Reduced order modeling and parameter identification for coupled nonlinear PDE systems

Abstract

In this work mathematical systems arising from the modeling of lithium ion batteries are investigated. These models are expressed in terms of highly nonlinear and coupled partial differential equations (PDEs) of different types. There are several parameters in the PDE system which are not known a-priori or which cannot be determined experimentally. Hence, efficient numerical algorithms to estimate unknown parameters are needed. For this purpose a parameter identification problem is formulated as a nonlinear least squares problem. To investigate the parameter depending behavior of the nonlinear system output a sensitivity analysis is carried out. By utilizing a subset selection method the relevant parameters for the optimization process are determined. To speed up the optimization algorithms a model reduction approach based on proper orthogonal decomposition (POD) is applied. Different techniques for the realization of the reduced order models and the parameter estimation are discussed. Numerical examples are presented to illustrate the efficiency of the proposed methods.