Automated shape differentiation in the Unified Form Language

TL;DR

This paper presents a method to automate the calculation of weak shape derivatives within the Unified Form Language, simplifying the process through an additional pullback step that computes Gâteaux derivatives.

Contribution

It introduces an automated approach for calculating weak shape derivatives in the Unified Form Language by adding a new step in the pullback process.

Findings

Simplifies shape derivative calculations in UFL

Demonstrates ease of use with multiple examples

Enhances automation in shape optimization workflows

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.