Computational aspects of cyclic voltammetry simulation for the case of porous electrodes of fractal structure
Abstract
Considering the simulation of cyclic voltammetry response in the case of porous electrodes that exhibit fractal properties, we propose a numerical technique to solve parameters' identification problem for the corresponding fractional differential model and study the properties of its implementations in multi-threaded and GPU environments. The one-dimensional model consists of a space-fractional differential equation that describes diffusion and electrochemical reaction processes in a porous electrode and an integer-order diffusion equation for modeling solute transport towards an electrode.
Using the L1-approximation of the Caputo derivative, we solve the problem by a finite-difference scheme on a non-uniform grid. Several variants of the particle swarm optimization (PSO) algorithm are applied to reconstruct the values of structural parameters of an electrode & mdash;its thickness, roughness, and fractional derivative's order.
Taking into account significantly different solution time for direct problems when the values of parameters vary, we consider an asynchronous and memetic variants of PSO. Testing was performed reconstructing parameters' values based on the noised solution of the direct problem.
Testing results show that memetic PSO algorithm is characterized by the most stable convergence while asynchronous versions of PSO allow the most even loading of CPU cores. Involvement of GPU in the computation process yields its acceleration only on grids with more than 1600 nodes allowing up to 10% performance gain.
Successful testing of the developed technique shows its ability to be used for the analysis of real-world observations and for the prediction of the corresponding processes' dynamics.