Journal of Computational Physics
Algorithms and design for a second-order automatic differentiation module
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
A conserving discretization for the free boundary in a two-dimensional Stefan problem
Journal of Computational Physics
Aerofoil optimisation via AD of a multigrid cell-vertex Euler flow solver
Automatic differentiation of algorithms
Adifor 2.0: Automatic Differentiation of Fortran 77 Programs
IEEE Computational Science & Engineering
Cross-diffusion controlled particle dissolution in metallic alloys
Computing and Visualization in Science
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
Generating efficient derivative code with TAF
Future Generation Computer Systems
Sensitivities for a single drop simulation
ICCS'03 Proceedings of the 2003 international conference on Computational science: PartII
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Second-order derivatives are crucial ingredients to a variety of numerical methods. Often, they are difficult to get with numerical differentiation by divided differencing. Automatic differentiation provides an alternative by a program transformation capable of evaluating Jacobians, Hessians, or higher-order derivatives of functions given in the form of computer programs. SEPRAN is a general-purpose finite element package written in Fortran 77 used in various scientific areas ranging from fluid dynamics to structural mechanics to electromagnetism. By transforming SEPRAN twice using the automatic differentiation tool ADIFOR, second-order derivatives are evaluated without truncation error. Numerical experiments are reported in which second-order derivatives of a flow field with respect to an inflow velocity are computed, demonstrating the feasibility of this approach.