• 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.

• International Journal of CAD/CAM
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• v.9 no.1
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• pp.103-109
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• 2010

Recently, various conformal geometric methods have been presented for non-rigid surface matching and registration. This work proposes to improve the robustness of conformal geometric methods to the boundaries by incorporating the symmetric information of the input surface. We presented two symmetric conformal mapping methods, which are based on solving Riemann-Cauchy equation and curvature flow respectively. Experimental results on geometric data acquired from real life demonstrate that the symmetric conformal mapping is insensitive to the boundary occlusions. The method outperforms all the others in terms of robustness. The method has the potential to be generalized to high genus surfaces using hyperbolic curvature flow.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.8
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• pp.71-77
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• 1995

Evaluated are errors of the conformal mapping method in the analysis of a coplanar waveguides and asmmetric coplanar strips. The errors are mainly due to the negligence of fringe field effect after electrode structures are transformed to parallel electrodes. For the purpose of comparison, results of the conformal mapping(CM) method are compared with those of the successive over relaxation(SOR) method.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.48 no.3
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• pp.104-109
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• 1999

In order to design and predict the performance of the harmonic side drive motor, it is necessary to analyze the torque generated by the structure. In this paper, an analytical model is proposed for design. Conformal mapping is used to model the capacitance and torque of the motor as a function of the rotor angular position with two-dimensional approximation. Then the result of conformal mapping analysis is verified with F.E.M result.

• 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 the Chungcheong Mathematical Society
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• v.23 no.3
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• pp.463-470
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• 2010

If P(f, r) is the set of endpoints of radii which have length greater than or equal to r > 0 under a conformal mapping f of the unit disc. Then for large r, the logarithmic capacity of P(f, r), $\frac{1}{\sqrt[2]{r}}{\leq}cap(P(f,r)){\leq}\frac{k}{\sqrt{r}}$. Where k is the positive constant.

• The Journal of the Acoustical Society of Korea
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• v.19 no.4
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• pp.77-83
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• 2000

The previous synthetic aperture techniques have been investigated to increase signal gain, improve angular resolution and peak-to-sidelobe level ratios for towed line array sonar systems. The synthetic aperture method in this paper is performed for conformal array systems by mapping real elements on an axis to control like a linear array. The proposed method for the conformal array performs coherent processing of subaperture signals at successive time intervals in the beam domain via FFT transformations. This was confirmed by the simulation results and compared to the results from use of the synthetic aperture technique under the conformal array.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.24 no.6
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• pp.35-42
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• 2010

We use conformal mapping method to derive the analytical expressions for calculating electrostatic fields and electric potentials surrounding the conductor-backed coupled coplanar waveguide(CBCCPW) structure. Using the derived expressions, the electrostatic fields and potentials are computed at various points of the CBCCPW's geometry and the field and potential distributions are analyzed. The proposed method provides a faster and simpler calculation of the field distributions than the full-wave analysis method because no iterations are required. This method can be widely applied to the analysis of microwave integrated circuits using coupled line, such as coupler, filter, and microstrip antenna.

• 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.

• 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.