The second approach employs free-moving boundary condition (FM-BC) at the cathode edge and reflecting boundary condition (R-BC) for the anode and putting the constant current source (CCS) into the operation from the beginning of the simulation experiments rather then waiting for the end of the complete cathode failure by the shrinkage of the contact area.
Physically this can be realized if the underlayer of high resistance material
(Ta, TiN and TiAl3) is acting as a shunt,
similar to Blech’s experiments (1975).
This procedure requires modification of the Neuman bounday conditions.
Usual Neumann BC:
The induced (virtual) electric field intensity at the sidewalls counter act against to the normal component of the external field at
Modified Neumann BC:
The part of the cathode end bounded by the
original sidewalls of the specimen, and the
whole anode edge have zero virtual electric
field intensity distribution.