• Title, Summary, Keyword: Conformal Mapping

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A Study on the Effective Algorithm by Fourier Transform for Numerical Conformal Mapping

  • Song, Eun-Jee
    • 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.

Symmetric Conformal Mapping for Surface Matching and Registration

  • Zeng, Wei;Hua, Jing;Gu, Xianfeng David
    • 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.

LOGARITHMIC CAPACITY UNDER CONFORMAL MAPPINGS OF THE UNIT DISC

  • Chung, Bohyun
    • 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.

Errors of the conformal mapping method in the analysis of electrodes (전극 해석에서 등각사상법의 오차 평가)

  • 한영진;김창민
    • 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.

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Torque Characteristics Analysis of Harmonic Side Drive Motor by Conformal Mapping (등각사상에 의한 하모닉 모터의 토오크 특성 해석)

  • Yun, Seo-Jin;Lee, Eun-Ung;Lee, Dong-Ju
    • 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.

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A Study on the Methods for Solving the Theodorsen Equation for Numerical Conformal Mapping

  • Song, Eun-Jee
    • 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.

Synthetic Aperture Sonar for Conformal Towed Array (왜곡된 형상을 갖는 어레이를 위한 합성 처리 기법)

  • 김준환;양인식;김기만;오원천;도경철
    • 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.

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Analysis of Electrostatic Field and Potential Distributions in Conductor-Backed Coupled Coplanar Waveguide Using Conformal Mapping Method (등각사상방법을 이용한 도체로 보강된 결합 도파 선로의 정전기장과 전위 분포 해석)

  • Yoo, Tae-Hoon;Han, Ki-Soo
    • 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.

Variational Calculations for Higher Order Mode Cut-off Frequencies of Symmetrical Striplines by the Conformal Mapping (등각사상에 의한 대칭 스트립 전송선의 고차모드 차단주파수의 변분적 계산)

  • 양현규;이상설
    • 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.

A study on the solution stability by the position of internal nodes in hihger order isoparametric elements (고차 등매개요소에서 내부절점의 위치와 해의 안정성 연구)

  • Lee, Joon-Hee;Lim, Jang-Keun
    • 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.