CSE/CSAR Noon Seminar (joint with Chemical & Biomolecular Engineering)
Linda Petzold, University of California - Santa Barbara
DATE: Wednesday, October 2, 2002
TIME: 12:00 Noon
PLACE: 2240 DCL
1304 W. Springfield Ave., Urbana, IL
TITLE: Adaptive Numerical Methods for Sensitivity Analysis of
Differential-Algebraic Equations and Partial Differential Equations
Abstract
Sensitivity analysis of differential-algebraic equation (DAE) systems
generates essential information for design optimization, parameter
estimation, optimal control, model reduction, process sensitivity and
experimental design. Recent work on methods and software for
sensitivity analysis of DAE systems has demonstrated that forward
sensitivities can be computed reliably and efficiently. However, for
problems which require the sensitivities with respect to a large number
of parameters, the forward sensitivity approach is intractable and the
adjoint (reverse) method is advantageous. In this talk we give the
adjoint system for general DAEs and investigate some of its fundamental
analytical and numerical properties. We describe our new adjoint DAE
software and outline some issues which are critical to the
implementation.
Defining the adjoint sensitivity system and writing the appropriate
software to describe it can be a very challenging problem for
large-scale engineering systems, particularly when it comes to finding
appropriate boundary conditions for the adjoint partial differential
equation (PDE) system. Therefore our goal for both DAE and PDE systems
has been the development of methods and software in which generation
and solution of the sensitivity system are transparent to the user.
This has been largely achieved for DAE systems. We will propose a
solution to this problem for PDE systems solved with adaptive mesh
refinement.