A-posteriori error analysis for lithium-ion concentrations in batteries utilizing the reduced-basis method
2016-07-03, Iapichino, Laura, Volkwein, Stefan, Wesche, Andrea
In this paper, the authors consider a parametrized non-linear parabolic differential equation, which is motivated by lithium-ion battery models. A standard finite volume discretization leads to a high-dimensional discrete non-linear problem so that simulation of the parametrized problem for various different parameters is very costly. Therefore, the reduced-basis method is applied, so that the number of degrees of freedom is reduced significantly and a fast numerical simulation of the model is possible. To control the error, an a-posteriori error estimator is derived. Numerical experiments show the efficiency of the approach.
The reduced basis method applied to transport equations of a lithium-ion battery
2013, Volkwein, Stefan, Wesche, Andrea
Purpose: in this paper, the authors aim to show how to apply the reduced basis method to the transport equations of a lithium-ion battery.
Design/methodology/approach: the authors consider a coupled system of nonlinear parameterized partial differential equations (P2DEs), which models the concentrations and the potentials in lithium-ion batteries.
Findings: the authors develop an efficient reduced basis approach for the fast and robust numerical solution of the P2DE system.
Originality/value: by the reduced basis method, the authors get (reduced) solutions with a speed up factor of up to 18 in the presented examples in comparison to the original finite volume solutions.