Efficient connection processing in equation–based object–oriented models

MARZORATI, DENISE; FERNÁNDEZ, JOAQUIN; KOFMAN, ERNESTO

APPLIED MATHEMATICS AND COMPUTATION

ELSEVIER SCIENCE INC

Año: 2022 vol. 418

0096-3003

This work introduces a novel methodology for transforming a large set of connections into the corresponding set of equations as required by the flattening stage of the compilation process of object oriented models. The proposed methodology uses a compact representation of the connections in the form of a Set–Based Graph, in which different sets of vertices and different sets of edges are formed exploiting the presence of regular structures. Using this compact representation, a novel algorithm is proposed to find the connected components of the Set–Based Graph. This algorithm, under certain restrictions, has the remarkable property of achieving constant computational costs with respect to the number of vertices and edges contained in each set. That way, under the mentioned restrictions, the proposed methodology can transform a large set of connections into the corresponding set of equations within a time that is independent on the size of the arrays contained in the model. Besides describing the new algorithm and studying its computational cost, the work describes its implementation in a Modelica compiler and shows its application in different examples.