An Implicit-Explicit Local Discontinuous Galerkin Scheme for Analysis of Organic Electrochemical Transistors

In this paper, an implicit-explicit (IMEX) local discontinuous Galerkin (LDG) method is proposed to analyze the organic electrochemical transistors (OECTs). The LDG method is used to spatially discretize the coupled system of Poisson and drift-diffusion (DD) equations. For the time integration, the IMEX scheme uses implicit and explicit methods for the linear diffusion and the nonlinearly coupled drift terms, respectively. This results in a time marching scheme where the time-step size is upper-bounded by a positive constant but can be selected independently from spatial mesh size. Numerical results demonstrate that the proposed IMEX-LDG scheme allows for a significantly larger time-step size than its fully-explicit counterpart, and therefore much faster in simulation of OECTs.