Automated shape differentiation in the Unified Form Language
Numerical Analysis
2020-08-26 v2
Abstract
We discuss automating the calculation of weak shape derivatives in the Unified Form Language (Aln{\ae}s et al., ACM Trans. Math. Softw., 2014) by introducing an appropriate additional step in the pullback from physical to reference space that computes G\^ateaux derivatives with respect to the coordinate field. We illustrate the ease of use with several examples.
Cite
@article{arxiv.1808.08083,
title = {Automated shape differentiation in the Unified Form Language},
author = {David A. Ham and Lawrence Mitchell and Alberto Paganini and Florian Wechsung},
journal= {arXiv preprint arXiv:1808.08083},
year = {2020}
}