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Construction of conformal mappings by generalized polarization tensors
Author(s) -
Kang Hyeonbae,
Lee Hyundae,
Lim Mikyoung
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3195
Subject(s) - conformal map , mathematics , riemann hypothesis , mathematical analysis , polarization (electrochemistry) , domain (mathematical analysis) , riemann problem , unit disk , pure mathematics , chemistry
We present a new systematic method to compute the Riemann mapping from the outside of the unit disc to the outside of a simply connected domain. We derive explicit relations between the coefficients of the Riemann mapping and the generalized polarization tensors associated with the domain. Because the generalized polarization tensors can be computed numerically, we are able to compute the coefficients of the Riemann mapping using these relations. Effectiveness of the method is validated by numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.