Mathmod 2018 Extended Abstracts

Implicit Schur Complement for Model Order Reduction of Second Order Piezoelectric Energy Harvester Model

MATHMOD 2018 Extended Abstract Volume​, ARGESIM Report 55 (ISBN 978-3-901608-91-9), p 77-78, DOI: 10.11128/arep.55.a55255


As energy efficiency becomes increasingly important in everyday life, different energy harvesting systems are being developed to recycle the energy wasted in the surrounding. In this work, we have introduced an energy harvester which transfroms vibrations into electrical energy, using the piezoelectric effect. The direct application of one-sided Krylov-subspace-based model order reduction (MOR) to the harvester model may lead to unstable reduced models. A suggested a approach called `MOR after Schur' enables obtaining stable reduced models, when a Schur complement transformation was performed before MOR. However, a Schur complement transformation increases the number of non-zero entries in the stiffness matrix and therefore the computational effort. In this work, we consider an alternative approach for efficient one-sided reduction of the second-order piezoelectric energy harvester model, and establish an implicit Schur complement transformation.