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Automated shape differentiation in the Unified Form Language

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arxiv 1808.08083 v2 pith:IL5RRZN7 submitted 2018-08-24 math.NA cs.NA

David A. Ham , Lawrence Mitchell , Alberto Paganini , Florian Wechsung This is my paper · ORCID
classification math.NAcs.NA
keywords derivativesformlanguageshapeunifiedadditionalappropriateateaux
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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.

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  1. Discrete Total Variation of the Normal Vector Field as Shape Prior with Applications in Geometric Inverse Problems

    math.NA 2019-08 conditional novelty 6.0 of 10

    A discrete total variation of the surface normal, equal to the discrete total mean curvature, is proposed as a shape prior that lets reconstruction recover polyhedral shapes instead of rounding them.

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