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Application of techniques of computational differentiation to a cooling system. (English) Zbl 0955.65058

Summary: Mathematical functions are often evaluated by computer programs. Using the technique of computational differentiation (CD), one can determine in addition exact gradients of these functions. This article considers two software tools implementing the forward and the reverse made of CD, namely ADOL-C and FADBAD. Then the model of a cooling system within steel manufacturing is described. The gradient of the corresponding function is calculated by CD applying both software tools separately and alternatively, by divided differences. After a short account of our experience installing and running the software tools the results obtained are presented. A comparison of the run-time needed by CD to the run-time needed by the divided difference method is given.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65L05 Numerical methods for initial value problems involving ordinary differential equations
45K05 Integro-partial differential equations
80A20 Heat and mass transfer, heat flow (MSC2010)
80M20 Finite difference methods applied to problems in thermodynamics and heat transfer

Software:

FADBAD++; ADOL-C
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References:

[1] Bendtsen C., a flexible C++package for automatic differentiation (1996)
[2] Griewank A., In Mathematical Programming: Recent Developments and Applications pp 83– (1989)
[3] DOI: 10.1145/229473.229474 · Zbl 0884.65015 · doi:10.1145/229473.229474
[4] Hohfeld M., Automatisierungstechnische Praxis 40 pp 56– (1998)
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