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A systematic procedure for generating useful conformal mappings
Author(s) -
Caughey D. A.
Publication year - 1978
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620121103
Subject(s) - conformal map , transformation (genetics) , variety (cybernetics) , class (philosophy) , ordinate , domain (mathematical analysis) , simple (philosophy) , mathematics , christoffel symbols , geometry , algebra over a field , mathematical analysis , pure mathematics , computer science , artificial intelligence , biochemistry , chemistry , statistics , philosophy , epistemology , gene
A Procedure is presented for generating a class of conformal mappings useful in the formulation of finite−difference problems involving curved boundaries. The method provides a systematic approach that is capable, in principle, of reducing the geometry to a nearly−rectangular domain for a wide variety of partical problems. The introduction of sheared co−ordinates in this computational domain then provides for solution of the problem in a nearly−orthogonal (in fact, nearly−conformal) co−ordinate system, with its boundaries corresponding to co−ordinate lines. The method is based upon the Schwarz−Christoffel transformation and is quite simple to apply. Several examples illustrating the types of geometries which can be treated in this manner are presented.