Dr. Dagmar Monett Díaz

Mathematical Optimization Dept.
Institute of Mathematics
Humboldt University of Berlin
Unter den Linden 6, 10099 Berlin
Germany
Phone: +49 (0)30 2093 4554
Fax: +49 (0)30 2093 5859
Email: monett [at] math.hu-berlin.de

Visits:
  Rudower Chaussee 25, 2nd building, 4th floor, room 412
  12489 Berlin (Berlin-Adlershof)

Project: Analysis and treatment of DAEs using Automatic Differentiation

Heads:

   Prof. Dr. Andreas Griewank
   Prof. Dr. Caren Tischendorf

Members:

   Dr. René Lamour
   Dr. Dagmar Monett Díaz

Short description:

Analysis and treatment of DAEs, for example, index determination for DAEs, using AD techniques.

Funding:

   Max-Planck Research Prize 2001 from Prof. Griewank (Jan. 2006 - Sep. 2006)

Background and Research Goals:

   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 (see also [1]) 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.

Literature:

   [1] Berz, M. et al.: Computational Differentiation: Techniques, Applications, and Tools. In Proceedings of the Second International Workshop on Computational Differentiation, Santa Fe, New Mexico, SIAM, 1996.

   [2] Griewank, A.: Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. In Frontiers in Applied Mathematics Nr. 19, SIAM, Philadelphia, PA, 2000.

   [3] Lamour, A.: Index Determination and Calculation of Consistent Initial Values for DAEs. Computers and Mathematics with Applications 50, 1125-1140, Elsevier, 2005.

   [4] März, R.: The index of linear differential algebraic equations with properly stated leading terms. Result. Math. 42, 308-338, Birkhäuser Verlag, Basel, 2002.

   [5] März, R.: Differential Algebraic Systems with Properly Stated Leading Term and MNA Equations. In K. Antreich, R. Bulirsch, A. Gilg, and P. Rentrop (eds.): Modeling, Simulation and Optimization of Integrated Circuits, International Series of Numerical Mathematics, Vol. 146, 135-151, Birkhäuser Verlag, Basel, 2003.

   [6] März, R.: Fine decoupling of regular differential algebraic equations. Result. Math. 46, 57-72, Birkhäuser Verlag, Basel, 2004.

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Last update: Jan.18.2006
Comments to: monett [at] math.hu-berlin.de