Michael Anderson, Wolfgang
Bangerth, Graham F. Carey
Analysis of parameter sensitivity and
experimental design for a class of nonlinear partial
differential equations
International Journal for Numerical Methods
in Fluids, vol. 48 (2005), pp. 583-605.
The purpose of this work is to analyze the parameter sensitivity problem for
a class of nonlinear elliptic partial differential equations, and to show
how numerical simulations can help to optimize experiments for the
estimation of parameters in such equations. As a representative example we
consider the Laplace-Young problem describing the free surface
between two fluids in contact with the walls of a bounded domain, with the
parameters being those associated with surface tension and contact. We
investigate the sensitivity of the solution and associated functionals to
the parameters, examining in particular under what conditions the solution
is sensitive to parameter choice. From this, the important
practical question of how to optimally design experiments is discussed;
i.e., how to choose the shape of the domain and the type of measurements to
be performed, such that a subsequent inversion of the measured data for the
model parameters yields maximal accuracy in the parameters. We investigate
this through numerical studies of the behavior of the eigenvalues of the
sensitivity matrix and their relation to experimental design. These studies
show that the accuracy with which parameters can be identified from given
measurements can be improved significantly by
numerical experiments.
Wolfgang Bangerth
Sat Apr 20 09:13:53 MDT 2024