Passivity-Preserving Parameterized Model Order Reduction Using Singular Values and Matrix Interpolation

Abstract

We present a parameterized model order reduction method based on singular values and matrix interpolation. First, a fast technique using grammians is utilized to estimate the reduced order, and then common projection matrices are used to build parameterized reduced order models (ROMs). The design space is divided into cells, and a Krylov subspace is computed for each cell vertex model. The truncation of the singular values of the merged Krylov subspaces from the models located at the vertices of each cell yields a common projection matrix per design space cell. Finally, the reduced system matrices are interpolated using positive interpolation schemes to obtain a guaranteed passive parameterized ROM. Pertinent numerical results validate the proposed technique.