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Description
In this presentation, I will present results from recent works on the mathematical and numerical analysis of models describing charge transport in perovskite solar cells. The dynamics of charges in these semiconductors can be modeled by parabolic drift-diffusion systems, which have been well studied for several decades in classical devices. However, in the context of perovskite cells, new phenomena must be taken into account: ionic transport with volume exclusion effects, as well as photogeneration. Incorporating these effects makes the models stiffer, multi-scale, and more nonlinear than conventional drift-diffusion systems.
On one hand, I will present the construction, analysis, and implementation of a finite volume numerical scheme for this class of models, and on the other hand, the mathematical analysis of the stationary problem, based on iterative energy estimates in the Stampacchia/De Giorgi style. These results were obtained in collaboration with colleagues from Inria Lille, the University of Bordeaux, and the Weierstrass Institute in Berlin.
