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 58 articles )

Showing results 21 to 40 of 58.
Sorted by year (citations)
  1. Hogan, Robin J.: Fast reverse-mode automatic differentiation using expression templates in C++ (2014)
  2. Li, Xiang; Zhang, Dongxiao: A backward automatic differentiation framework for reservoir simulation (2014)
  3. Maïga, Moussa; Ramdani, Nacim; Travé-Massuyès, Louise; Combastel, Christophe: A CSP versus a zonotope-based method for solving guard set intersection in nonlinear hybrid reachability (2014)
  4. Pellegrini, Etienne; Russell, Ryan P.; Vittaldev, Vivek: (F) and (G) Taylor series solutions to the Stark and Kepler problems with Sundman transformations (2014)
  5. Rauh, Andreas; Senkel, Luise; Auer, Ekaterina; Aschemann, Harald: Interval methods for real-time capable robust control of solid oxide fuel cell systems (2014)
  6. 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
  7. Fazal, Qaisra; Neumaier, Arnold: Error bounds for initial value problems by optimization (2013)
  8. Krause, Mathias J.; Heuveline, Vincent: Parallel fluid flow control and optimisation with lattice Boltzmann methods and automatic differentiation (2013)
  9. Dyllong, Eva; Kiel, Stefan: A comparison of verified distance computation between implicit objects using different arithmetics for range enclosure (2012)
  10. Nehmeier, Marco: Interval arithmetic using expression templates, template meta programming and the upcoming C++ standard (2012)
  11. Nehmeier, Marco: Generative programming for automatic differentiation (2012)
  12. Rauh, Andreas; Auer, Ekaterina; Dötschel, Thomas; Aschemann, Harald: Verified stability analysis of continuous-time control systems with bounded parameter uncertainties and stochastic disturbances (2012)
  13. Asaithambi, Asai: Numerical solution of a third-order nonlinear boundary-value problem by automatic differentiation (2011)
  14. Lamour, René; Monett, Dagmar: A new algorithm for index determination in DAEs using algorithmic differentiation (2011)
  15. Aschemann, H.; Minisini, J.; Rauh, A.: Interval arithmetic techniques for the design of controllers for nonlinear dynamical systems with applications in mechatronics (2010)
  16. 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)
  17. Rauh, Andreas; Minisini, Johanna; Hofer, Eberhard P.: Verification techniques for sensitivity analysis and design of controllers for nonlinear dynamical systems with uncertainties (2010)
  18. Auer, Ekaterina; Luther, Wolfram: Uses of new sensitivity and DAE solving methods in SmartMobile for verified analysis of mechanical systems (2009)
  19. Enciu, P.; Wurtz, F.; Gerbaud, L.; Delinchant, B.: Automatic differentiation for electromagnetic models used in optimization (2009)
  20. Freihold, Mareile; Hofer, Eberhard P.: Derivation of physically motivated constraints for efficient interval simulations applied to the analysis of uncertain dynamical systems (2009)