AN EMBEDDING METHOD FOR THE NUMERICAL-SOLUTION OF THE CATHODE DESIGN PROBLEM IN ELECTROCHEMICAL MACHINING

An embedding method is considered for the numerical determination of the cathode shape for a given anode shape in a two‐dimensional electrolytic cell. Reference is made to an analytic solution to illustrate the difficulties which have to be overcome by any numerical method applied to this ill‐posed problem. The embedding method searches amongst the direct solutions (i.e. anodes for given cathodes) since these, resulting from a well‐posed problem, are less troublesome to compute. For anodes of the form βG(x), x the transverse direction, the embedding method gives good results for β less than 30–60 percent of the β for which the cathode first contains cusps or becomes triple‐valued. It is shown that the embedding method performs better than some other numerical methods in overcoming the error growth difficulties associated with the illposedness of the problem. Copyright © 1990 John Wiley & Sons, Ltd