Faster Structural Analysis of Differential-Algebraic Equations by Graph Compression★ ★

Structural Analysis of Differential Algebraic Equations is a computationally expensive task, because it relies on the solution of a highest value assignment in the bipartite structure graph of the model. Therefore the size of models that can be simulated is limited in practice by the runtime of the index reduction method. We present a technique to optimize the analysis by leveraging structural properties of hierarchical models: If a sub-component contains one more equation than protected variables, its protected variables may be removed from the structure graph by a compression transformation, thus reducing its size. A corresponding decompression operation allows to compute a highest-value assignment for the original graph from the compressed one. This can lead to drastically reduced runtime for the structural analysis of large models.