Fast geometric parameter sweep of FEM models via a nonlinear BT-POD model reduction

A finite element method (FEM) model-order reduction (MOR) methodology for the fast parametric sweep of geometrical features is presented. The proposed method first linearizes the otherwise non-linear FEM matrix dependence with respect to the geometry variation, and then uses a uniformly sampled balanced truncation proper orthogonal decomposition (BT-POD) reduction algorithm to expediently sweep over the parametric geometry space. The approach avoids slow re-meshing and full matrix reassembly by using mesh morphing approaches. Moreover, BT-POD is known to provide close to optimal size reduced problems using only a small number of samples, thus minimizing the the number of full-model solutions. Numerical results on two large-scale filter design examples are used to study the accuracy and efficiency of the proposed method.