Index reduction for differential-algebraic equations in circuit simulation

Source file is available as :   Postscript Document
Portable Document Format (PDF)

Author(s) : Simone Bächle

Preprint series : Matheon - DFG Research Center

MSC 2000

65L80 Methods for differential-algebraic equations
94C05 Analytic circuit theory

Abstract :
Transient analysis in industrial chip design leads to very large systems of differential-algebraic equations (DAEs). The numerical solution of these DAEs strongly depends on the so called index of the DAE. In general, the higher the index of the DAE is, the more sensitive the numerical solution will be to errors in the computation. So, it is advisable to use mathematical models with small index or to reduce the index. This paper presents an index reduction method that uses information based on the topology of the circuit. In addition, we show that the presented method retains structural properties of the DAE.

Keywords : differential-algebraic equations, index reduction, circuit simulation