DFG-Research Centre "Mathematics for key technologies - MATHEON": Numerical simulation of integrated circuits for future chip generations (TP D 7)

The analysis and treatment of systems of differential algebraic equations (DAEs) may involve high order derivatives, as it is the case in much practical problems. Solving such DAEs, for example, may be very difficult numerically but also of high complexity. Most solving methods for ordinary differential equations (ODEs) are not practicable anymore for such systems; new techniques should be considered indeed.

Algorithmic, or automatic, differentiation (AD) is concerned with the accurate and efficient evaluation of derivatives for functions defined by computer programs. AD is quite useful for analyzing and numerically solving DAEs. This is why it is to become an important component of general-purpose analysis and integration schemes in the future. The analysis and treatment of systems of differential algebraic equations (DAEs) may involve high order derivatives, as it is the case in much practical problems. Solving such DAEs, for example, may be very difficult numerically but also of high complexity. Most solving methods for ordinary differential equations (ODEs) are not practicable anymore for such systems; new techniques should be considered indeed.

Algorithmic, or automatic, differentiation (AD) is concerned with the accurate and efficient evaluation of derivatives for functions defined by computer programs [2]. AD is quite useful for analyzing and numerically solving DAEs. This is why it is to become an important component of general-purpose analysis and integration schemes in the future.

Our main research goal is to contribute to the use of AD in the theoretical analysis and numerical solution of DAEs. For example, we want to develop and implement an algorithm for the determination of the index in DAEs. Similarly to [3], we consider DAEs as presented in [4, 5, 6]: DAEs with properly stated leading terms. The calculation of the index of these systems is based on a matrix sequence with suitable chosen projectors [3]. We expect to permorm all needed differentiations by using AD.

Our main research goal is to contribute to the use of AD in the theoretical analysis and numerical solution of DAEs. For example, we want to develop and implement an algorithm for the determination of the index in DAEs. We consider DAEs with properly stated leading terms. The calculation of the index of these systems is based on a matrix sequence with suitable chosen projectors]. We expect to permorm all needed differentiations by using AD.

Financer

Duration of project

Start date: 06/2002

End date: 12/2007