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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Bibliographic Details
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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Summary: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.
ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-009-0395-2