Benchmarking the Modular Structural Analysis Algorithm

In a 2023 Modelica Conference paper, we proposed a novelmethod for the modular structural analysis of DAE systems,in which the structural analysis is not performed onflattened models, but rather at the class level. A newnotion of structural interface was proposed, in whichclasses are enriched with context information. That paperdeveloped our approach based on a few illustrative examples.In this paper, we provide the details of our algorithm. Itsperformance depends on the system architecture: theanalysis of models having a small number of classes (possi-bly instantiated many times), with a low treewidth systemarchitecture, scales up very efficiently with thisapproach. We then present additional benchmarks, amongwhich a urban heating network, a representative real-lifeexample on which a near-logarithmic scaling up is shown.