Geodesic
Simulation of electrochemical machining using the boundary element method with no saturation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 10, pp. 1810-1820

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The simulation of electrochemical machining (ECM) is based on determining the surface shape at each point in time. The change in the shape of the surface depends on the rate of the electrochemical dissolution of the metal (conducting material), which is assumed to be proportional to the electric field strength on the boundary of the workpiece. The potential of the electric field is a harmonic function outside the two domains–the tool electrode and the workpiece. Constant potentials are specified on the boundaries of the tool electrode and the workpiece. A scheme with no saturation in which the strength of the electric field created by the potential difference on the boundary of the workpiece is proposed. The scheme converges exponentially in the number of grid elements on the workpiece boundary. Given the rate of electrochemical dissolution, the workpiece boundary, which depends on time, is found. The numerical solutions are compared with exact solutions, examples of the ECM simulation are discussed, and the results are compared with those obtained by other numerical methods and the ones obtained using ECM machines. 
@article{ZVMMF_2016_56_10_a11,
     author = {A. G. Petrov and Sh. V. Sanduleanu},
     title = {Simulation of electrochemical machining using the boundary element method with no saturation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1810--1820},
     publisher = {mathdoc},
     volume = {56},
     number = {10},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_10_a11/}
}
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A. G. Petrov; Sh. V. Sanduleanu. Simulation of electrochemical machining using the boundary element method with no saturation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 10, pp. 1810-1820. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_10_a11/