An efficient, scalable numerical algorithm for the simulation of electrochemical systems on irregular domains

We present a projection method for the solution of the diffusive transport and reaction equations of electrochemical systems on irregular time-dependent domains. Specific applications include electrodeposition of copper in sub-micron trenches, as well as any other electrochemical system with an arbitrarily shaped bulk region of dilute electrolyte solution. Our method uses a finite volume spatial discretization that is second-order accurate throughout, including a nonuniform region used as a transition to the far-field chemical concentrations. Time integration is performed with a splitting technique that includes a projection step to solve for the electric potential. The resulting method is first-order accurate in time, and is observed to be stable for relatively large time steps. Furthermore, the algorithm complexity scales very respectably with grid refinement and is naturally parallelizable.