Model order reduction of large-scale dynamical systems with Jacobi-Davidson style eigensolvers

Many applications concerning physical and technical processes employ dynamical systems for simulation purposes. The increasing demand for a more accurate and detailed description of realistic phenomena leads to high dimensional dynamical systems and hence, simulation often yields an increased computational effort. An approximation, e.g. with model order reduction techniques, of these large-scale systems becomes therefore crucial for a cost efficient simulation. This paper focuses on a model order reduction method for linear time in-variant (LTI) systems based on modal approximation via dominant poles. There, the original large-scale LTI system is projected onto the left and right eigenspaces corresponding to a specific subset of the eigenvalues of the system matrices, namely the dominant poles of the system's transfer function. Since these dominant poles can lie anywhere in the spectrum, specialized eigenvalue algorithms that can compute eigentriplets of large and sparse matrices are required. The Jacobi-Davidson method has proven to be a suitable and competitive candidate for the solution of various eigenvalue problems and hence, we discuss how it can be incorporated into this modal truncation approach. Generalizations of the reduction technique and the application of the algorithms to second-order systems are also investigated. The computed reduced order models obtained with this modal approximation can be combined with the ones constructed with Krylov subspace or balanced truncation based model order reduction methods to get even higher accuracies.