  The amorphous propagation of microstructures during the electrochemical
charging of a battery is the main reason for the capacity decay and short
circuit. The charge distribution across the micro-structure is the result of
both local and global equilibrium and is non-convex problem merely due to
stochastic placement of the atoms. As such, obtaining the charge equilibrium
(QEq) is a critical factor, since the amount of charge determines the success
rate of the bond formation for the ionic species approaching the microstructure
and consequently the ultimate morphology of the electrochemical deposits.
Herein we develop a computationally-affordable method for determining the
charge allocation within such microstructures. The cost function and the span
of the charge distribution correlates very closely with the trivial method as
well as a conventional method, albeit having significantly less computational
cost. The method can be used for optimization in non-convex environments,
specially those of stochastic nature.
