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Automatic derivation of sensitivity terms for mixed Galerkin‐collocation problems
Author(s) -
Korelc J.
Publication year - 2000
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200008014137
Subject(s) - collocation (remote sensing) , galerkin method , sensitivity (control systems) , automatic differentiation , symbolic computation , computation , finite element method , computer science , collocation method , mathematics , algorithm , algebra over a field , theoretical computer science , mathematical analysis , pure mathematics , differential equation , ordinary differential equation , machine learning , electronic engineering , engineering , physics , thermodynamics
The paper presents the use of the SMS system (Symbolic Mechanics System) for the automatic derivation and coding of sensitivity terms in finite element analysis. General symbolic derivation of analytical sensitivity terms for general mixed Galerkin‐collocation problems is difficult due to the complex (implicit) interactions between different levels of computation. The approach implemented in SMS avoids this problem by combining several techniques: symbolic capabilities of Mathematica, automatic differentiation technique, simultaneous optimisation of expressions and stochastic evaluation of the formulae.