Automatic implementation of material laws: Jacobian calculation in a finite element code with TAPENADE

DOI10.1016/j.camwa.2016.10.010zbMath1368.65239arXiv1702.06365OpenAlexW2552187097MaRDI QIDQ2012746

Florian Zwicke, Philipp Knechtges, Stefanie Elgeti, Marek Behr

Publication date: 3 August 2017

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.06365

zbMATH Keywords

finite element methodNewton-Raphson methodautomatic differentiation

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Uses Software

• ADIFOR
• TAPENADE
• OpenAD/F
• Odyssee

Cites Work

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• Efficient nonlinear solvers for nodal high-order finite elements in 3D
• Perturbation theory for linear operators.
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• Constitutive laws for the matrix-logarithm of the conformation tensor
• Sparse Jacobian Construction for Mapped Grid Visco-Resistive Magnetohydrodynamics
• The Tapenade automatic differentiation tool
• Evaluating Derivatives
• OpenAD/F
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Automatic Differentiation of Computer Programs
• The Efficient Computation of Sparse Jacobian Matrices Using Automatic Differentiation
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• Historical Development of the Newton–Raphson Method
• Jacobian code generated by source transformation and vertex elimination can be as efficient as hand-coding
• Parallel simulation of compressible flow using automatic differentiation and PETSc

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