We demonstrate how the structure that arises in inverse and optimal design problems can be used to aid in the efficient application of automatic differentiation ideas. We discuss the program structure of generic inverse problems and then illustrate, with two examples (one example involves the heat equation, the other involves wave propagation) how structure can be used in combination with automatic differentiation. Finally, we report numerical results and describe the ADMIT-2 software package which enables efficient derivative computation of structured problems.
KeywordsInverse Problem Heat Equation Extended Function Automatic Differentiation Newton Step
Unable to display preview. Download preview PDF.
- T. F. Coleman and A. Verma. Structure and efficient Hessian calculation, Tech. Report TR96–258, Cornell Theory Center, Cornell University, September 1996.Google Scholar
- T. F. Coleman and A. Verma. Structure and efficient Jacobian calculation, in Computational Differentiation: Techniques, Applications, and Tools, M. Berz, C. Bischof, G. Corliss, and A. Griewank, eds., SIAM, Philadelphia, Penn., 149–159, 1996.Google Scholar
- T. E. Coleman and A. Verma. The efficient computation of sparse Jacobian matrices using automatic differentiation, SISC, (1997 (to appear)).Google Scholar
- N. Zabaras, S. Mukherjee and O. Richmond. An analysis of inverse heat transfer problems with phase changes using an integral method, Transactions of American Society of Mechanical Engineers (ASME), 110:554–561, 1988.Google Scholar