FADBAD++ implements the forward, backward and Taylor methods utilizing C++ templates and operator overloading. These AD-templates enable the user to differentiate functions that are implemented in arithmetic types, such as doubles and intervals. One of the major ideas in FADBAD++ is that the AD-template types also behave like arithmetic types. This property of the AD-templates enables the user to differentiate a C++ function by replacing all occurrences of the original arithmetic type with the AD-template version. This transparency of behavior also makes it possible to generate high order derivatives by applying the AD-templates on themselves, enabling the user to combine the AD methods very easily.

References in zbMATH (referenced in 53 articles )

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  1. Dötschel, Thomas; Auer, Ekaterina; Rauh, Andreas; Aschemann, Harald: Thermal behavior of high-temperature fuel cells: reliable parameter identification and interval-based sliding mode control (2013) ioport
  2. Fazal, Qaisra; Neumaier, Arnold: Error bounds for initial value problems by optimization (2013)
  3. Krause, Mathias J.; Heuveline, Vincent: Parallel fluid flow control and optimisation with lattice Boltzmann methods and automatic differentiation (2013)
  4. Dyllong, Eva; Kiel, Stefan: A comparison of verified distance computation between implicit objects using different arithmetics for range enclosure (2012)
  5. Nehmeier, Marco: Generative programming for automatic differentiation (2012)
  6. Nehmeier, Marco: Interval arithmetic using expression templates, template meta programming and the upcoming C++ standard (2012)
  7. Rauh, Andreas; Auer, Ekaterina; Dötschel, Thomas; Aschemann, Harald: Verified stability analysis of continuous-time control systems with bounded parameter uncertainties and stochastic disturbances (2012)
  8. Asaithambi, Asai: Numerical solution of a third-order nonlinear boundary-value problem by automatic differentiation (2011)
  9. Lamour, René; Monett, Dagmar: A new algorithm for index determination in DAEs using algorithmic differentiation (2011)
  10. Aschemann, H.; Minisini, J.; Rauh, A.: Interval arithmetic techniques for the design of controllers for nonlinear dynamical systems with applications in mechatronics (2010)
  11. Koutsawa, Yao; Belouettar, Salim; Makradi, Ahmed; Nasser, Houssein: Sensitivities of effective properties computed using micromechanics differential schemes and high-order Taylor series: application to piezo-polymer composites (2010)
  12. Rauh, Andreas; Minisini, Johanna; Hofer, Eberhard P.: Verification techniques for sensitivity analysis and design of controllers for nonlinear dynamical systems with uncertainties (2010)
  13. Auer, Ekaterina; Luther, Wolfram: Uses of new sensitivity and DAE solving methods in SmartMobile for verified analysis of mechanical systems (2009)
  14. Enciu, P.; Wurtz, F.; Gerbaud, L.; Delinchant, B.: Automatic differentiation for electromagnetic models used in optimization (2009)
  15. Freihold, Mareile; Hofer, Eberhard P.: Derivation of physically motivated constraints for efficient interval simulations applied to the analysis of uncertain dynamical systems (2009)
  16. Kamikawa, Ayako; Kawahara, Mutsuto: Optimal control of fluid forces using second order automatic differentiation (2009)
  17. Rauh, Andreas; Brill, Michael; Günther, Clemens: A novel interval arithmetic approach for solving differential-algebraic equations with \textscValEncIA-IVP (2009)
  18. Rauh, Andreas; Minisini, Johanna; Hofer, Eberhard: Verification techniques for sensitivity analysis and design of controllers for nonlinear dynamic systems with uncertainties (2009)
  19. Bischof, Christian H.; Hovland, Paul D.; Norris, Boyana: On the implementation of automatic differentiation tools (2008)
  20. Giles, M. B.: Monte Carlo evaluation of sensitivities in computational finance (2008)