Automatic differentiation of iterative processes
ICCAM'92 Proceedings of the fifth international conference on Computational and applied mathematics
The if-problem in automatic differentiation
ICCAM'92 Proceedings of the fifth international conference on Computational and applied mathematics
Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++
ACM Transactions on Mathematical Software (TOMS)
Programming python
ADIC: an extensible automatic differentiation tool for ANSI-C
Software—Practice & Experience
Automatic differentiation of algorithms: from simulation to optimization
Automatic differentiation of algorithms: from simulation to optimization
Numerical algorithms based on the theory of complex variable
ACM '67 Proceedings of the 1967 22nd national conference
The complex-step derivative approximation
ACM Transactions on Mathematical Software (TOMS)
The complex-step derivative approximation
ACM Transactions on Mathematical Software (TOMS)
Accurate numerical derivatives in MATLAB
ACM Transactions on Mathematical Software (TOMS)
Adjoint sensitivity computations for an embedded-boundary Cartesian mesh method
Journal of Computational Physics
Hybrid differentiation strategies for simulation and analysis of applications in C++
ACM Transactions on Mathematical Software (TOMS)
Extensions of the first and second complex-step derivative approximations
Journal of Computational and Applied Mathematics
A methodology for the development of discrete adjoint solvers using automatic differentiation tools
International Journal of Computational Fluid Dynamics
A continuous shape sensitivity equation method for unsteady laminar flows
International Journal of Computational Fluid Dynamics
A Jacobian-free Newton-Krylov algorithm for compressible turbulent fluid flows
Journal of Computational Physics
pyMDO: An Object-Oriented Framework for Multidisciplinary Design Optimization
ACM Transactions on Mathematical Software (TOMS)
Reduced-order models for parameter dependent geometries based on shape sensitivity analysis
Journal of Computational Physics
ACM Transactions on Mathematical Software (TOMS)
pyOpt: a Python-based object-oriented framework for nonlinear constrained optimization
Structural and Multidisciplinary Optimization
PopED: An extended, parallelized, nonlinear mixed effects models optimal design tool
Computer Methods and Programs in Biomedicine
On the generalization of the Complex Step Method
Journal of Computational and Applied Mathematics
An efficient overloaded method for computing derivatives of mathematical functions in MATLAB
ACM Transactions on Mathematical Software (TOMS)
Animating human lower limbs using contact-invariant optimization
ACM Transactions on Graphics (TOG)
Dual consistency and functional accuracy: a finite-difference perspective
Journal of Computational Physics
Concurrent aerostructural topology optimization of a wing box
Computers and Structures
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The complex-step derivative approximation and its application to numerical algorithms are presented. Improvements to the basic method are suggested that further increase its accuracy and robustness and unveil the connection to algorithmic differentiation theory. A general procedure for the implementation of the complex-step method is described in detail and a script is developed that automates its implementation. Automatic implementations of the complex-step method for Fortran and C/C++ are presented and compared to existing algorithmic differentiation tools. The complex-step method is tested in two large multidisciplinary solvers and the resulting sensitivities are compared to results given by finite differences. The resulting sensitivities are shown to be as accurate as the analyses. Accuracy, robustness, ease of implementation and maintainability make these complex-step derivative approximation tools very attractive options for sensitivity analysis.