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.
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)
CitationHam, 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
VersionVoR (Version of Record)
Published inStructural and Multidisciplinary Optimization
PublisherSpringer Verlag (Germany) for International Society of Structural and Multidisciplinary Optimization (ISSMO)
NotesThe code for the numerical experiments is available at
Software used in ‘Automated shape differentiation in the
Unified Form Language’ (2019).