"Relaxing" - A Symbolic Sparse Matrix Method Exploiting the Model Structure
in Generating Efficient Simulation Code
Keywords
- Sparse Matrices
- Symbolic Formulae Manipulation
- Object-Oriented Modeling
- Relaxing
- Tearing
Abstract
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 defines 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.
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Last modified: June 17, 2005 -- © François Cellier