Block structure preserving model order reduction

We propose a block structure preserving model reduction (BSMOR), which generalizes the structure preserving model order reduction (SPRIM). The blocks can be derived based on specific applications such as block current characterization of the substrate. Increasing block numbers leads to more matched poles or moments using the same Krylov space and also increases the sparse ratio of the state matrices of the resulting macro-model. Experiment shows that BSMOR has a 20X smaller reduction time than PRIMA does under a same error bound. To efficiently analyze the resulting macro-model with a large number of ports, we further propose a bordered-block diagonal (BBD) partitioning with a bottom-up hierarchical clustering (BBDC) where the macro-model is partitioned into a number of subset-port models, each with a manageable model size. With a similar accuracy, BBDC obtains 30X speedup compared to the original macro-model.