Inline Integration: A New Mixed Symbolic/Numeric Approach
for Solving Differential-Algebraic Equation Systems
Keywords
- Inline Integration
- Tearing Structure
- Symbolic Formulae Manipulation
- Differential-Algebraic Equation Solving
- Simulation Efficiency
Abstract
This paper presents a new method for solving differential-algebraic equation
systems using a mixed symbolic and numeric approach. Discretization formulae
representing the numerical integration algorithm are symbolically inserted into
the differential-algebraic equation model. The symbolic formulae manipulation
algorithm of the model translator treats these additional equations in the same
way as it treats the physical equations of the model itself, i.e., it looks at
the augmented set of algebraically coupled equations and generates optimized
code to be used with the underlying simulation run-time system. For implicit
integration methods, a large nonlinear system of equations needs to be solved
at every time step. It is shown that the presented uniform treatment of model
equations and discretization formulae often leads to a significant reduction of
the number of iteration variables and therefore to a substantial increase in
execution speed.
In a large mechatronics system consisting of a six degree-of-freedom robot
together with its motors, drive trains, and control systems, this approach led
to a speedup factor of more than ten.
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Last modified: June 17, 2005 -- © François Cellier