Time-Galerkin integrators for the dynamic simulation of local reduced order models

Over the past decades, model order reduction (MOR) techniques have aided in the e cient description of many highly computationally demanding models. One of the basic requirements for most developed approaches, is that the response of a model can be well captured by a smaller (fewer variables, less nonlinear equation evaluations, . . . ) model. However, some systems exhibit such strong nonlinearities or are excited over such a wide range, that one such model cannot be constructed. In these cases regular MOR methods cannot create a su ciently small model to obtain the required size reduction. Local reduced order models (LROM) can o er a solution when traditional MOR techniques are not su cient [1, 2]. In this approach a series of LROMs are constructed where each one provides good accuracy only over a subregion of the system behavior. During the online evaluation the most suitable LROM for a certain subregion is selected and evaluated. However, in a dynamic context, many jumps from one LROM to the other can occur. These changes are generally nontrivial and have to be handled properly in order to avoid parasitic dynamic e ects. This is especially problematic for systems which naturally exhibit a strongly energy conserving behavior, like (nonlinear) elastodynamic systems. In this work we propose a time-Galerkin integrator which enables a highly exible choice in how the LROMs of (nonlinear) elastodynamic problems are handled while providing a guarantee of energy conserving behavior, even over sudden model changes. Due to the common time-points between two timeslabs, the time-Galerkin is perfectly suitable to perform model changes online. The proposed approach is demonstrated on both linear and nonlinear examples. Through these examples, good convergence and stability are demonstrated.