<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Computational meshes arising from shape optimization routines commonly suffer from decrease of mesh quality or even destruction of the mesh. In this work, we provide an approach to regularize general shape optimization problems to increase both shape and volume mesh quality. For this, we employ pre-shape calculus as established in Luft and Schulz (2021). Existence of regularized solutions is guaranteed. Further, consistency of modified pre-shape gradient systems is established. We present pre-shape gradient system modifications, which permit simultaneous shape optimization with mesh quality improvement. Optimal shapes to the original problem are left invariant under regularization. The computational burden of our approach is limited, since additional solution of possibly larger (non-)linear systems for regularized shape gradients is not necessary. We implement and compare pre-shape gradient regularization approaches for a 2D problem, which is prone to mesh degeneration. As our approach does not depend on the choice of metrics representing shape gradients, we employ and compare several different metrics.</p>
</abstract>

Computational meshes arising from shape optimization routines commonly suffer from decrease of mesh quality or even destruction of the mesh. In this work, we provide an approach to regularize general shape optimization problems to increase both shape and volume mesh quality. For this, we employ pre-shape calculus as established in Luft and Schulz (2021). Existence of regularized solutions is guaranteed. Further, consistency of modified pre-shape gradient systems is established. We present pre-shape gradient system modifications, which permit simultaneous shape optimization with mesh quality improvement. Optimal shapes to the original problem are left invariant under regularization. The computational burden of our approach is limited, since additional solution of possibly larger (non-)linear systems for regularized shape gradients is not necessary. We implement and compare pre-shape gradient regularization approaches for a 2D problem, which is prone to mesh degeneration. As our approach does not depend on the choice of metrics representing shape gradients, we employ and compare several different metrics.

Simultaneous shape and mesh quality optimization using pre-shape calculus

Control and Cybernetics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Simultaneous shape and mesh quality optimization using pre-shape calculus"}

Computational meshes arising from shape optimization routines commonly suffer from decrease of mesh quality or even destruction of the mesh. In this work, we...

Simultaneous shape and mesh quality optimization using pre-shape calculus

Publié en ligne: 27 juin 2022

Pages: 473 - 520

Reçu: 01 mai 2021

Accepté: 01 août 2021

DOI: https://doi.org/10.2478/candc-2021-0028

Mots clés
shape optimization, mesh quality, mesh deformation method, shape calculus

© 2021 Daniel Luft et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Simultaneous shape and mesh quality optimization using pre-shape calculus

Publié en ligne: 27 juin 2022

Pages: 473 - 520

Reçu: 01 mai 2021

Accepté: 01 août 2021

DOI: https://doi.org/10.2478/candc-2021-0028

Mots clésshape optimization, mesh quality, mesh deformation method, shape calculus

© 2021 Daniel Luft et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
shape optimization, mesh quality, mesh deformation method, shape calculus