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Computational Methods for Sensitivity Analysis with Applications to Elliptic Boundary Value Problems
Sensitivity analysis is a useful mathematical tool for many designers,
engineers and mathematicians. This work presents a study of
sensitivity equation methods for elliptic boundary value problems
posed on parameter dependent domains.
The current focus of our efforts is the construction of a
rigorous mathematical framework for sensitivity analysis and the
subsequent development of efficient, accurate algorithms for
In order to construct the framework, we use the classical
theory of partial differential equations along with the method of
mappings and the Implicit Function Theorem. Examples are given which
illustrate the use of the framework, and some of the shortcomings of
the theory are also identified. An overview of some computational
methods which make use of the method of mappings is also included.
Numerical results for a specific example show that convergence (energy norm)
of the sensitivity
approximations can be influenced by the specific structure of the