• 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.

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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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.

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.

Conformal Mapping for Cogging Torque computation in IPM motor (등각 사상법을 이용한 매입형 영구자석 전동기의 코깅토크 해석)

  • Fang, Liang;Kwon, Soon-O;Jung, Jae-Woo;Hong, Jung-Pyo;Ha, Kyung-Ho
    • Proceedings of the KIEE Conference
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    • pp.1204-1206
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    • 2005
  • This paper deals with magnetic field analysis and computation of cogging torque in IPM motor with an analytical method, which is based on the Conformal Mapping technique. The magnetic field is analyzed by solving space harmonic field analysis due to inserted PM magnetizing distribution. Conformal Mapping method is then used for considering the slot opening effect and rotor saliency effect on the air-gap field magnetic distribution. Then, by integrating the field over the stator surface, cogging torque is calculated. The validity of the proposed analytical method is confirmed by comparing the results with 2-D FEA results.

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Some general properties in the degenerate scale problem of antiplane elasticity or Laplace equation

  • Chen, Y.Z.
    • 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.

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.

A STUDY ON STABILIZATION FOR NUMERICAL CONFORMAL MAPPING

  • SONG EUN-JEE
    • 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.