Asymptotic Homogenization of a Three-Dimensional Organic Photovoltaic Model : Second-Order Correctors and Numerical Implementation in FreeFEM++

Sammanfattning

We study a three-dimensional multiscale model for charge transport in organic photovoltaic devices. The microscopic description is given by a coupled Poisson–drift–diffusion system for the electric potential, excitons, electrons, and holes in a periodically structured donor–acceptor geometry, including interfacial dissociation and recombination. Using formal asymptotic homogenization, effective macroscopic equations are derived together with periodic cell problems that characterize the homogenized transport tensors. In addition to the leading-order asymptotic analysis, second-order correctors are investigated for the electric potential and the particle species. These show that microscale oscillations can be encoded in suitable cell functions, while the macroscopic dependence is carried by the homogenized solution and its derivatives. The homogenized model is implemented numerically in FreeFEM++, where the cell problems, effective tensors, and time-dependent macroscopic system are computed. The results support the analytical derivation and illustrate the usefulness of the homogenization method for effective three-dimensional organic photovoltaic modeling.