A study on the Automatic Algorithm for Numerical Conformal Mapping


The KIPS Transactions:PartA, Vol. 14, No. 1, pp. 73-76, Feb. 2007
10.3745/KIPSTA.2007.14.1.73,   PDF Download:

Abstract

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 method 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 not acquired[3]. In this paper, we propose an automatic algorithm for numerical conformal mapping based 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 proved by numerical experience.


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Cite this article
[IEEE Style]
E. J. Song, "A study on the Automatic Algorithm for Numerical Conformal Mapping," The KIPS Transactions:PartA, vol. 14, no. 1, pp. 73-76, 2007. DOI: 10.3745/KIPSTA.2007.14.1.73.

[ACM Style]
Eun Jee Song. 2007. A study on the Automatic Algorithm for Numerical Conformal Mapping. The KIPS Transactions:PartA, 14, 1, (2007), 73-76. DOI: 10.3745/KIPSTA.2007.14.1.73.