• Journal of information and communication convergence engineering
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• v.8 no.3
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• pp.312-316
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• 2010

Conformal mapping has been a familiar tool of science and engineering for generations. The methods of numerical mapping are usually classified into those which construct the map from standard domain such as the unit disk onto the 'problem domain', and those which construct the map in the reverse direction. We treat numerical conformal mapping from the unit disk onto the Jordan regions as the problem domain in this paper. The traditional standard methods of this type are based on Theodorsen integral equation. Wegmann's method is well known as a Newton-like efficient one for solving Theodorsen equation. An improved method for convergence by applying low frequency pass filter to the Wegmann's method was proposed. In this paper we propose an effective algorithm for numerical conformal mapping based on the improved method. This algorithm is able to determine the discrete numbers and initial values automatically in accordance with the given region and the required accuracy. This results come from analyzing the shape of given domain as seen in the Fourier Transform.

• Journal of information and communication convergence engineering
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• v.10 no.1
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• pp.66-70
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• 2012

Conformal mapping has been a familiar tool of science and engineering for generations. Determination of a conformal map from the unit disk onto the Jordan region is reduced to solving the Theodorsen equation, which is an integral equation for boundary correspondence functions. There are many methods for solving the Theodorsen equation. It is the goal of numerical conformal mapping to find methods that are at once fast, accurate, and reliable. In this paper, we analyze Niethammer’s solution based on successive over-relaxation (SOR) iteration and Wegmann’s solution based on Newton iteration, and compare them to determine which one is more effective. Through several numerical experiments with these two methods, we can see that Niethammer’s method is more effective than Wegmann’s when the degree of the problem is low and Wegmann’s method is more effective than Niethammer’s when the degree of the problem is high.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.611-621
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• 2006

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.

• Progress in Superconductivity and Cryogenics
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• v.4 no.1
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• pp.124-128
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• 2002

A numerical model to obtain the temperature distribution in a radiation shield of cryogenic systems was proposed. Conformal mapping was used to transform the eccentric physical region of the upper plate to the concentric numerical region. The effects of the thickness of the radiation shield, the emissivities of the vacuum chamber and the radiation shield, and the eccentricity between the centers of the upper plate and the contact area with a cryocooler on the maximum temperature difference in a radiation shield were shown.

• 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.

• Structural Engineering and Mechanics
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• v.64 no.6
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• pp.695-701
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• 2017

This paper investigates some general properties in the degenerate scale problem of antiplane elasticity or Laplace equation. For a given configuration, the degenerate scale problem is solved by using conformal mapping technique, or by using the null field BIE (boundary integral equation) numerically. After solving the problem, we can define and evaluate the degenerate area which is defined by the area enclosed by the contour in the degenerate configuration. It is found that the degenerate area is an important parameter in the problem. After using the conformal mapping, the degenerate area can be easily evaluated. The degenerate area for many configurations, from triangle, quadrilles and N-gon configuration are evaluated numerically. Most properties studied can only be found by numerical computation. The investigated properties provide a deeper understanding for the degenerate scale problem.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.12
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• pp.1973-1983
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• 1997

Higher order isoparametric elements are usually used in the finite element analysis because they can represent easily the geometric shape of a complex structure ad can improve the solution quality. When these elements are used, the position of internal nodes affects greatly on the solution accuracy. Decreasing of the accuracy related to the position of internal nodes is due to non-conformal mapping often results in an unstable Jacobian value. This paper, in order to remove this difficulty, suggests a modified shape function which can establish conformal mapping between two coordinate systems. Numerical experiments with the proposed shape function show that a stable solution can be obtained without respect to the position of internal nodes, and offer convenience that one can take arbitrarily the position of internal nodes considering only the geometric shape of element boundaries.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.13 no.2
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• pp.170-175
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• 2002

The cut-off frequencies of higher order modes in a symmetrical stripline are calculated using the variational finite element method combined with the conformal mapping. The conformal mapping is used to Improve the modeling of the infinite transverse extents of a stripline. And then the finite element method is employed to solve the variational equation in the transformed finite region. Comparisons with numerical results found in the literature validate the presented method.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.595-602
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• 2006

Determinations of conformal map from the unit disk onto a Jordan region are reduced to solve the Theodorsen equation which is an integral equation for the boundary correspondence function. Among numerical conformal maps the Wegmann's method is well known as a Newton efficient one for solving Theodorsen equation. However this method has not so wide class of convergence. We proposed as an improved method for convergence by applying a low frequency filter to the Wegmann's method. In this paper, we investigate error analysis and propose an automatic algorithm based on this analysis.