Analysis and Implementation for the Algorithm Based on Combinatorial Relaxation for Computing the Structure Index of DAE

Abstract

AbstractAs the society industrialized, mathematical modeling and simulation become increasingly important in the product design. At present, the multi-domain unified modeling with Modelica is a mainstream technology in the field of complex systems. Modeling of complex physical systems with Modelica often produces a high-index differential algebraic equation (DAE) system. It needs to be transformed to low-index DAE before solving it. The structure index reduction algorithm is one of the popular index reduction methods. But in some special circumstances, its solution may be incorrect. At present, combinatorial relaxation algorithm is a widely used method for solving the problem. Solving maximum weighted matching is one of important problems of the combinatorial relaxation algorithm. This paper describes the combinatorial relaxation algorithm and proposes three different implementations of Hungarian algorithm for the maximum weighted matching problem. The theory results are consistent with the experiment results,KeywordsModelicaDAECombinatorial RelaxationHungarian algorithm