Tangential Tensor Fields on Deformable Surfaces – How to Derive Consistent L2-Gradient Flows

Ingo  Nitschke; Souhayl Sadik; Axel  Voigt

doi:10.1093/imamat/hxae006

Tangential Tensor Fields on Deformable Surfaces – How to Derive Consistent L²-Gradient Flows

Ingo Nitschke, Souhayl Sadik, Axel Voigt^*

^*Corresponding author for this work

Department of Mechanical and Production Engineering - Mechanics and Materials

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

1 Citation (Scopus)

Abstract

We consider gradient flows of surface energies that depend on the surface by a parameterization and on a tangential tensor field. The flow allows for dissipation by evolving the parameterization and the tensor field simultaneously. This requires the choice of a notation for independence. We introduce different gauges of surface independence and show their consequences for the evolution. In order to guarantee a decrease in energy, the gauge of surface independence and the time derivative have to be chosen consistently. We demonstrate the results for a surface Frank–Oseen–Helfrich energy.

Original language	English
Journal	IMA Journal of Applied Mathematics
Volume	88, 2023
Issue	6
Pages (from-to)	917-958
Number of pages	42
ISSN	1464-3634
DOIs	https://doi.org/10.1093/imamat/hxae006
Publication status	Published - Mar 2024

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abstract = "We consider gradient flows of surface energies that depend on the surface by a parameterization and on a tangential tensor field. The flow allows for dissipation by evolving the parameterization and the tensor field simultaneously. This requires the choice of a notation for independence. We introduce different gauges of surface independence and show their consequences for the evolution. In order to guarantee a decrease in energy, the gauge of surface independence and the time derivative have to be chosen consistently. We demonstrate the results for a surface Frank–Oseen–Helfrich energy.",

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Tangential Tensor Fields on Deformable Surfaces – How to Derive Consistent L²-Gradient Flows. / Nitschke, Ingo ; Sadik, Souhayl; Voigt, Axel .
In: IMA Journal of Applied Mathematics, Vol. 88, 2023, No. 6, 03.2024, p. 917-958.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

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N2 - We consider gradient flows of surface energies that depend on the surface by a parameterization and on a tangential tensor field. The flow allows for dissipation by evolving the parameterization and the tensor field simultaneously. This requires the choice of a notation for independence. We introduce different gauges of surface independence and show their consequences for the evolution. In order to guarantee a decrease in energy, the gauge of surface independence and the time derivative have to be chosen consistently. We demonstrate the results for a surface Frank–Oseen–Helfrich energy.

AB - We consider gradient flows of surface energies that depend on the surface by a parameterization and on a tangential tensor field. The flow allows for dissipation by evolving the parameterization and the tensor field simultaneously. This requires the choice of a notation for independence. We introduce different gauges of surface independence and show their consequences for the evolution. In order to guarantee a decrease in energy, the gauge of surface independence and the time derivative have to be chosen consistently. We demonstrate the results for a surface Frank–Oseen–Helfrich energy.

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Tangential Tensor Fields on Deformable Surfaces – How to Derive Consistent L²-Gradient Flows

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