Automation of primal and sensitivity analysis of transient coupled problems

The paper describes a hybrid symbolic–numeric approach to automation of primal and sensitivity analysis of computational models formulated and solved by finite element method. The necessary apparatus for the automation of steady-state, steady-state coupled, transient and transient coupled problems i...

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Published in:Computational mechanics 2009-10, Vol.44 (5), p.631-649
Main Author: Korelc, Jože
Format: Article
Language:English
Subjects:
Automation
Classical and Continuum Physics
Computation
Computational Science and Engineering
Engineering
Finite element method
Mathematical analysis
Original Paper
Sensitivity analysis
Steady state
Subroutines
Theoretical and Applied Mechanics
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description The paper describes a hybrid symbolic–numeric approach to automation of primal and sensitivity analysis of computational models formulated and solved by finite element method. The necessary apparatus for the automation of steady-state, steady-state coupled, transient and transient coupled problems is introduced as combination of a symbolic system, an automatic differentiation (AD) technique and an automatic code generation. For this purpose the paper extends the classical formulation of AD by additional operators necessary for a high abstract description of primal and sensitivity analysis of the typical computational models. An appropriate abstract description for the fully implicit primal and sensitivity analysis of hyperelastic and elasto-plastic problems and a symbolic input for the generation of necessary user subroutines for the two-dimensional, hyperelastic finite element are presented at the end.
doi_str_mv 10.1007/s00466-009-0395-2
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subjects Automation
Classical and Continuum Physics
Computation
Computational Science and Engineering
Engineering
Finite element method
Mathematical analysis
Original Paper
Sensitivity analysis
Steady state
Subroutines
Theoretical and Applied Mechanics
title Automation of primal and sensitivity analysis of transient coupled problems
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