Stable reduced order modeling of piezoelectric energy harvesting modules using implicit Schur complement

In this work, we present an improved technique for reduced order modeling of a micro-machined piezoelectric energy harvester, presented in Kudryavtsev et al. (2015), and a novel frequency-tunable piezoelectric energy harvester with segmented electrodes for improved power generation. A computationally efficient implicit Schur complement is developed for better conditioning of the numerical models. In combination with Krylov subspace-based model order reduction methods, it offers an efficient way to generate guaranteed stable reduced order models of multi-physical device models. We demonstrate an excellent match between the full-scale and the reduced order models of the harvester devices, and establish a new methodology for system-level simulation based on these reduced order numerical models.