Automated shape differentiation in the Unified Form Language
This work provides a practical tool for researchers using finite element methods to compute shape derivatives automatically, but it is an incremental improvement over existing manual approaches.
The authors automate the calculation of weak shape derivatives in the Unified Form Language by adding a step that computes Gâteaux derivatives with respect to the coordinate field, demonstrating ease of use with examples.
We discuss automating the calculation of weak shape derivatives in the Unified Form Language (Alnæs et al., ACM Trans. Math. Softw., 2014) by introducing an appropriate additional step in the pullback from physical to reference space that computes Gâteaux derivatives with respect to the coordinate field. We illustrate the ease of use with several examples.