 해법을 저주파 필터를 적용하여 개량한 바 있다. 또한 이 해법에 있어 참값을 모르더라도 오차평가가 가능한 방법을 제안하였다 [1,2]. 본 논문에서는 참값을 모르더라도 오차평가가 가능한 연구결과를 이용하여 저주파필터를 적용한 Wegmann 방법에서 지금까지 경험에 의존했었던 표본수와 저주파필터의 파라메터가 주어진 문제 영역에 따라 자동적으로 결정되는 알고리즘을 제안한다. 이것은 문제의 난이도가 문제영역의 변형에 의존한다는 전제로 문제영역의 모양을 결정하는 함수를 Fourier 급수로 분석하여 얻을 수 있다. 수치실험을 통해 그 유효성을 입증한다.

• The Transactions of the Korea Information Processing Society
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• v.6 no.10
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• pp.2716-2721
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• 1999

The problem of determining the conformal maps from the unit disk onto a jordan region has been completed by solving the theodorsen equation that is nonlinear. For the hubners method, which has been well known for the efficient method among the many suggestions for the Theodorsen equation, it has been reproved in our early study that the convergence rate could be remarkably improved by exploring and applying a low-frequency pass filter[1]. However, in the Hubner's method with the low-frequency filter, the discrete numbers and parameters of the low-frequency filter were able to be acquired only by experience. In this paper we show algorithms that determine the discrete numbers and parameters of the low-frequency filter automatically in accordance with the given region. This results from analyzing the function, which decides the shape of the given domain under the assumption that the degree of the problem depends of the transformation of a given domain, as seen in the Fourier Transform.