Adjoint Sensitivity Analysis for Differential-Algebraic Equations: The Adjoint DAE System and Its Numerical Solution
Abstract
An adjoint sensitivity method is presented for parameter-dependent differential-algebraic equation systems (DAEs). The adjoint system is derived, along with conditions for its consistent initialization, for DAEs of index up to two (Hessenberg). For stable linear DAEs, stability of the adjoint system (for semi-explicit DAEs) or of an augmented adjoint system (for fully implicit DAEs) is shown. In addition, it is shown for these systems that numerical stability is maintained for the adjoint system or for the augmented adjoint system.
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References
1.
Uri Ascher, Linda Petzold, Stability of computational methods for constrained dynamics systems, SIAM J. Sci. Comput., 14 (1993), 95–120
2.
Uri Ascher, Linda Petzold, Computer methods for ordinary differential equations and differential‐algebraic equations, Society for Industrial and Applied Mathematics (SIAM), 1998xviii+314
3.
K. Balla, Linear subspaces for linear DAEs of index 1, Comput. Math. Appl., 31 (1996), 81–86, Selected topics in numerical methods (Miskolc, 1994)
4.
K. Balla, Boundary conditions and their transfer for differential‐algebraic equations of index 1, Comput. Math. Appl., 31 (1996), 1–5
5.
Katalin Balla, Roswitha März, Transfer of boundary conditions for DAEs of index 1, SIAM J. Numer. Anal., 33 (1996), 2318–2332
6.
K. Balla and R. März, An Unified Approach to Linear Differential Algebraic Equations and Their Adjoint Equations, Institute of Mathematics Technical report, Humboldt University, Berlin, 2000.
7.
Katalin Balla, Roswitha März, Linear differential algebraic equations of index 1 and their adjoint equations, Results Math., 37 (2000), 13–35
8.
C. Bischof, A. Carle, G. Corliss, A. Griewank, and P. Hovland, ADIFOR ‐ Generating derivative codes from Fortran programs, Scientific Programming, 1 (1992), pp. 11–29.
9.
K. Brenan, S. Campbell, L. Petzold, Numerical solution of initial‐value problems in differential‐algebraic equations, Classics in Applied Mathematics, Vol. 14, Society for Industrial and Applied Mathematics (SIAM), 1996x+256, Revised and corrected reprint of the 1989 original
10.
Peter Brown, Alan Hindmarsh, Linda Petzold, Using Krylov methods in the solution of large‐scale differential‐algebraic systems, SIAM J. Sci. Comput., 15 (1994), 1467–1488
11.
Stephen Campbell, Nancy Nichols, William Terrell, Duality, observability, and controllability for linear time‐varying descriptor systems, Circuits Systems Signal Process., 10 (1991), 455–470
12.
Y. Cao, S. Li, and L. R. Petzold, Adjoint sensitivity analysis for differential‐algebraic equations: Algorithms and software, J. Comput. Appl. Math., to appear.
13.
Luca Dieci, Timo Eirola, On smooth decompositions of matrices, SIAM J. Matrix Anal. Appl., 20 (1999), 800–819
14.
R. M. Errico, What is an adjoint model?, Bulletin of the American Meteorological Society, 78 (1997), pp. 2577–2591.
15.
William Feehery, John Tolsma, Paul Barton, Efficient sensitivity analysis of large‐scale differential‐algebraic systems, Appl. Numer. Math., 25 (1997), 41–54
16.
E. Hairer, S. Nørsett, G. Wanner, Solving ordinary differential equations. I, Springer Series in Computational Mathematics, Vol. 8, Springer‐Verlag, 1987xiv+480, Nonstiff problems
17.
E. Hairer, G. Wanner, Solving ordinary differential equations. II, Springer Series in Computational Mathematics, Vol. 14, Springer‐Verlag, 1991xvi+601, Stiff and differential‐algebraic problems
18.
Michael Hanke, Ebroul Izquierdo Macana, Roswitha März, On asymptotics in case of linear index‐2 differential‐algebraic equations, SIAM J. Numer. Anal., 35 (1998), 1326–1346
19.
D. Knapp, V. Barocas, K. Yoo, L. R. Petzold, and R. Tranquillo, Rheology of reconstituted type I collagen gel in confined compression, J. Rheology, 41 (1997), pp. 971–993.
20.
Shengtai Li, Linda Petzold, Software and algorithms for sensitivity analysis of large‐scale differential algebraic systems, J. Comput. Appl. Math., 125 (2000), 131–145, Numerical analysis 2000, Vol. VI, Ordinary differential equations and integral equations
21.
S. Li and L. R. Petzold, Design of New DASPK for Sensitivity Analysis, Technical report, Dept. of Computer Science, UCSB, Santa Barbara, CA, 1999.
22.
Shengtai Li, Linda Petzold, Wenjie Zhu, Sensitivity analysis of differential‐algebraic equations: a comparison of methods on a special problem, Appl. Numer. Math., 32 (2000), 161–174
23.
Timothy Maly, Linda Petzold, Numerical methods and software for sensitivity analysis of differential‐algebraic systems, Appl. Numer. Math., 20 (1996), 57–79, Workshop on the method of lines for time‐dependent problems (Lexington, KY, 1995)
24.
R. März, Differential Algebraic Systems Anew, Institute of Mathematics Technical Report, Humboldt University, Berlin, 2000.
25.
L. L. Raja, R. J. Kee, R. Serban, and L. R. Petzold, Computational algorithm for dynamic optimization of chemical vapor deposition processes in stagnation flow reactors, J. Electrochemical Soc., 147 (2000), pp. 2718–2726.
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SIAM Journal on Scientific Computing
Pages: 1076 - 1089
ISSN (online): 1095-7197
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Copyright © 2003 Society for Industrial and Applied Mathematics.
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Published online: 25 July 2006
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