In this contribution, we present a modelling and simulation framework for parametrised lithium-ion battery cells. We first derive a continuum model for a rather general intercalation battery cell on the basis of non-equilibrium thermodynamics. In order to efficiently evaluate the resulting parameterised non-linear system of partial differential equations, the reduced basis method is employed. The reduced basis method is a model order reduction technique on the basis of an incremental hierarchical approximate proper orthogonal decomposition approach and empirical operator interpolation. The modelling framework is particularly well suited to investigate and quantify degradation effects of battery cells. Several numerical experiments are given to demonstrate the scope and efficiency of the modelling framework.

We consider using a discrete network model in combination with continuous nonlinear optimization models to solve the problem of optimizing channels in nanoporous materials. The problem and the hierarchical optimization algorithm are described in [2]. A key feature of the model is the fact that we use the edges of the finite element grid as the locations of the channels. The focus here is on the use of the discrete model within that algorithm. We develop several approximations to the relevant flow and a greedy algorithm for quickly generating a “good” tree connecting all of the nodes in the finite-element mesh to a designated root node. We also consider Metropolis-Hastings (MH) improvements to the greedy result. We consider both a regular triangulation and a Delaunay triangulation of the region, and present some numerical results.

We present an efficient computational procedure for the solution of bang–bang optimal control problems. The method is based on a well-known adaptive control parametrization method, which is one of the direct methods for numerical solution of optimal control problems. First, the adaptive control parametrization method is reviewed and then its advantages and disadvantages are illustrated. In order to resolve the need for a priori knowledge about the structure of optimal control and for resolving the sensitivity to an initial guess, a homotopy continuation technique is combined with the adaptive control parametrization method. The present combined method does not require any assumptions on the control structure and the number of switching points. In addition, the switching points are captured accurately; also, efficiency of the method is reported through illustrative examples.