The Application of the Combinatorial Relaxation Theory on the Structural Index Reduction of DAE

Multi-domain unified modeling is an important development direction in the study of complex system. Modelica is a popular multi-modeling language. It describes complex systems by mathematical equations, solves the high-index of Differential algebraic equations (DAE) generated by modeling. But in this process, the index reduction based on structural index, which is a key step of solving high-index DAE, will fail with small probability. Based on the combinatorial optimization theory, it analyzes the incorrect problem leaded by the index reduction algorithm for solving the DAE, gives the algorithm of detecting and correcting the incorrect of structural index reduction for matrix pencils. It implements the algorithm of detecting and correcting, and apply the algorithm into solving first-order linear time-invariant DAE system. The experiment result shows that for first-order linear time-invariant DAE, the problem about the failure of structural index reduction can be solved by the combinatorial optimization theory.