\relaxing" | a Symbolic Sparse Matrix Method Exploiting the Model Structure in Generating Eecient Simulation Code

This paper presents a new method for symbolically solving large sets of algebraically coupled equations as they are frequently encountered in the formulation of mathematical models of physical systems in object{ oriented modeling. The method, called \relaxing," enables the modeler to exploit the special matrix structure of the type of system under study by simply placing the keyword relax at appropriate places in the model class libraries. This procedure deenes an evaluation sequence for a sparse matrix Gaussian elimination scheme. The method is demonstrated at hand of several broad classes of physical systems: drive trains, electrical circuits, and tree{structured multibody systems. In particular, relaxing allows a model compiler, such as Dymola, to start from a declarative, object{ oriented description of the model, and to automatically derive the recursive O(f) algorithm used in modern multibody programs.