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On a Non‐symmetric Problem in Electrochemical Machining
Author(s) -
Wegert Elias,
Oestreich Dieter
Publication year - 1997
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/(sici)1099-1476(19970710)20:10<841::aid-mma886>3.0.co;2-l
Subject(s) - mathematics , riemann–hilbert problem , conformal map , uniqueness , holomorphic function , boundary value problem , gravitational singularity , unit disk , mathematical analysis , computation , boundary (topology) , riemann problem , riemann hypothesis , algorithm
We consider a free boundary value problem arising from a non‐symmetric problem of electrochemical machining (ECM). After a conformal mapping of the unknown domain the problem is transformed to a non‐smooth non‐linear Riemann–Hilbert problem for holomorphic functions in the complex unit disk. A special technique allows to remove the singularities in the boundary condition. Utilizing existence results for smooth non‐orientable Riemann–Hilbert problems, existence and uniqueness of a solution are shown. Finally, we propose an iterative method of Newton type for the effective numerical computation of the free boundary of the anode and present some test results. © 1997 B. G. Teubner Stuttgart–John Wiley & Sons Ltd.