An AD Technique for Computing Approximations to the Continuous Sensitivity Equation
by
Jeff Borggaard
Department of Mathematics, Virginia Tech, Blacksburg, VA, USA
Coauthors: Arun Verma (Cornell University)

Approaches for computing the sensitivity of PDE solutions to problem parameters can be loosely broken into two categories. One is the continuous approach, where the continuous sensitivity equation (CSE) is first derived from the PDE and is then approximated. The second, the so-called discrete approach, differentiates the approximation algorithm to arrive at an algorithm for the sensitivities. Although these two approaches are equivalent in many cases, there are many important cases where they are not, for example, when a parameter influences the shape of the domain. In these situations, it is usually more computationally advantageous to choose one approach over the other. While the discrete approach can be implemented by the ``straight-forward'' application of AD, the continuous approach is usually implemented manually. Although many portions of the PDE approximation algorithm can be reused in the implementation, this can be a cumbersome process. In this talk, we outline a technique that uses AD to implement the continuous approach. A new parameter is introduced to modify the original PDE (through the boundary conditions and forcing functions) so that when AD is applied to the modified algorithm, an approximation to the CSE results. Numerical experiments demonstrate up to twenty-five percent savings in total CPU time or a ten-fold decrease in memory requirements over the standard discrete approach.

Jeff Borggaard

Date received: December 30, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cads-36.