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Automated shape differentiation in the Unified Form Language

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journal contribution
posted on 06.04.2020, 09:32 by DA Ham, L Mitchell, A Paganini, F Wechsung
We discuss automating the calculation of weak shape derivatives in the Unified Form Language (ACM TOMS 40(2):9:1– 9:37 2014) by introducing an appropriate additional step in the pullback from physical to reference space that computes Gateaux derivatives with respect to the coordinate field. We illustrate the ease of use with several examples.

Funding

DAH is supported by the Natural Environment Research Council (grant no. NE/K008951/1). LM is supported by the Engineering and Physical Sciences Research Council (grant no. EP/L000407/1). FW is supported by the EPSRC Centre For Doctoral Training in Industrially Focused Mathematical Modelling (grant no. EP/L015803/1)

History

Citation

Ham, D.A., Mitchell, L., Paganini, A. et al. Automated shape differentiation in the Unified Form Language. Struct Multidisc Optim 60, 1813–1820 (2019). https://doi.org/10.1007/s00158-019-02281-z

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

VoR (Version of Record)

Published in

Structural and Multidisciplinary Optimization

Volume

60

Pagination

1813–1820

Publisher

Springer Verlag (Germany) for International Society of Structural and Multidisciplinary Optimization (ISSMO)

eissn

1615-1488

Acceptance date

11/04/2019

Copyright date

2019

Available date

02/08/2019

Publisher version

https://link.springer.com/article/10.1007/s00158-019-02281-z

Notes

The code for the numerical experiments is available at Software used in ‘Automated shape differentiation in the Unified Form Language’ (2019).

Language

en

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