Regularized Local Multivariate Reduced-Order Models With Nonaffine Parameter Dependence

This paper addresses a singular problem, not yet discussed in the literature, which occurs when parametric reduced-order models are created using a subspace projection approach with multiple concatenated projection bases. We show that this technique may lead to the appearance of localized artifacts in the frequency characteristics of a system, even when the reduced-order projection basis is rich enough to describe the original system. These artifacts are found to be related to nonphysical poles of the transfer function that emerge whenever more than one projection basis is used, each spanning is a similar space, and these bases are directly put together to build multivariate reduced-order models. These unwanted poles are identified using the Bauer-Fike theorem and then the parametrized reduced-order model is regularized with a simple deflation procedure that completely removes the artifacts due to nonphysical resonances from the circuit characteristics. Finally, real-life numerical examples illustrate the accuracy and abilities of the proposed approach.