Abstract
It is obvious that if we could find characters or signs suited for expressing all our thoughts as clearly and as exactly as arithmetic expresses numbers or geometry expresses lines, we could do in all matters insofar as they are subject to reasoning all that we can do in arithmetic and geometry.
It is obvious that if we could find characters or signs suited for expressing all our thoughts as clearly and as exactly as arithmetic expresses numbers or geometry expresses lines, we could do in all matters insofar as they are subject to reasoning all that we can do in arithmetic and geometry.
Gottfried Wilhelm Leibniz
Preface to the General Science, 1677
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Notes
- 1.
Here the particular finite element is meant to solve a particular physical problem. Large commercial finite element environments can include several hundreds of different finite elements for different physical applications.
- 2.
Of course, a general computer algebra system can be used for building the necessary apparatus to deal with the virtual quantities in a traditional way and then automatic code generation can be applied on the results. However, the elegance of using automatic differentiation would then be lost.
- 3.
By using the SMSFreeze operator a new auxiliary variable is created that can be safely used as independent variable within differentiation, see also Appendix A.2.2.
- 4.
This option also effects the selection of the algorithm applied to solve the resulting system of linear equations when AceFEM is used.
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Korelc, J., Wriggers, P. (2016). Automation of Research in Computational Modeling. In: Automation of Finite Element Methods. Springer, Cham. https://doi.org/10.1007/978-3-319-39005-5_2
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