Adaptive methods for MOR in non-linear FE simulations of unit cells

In this contribution, an adaptive method for Model Order Reduction (MOR) is presented for simulating physically non-linear material behavior of micro-heterogeneous structures. The method is purely online and includes a Galerkin projection, which is performed using a projection operator initially gained by a Proper Orthogonal Decomposition (POD). By this projection, the number of degrees of freedom to solve for is decreased drastically and can be projected back to the vector space of the high fidelity problem after the solution process. The composition of the projection operator follows an adaptive algorithm, which evaluates an update of the operator if convergence is not ensured during the Newton Raphson scheme. Later on, during the simulation, the number of degrees of freedom to solve is controlled using a POD-based control criterion for sorting out non-relevant basis vectors from previous updates. This results in an efficient method and leads to a satisfying speedup of the simulation process. The performance and efficiency of the presented adaptive MOR scheme is investigated in numerical simulations of a hexagon-shaped unit cell.