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Automation of primal and sensitivity analysis of transient coupled problems. (English) Zbl 1171.74043
Summary: The paper describes a hybrid symbolic-numeric approach to automation of primal and sensitivity analysis of computational models 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 highly abstract description of primal and sensitivity analysis of the typical computational models. At the end, we present 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.

74S05 Finite element methods applied to problems in solid mechanics
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
68W30 Symbolic computation and algebraic computation
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