Set-based graph methods for fast equation sorting in large DAE systems

Abstract

This paper introduces new algorithms for the efficient conversion of large sets of DAEs into ODEs based on the extension of maximum matching and Tarjan's strongly connected component algorithms using a novel concept of Set-Based Graph. These algorithms have the capability of solving the problems without expanding the arrays of unknowns and without unrolling the for-loop equations so that the complexity becomes independent on the size of the arrays. The implementation of the new algorithms in an experimental Modelica compiler is also described and two examples are presented.