Multi-Dimensional Automatic Sampling Schemes for Multi-Point Modeling Methodologies

This paper presents a methodology for optimizing sample point selection in the context of model order reduction (MOR). The procedure iteratively selects samples from a large candidate set in order to identify a projection subspace that accurately captures system behavior. Samples are selected in an efficient and automatic manner based on their relevance measured through an error estimator. Projection vectors are computed only for the best samples according to the given criteria, thus minimizing the number of expensive solves. The scheme makes no prior assumptions on the system behavior, is general, and valid for single and multiple dimensions, with applicability on linear and parameterized MOR methodologies. The proposed approach is integrated into a multi-point MOR algorithm, with automatic sample and order selection based on a transfer function error estimation. Different implementations and improvements are proposed, and a wide range of results on a variety of industrial examples demonstrate the accuracy and robustness of the methodology.