Geometric optimization of a lithium-ion battery with the Doyle–Fuller–Newman model

This paper studies the geometric optimization of the separator in a lithium-ion battery, following the Doyle–Fuller–Newman model. For a general objective function, we compute its derivative with respect to the interface position by means of the adjoint method. Our main numerical application is the maximization of the total electric energy during a discharge. Both cases of a fixed final time and a final time depending on the state of charge are examined. Our 2-d numerical implementation is performed in the finite element software FreeFEM with body-fitted meshes. Our main practical conclusion is that optimization over shorter time periods yields more interdigitated designs.