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http://dx.doi.org/10.3745/KIPSTA.2004.11A.2.203

A study on the convergence of Wegmann's method applying a low frequency pass filter  

Song, Eun-Jee (남서울대학교 컴퓨터학과)
Abstract
Wegmann's method has been known as the most efficient one for the Theodorsen equation that is needed to solve conformal mapping. It was researched in the earlier studies (1). However divergence was revealed in some difficult problems by numerical experiment using Wegmann's method. We analyzed the cause of divergence and proposed an improved method by applying a low frequency pass filter to Wegmann's method. Numerical experiments using the improved method showed convergence for all divergent problems using the Wegmann's method. In this paper, we prove theroretically the cause of convergence in the Numerical experiment using the improved method by applying a low frequency pass filter to Wegmann's method. We make use of Fourier transforms in this theoretical proof of convergence.
Keywords
Wegmann's Method; Low Frequency Pass Filter; Fourier Transforms; The Proof of Convergence;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 송은지, '저주파 필터를 이용한 Wegmann 방법의 개량에 관한 연구', 정보처리학회논문집, 제8-A권 제4호, pp.503-508, 2001   과학기술학회마을
2 최도형 외, 'Grid Generation and Laminar Flow Analysis', 한국항공우주학회지, Vol.22, No.2, pp.2001-2012, 1994
3 송은지, '등각사상에 있어 Theodorsen방정식의 고속해법', 정보처리학회 논문집, 제5권 제2호, pp. 372-379, 1998
4 송은지, 'Hubner 방법에 기초한 수치등각사상의 자동화 알고리즘', 정보처리학회논문집, 제6권 제10호, pp.2716-2722, 1999   과학기술학회마을
5 天野 要, '代用電荷法に基づく方向的な數値等角寫像の方法,' 日本情報處理學會論文集, Vol.31, No.5, pp.623-632, 1990
6 Wegmann, R., 'Discretized versions of Newton type iterative methods for conformal mapping,' J. Comput. Appl. Math., Vol.29, No.2, pp.207-224, 1990   DOI   ScienceOn
7 Gutknecht, M. H., 'Fast Algorithm for the conjugate Periodic Function,' J. Computing, No.22, pp.79-91, 1979   DOI
8 Wegmann, R., 'Convergence proofs and error estimates for an iteration method conformal mapping,' Numer Math., Vol.44, pp.435-461, 1984   DOI
9 Gutknecht, M.H., 'Numerical conformal Mapping Methods Based on Function Conjugation,' J. Comput. Appl. Math., Vol.14, No.1,2, pp.31-77, 1986   DOI   ScienceOn