Simultaneous shape and mesh quality optimization using pre-shape calculus

• Autorzy: Luft Daniel , Schulz Volker

Identyfikatory

DOI

10.2478/candc-2021-0028

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

shape optimization; mesh quality; mesh deformation method; shape calculus

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2021
• Tom: Vol. 50, No. 4
• Strony: 473--520
• Opis fizyczny: Bibliogr. 21 poz., rys., tab.

Twórcy

autor

Luft Daniel

• Trier University, Department of Mathematics, 54286 Trier, Germany

autor

Schulz Volker

• Trier University, Department of Mathematics, 54286 Trier, Germany

Bibliografia

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