A fast, robust, and low-error method is described for the simulation of transient diffusion in electrochemical systems, particularly those featuring complex, high surface area geometries in one, two, or three dimensions—like porous electrode structures used in electrocatalysis. Our approach reformulates the discrete solution of Fick’s laws by approximating the propagation matrix with a Gaussian convolution kernel. This methodology leverages the known spectral decomposition of symmetric tridiagonal matrices, significantly reducing computational cost compared to traditional methods that rely on large-scale matrix inversion or exponentiation. Furthermore, this method is highly amenable to parallelization and GPU acceleration. We detail the implementation of various electrochemical boundary conditions, including diffusion control and mixed kinetic-diffusion control, demonstrating the potential of the method as a fast, user-friendly, and powerful tool for electrochemical simulations. • Simulation of diffusion in complex geometries can be computationally expensive. • Application of Gaussian convolutional kernel accelerates diffusion calculations. • Different boundary conditions can be handled in combination with convolution. • Using graphical processing units accelerates convolution calculations.
Szakály et al. (Mon,) studied this question.