A Numerical Method for Conformal Mapping of Doubly Connected Regions

1984 ◽  
Vol 5 (4) ◽  
pp. 771-783 ◽  
Author(s):  
Bengt Fornberg
Keyword(s):  
Conformal Mapping ◽  
Numerical Method

A Numerical Method for Conformal Mapping

1982 ◽  
Vol 2 (2) ◽  
pp. 169-181 ◽  
Author(s):  
N. V. CHALLIS ◽  
D. M. BURLEY
Keyword(s):  
Conformal Mapping ◽  
Numerical Method

scholarly journals Convergence of Numerical Solution of Generalized Theodorsen’s Nonlinear Integral Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Mohamed M. S. Nasser
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Conformal Mapping ◽  
Uniform Convergence ◽  
Numerical Solution ◽  
Numerical Method ◽  
Nonlinear Integral Equation ◽  
Numerical Results ◽  
Simply Connected

We consider a nonlinear integral equation which can be interpreted as a generalization of Theodorsen’s nonlinear integral equation. This equation arises in computing the conformal mapping between simply connected regions. We present a numerical method for solving the integral equation and prove the uniform convergence of the numerical solution to the exact solution. Numerical results are given for illustration.

scholarly journals Investigation of symmetry breaking in periodic gravity–capillary waves

2016 ◽  
Vol 811 ◽  
pp. 622-641 ◽  
Author(s):  
T. Gao ◽  
Z. Wang ◽  
J.-M. Vanden-Broeck
Keyword(s):  
Conformal Mapping ◽  
Symmetry Breaking ◽  
Incompressible Fluid ◽  
Numerical Method ◽  
Finite Depth ◽  
Capillary Waves ◽  
Fully Nonlinear ◽  
Infinite Depth ◽  
Breaking Points ◽  
Continuation Parameter

In this paper, fully nonlinear non-symmetric periodic gravity–capillary waves propagating at the surface of an inviscid and incompressible fluid are investigated. This problem was pioneered analytically by Zufiria (J. Fluid Mech., vol. 184, 1987c, pp. 183–206) and numerically by Shimizu & Shōji (Japan J. Ind. Appl. Maths, vol. 29 (2), 2012, pp. 331–353). We use a numerical method based on conformal mapping and series truncation to search for new solutions other than those shown in Zufiria (1987c) and Shimizu & Shōji (2012). It is found that, in the case of infinite-depth, non-symmetric waves with two to seven peaks within one wavelength exist and they all appear via symmetry-breaking bifurcations. Fully exploring these waves by changing the parameters yields the discovery of new types of non-symmetric solutions which form isolated branches without symmetry-breaking points. The existence of non-symmetric waves in water of finite depth is also confirmed, by using the value of the streamfunction at the bottom as the continuation parameter.

A novel analytical calculation of magnetic field in the slotted air gap of spoke-type permanent-magnet machines using conformal mapping

2020 ◽  
pp. 1-15
Author(s):  
Jianqi Li ◽  
Yu Zhou ◽  
Jianying Li
Keyword(s):  
Magnetic Field ◽  
Conformal Mapping ◽  
Permanent Magnet ◽  
Flux Density ◽  
Analytical Method ◽  
Electromotive Force ◽  
Analytical Calculation ◽  
Air Gap ◽  
Permanent Magnet Machines ◽  
Peak Value

This paper presented a novel analytical method for calculating magnetic field in the slotted air gap of spoke-type permanent-magnet machines using conformal mapping. Firstly, flux density without slots and complex relative air-gap permeance of slotted air gap are derived from conformal transformation separately. Secondly, they are combined in order to obtain normalized flux density taking account into the slots effect. The finite element (FE) results confirmed the validity of the analytical method for predicting magnetic field and back electromotive force (BEMF) in the slotted air gap of spoke-type permanent-magnet machines. In comparison with FE result, the analytical solution yields higher peak value of cogging torque.

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