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On a Non-symmetric Problem in Electrochemical Machining

✍ Scribed by Elias Wegert; Dieter Oestreich

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
513 KB
Volume
20
Category
Article
ISSN
0170-4214

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✦ Synopsis

Communicated by W. Spro´ßig

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.

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