Optimal control of volume-preserving mean curvature flow
| Autor: | Antoine Laurain, Shawn W. Walker |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Surface (mathematics)
Numerical Analysis Mean curvature flow Physics and Astronomy (miscellaneous) Applied Mathematics Numerical analysis Mathematical analysis Perturbation (astronomy) 010103 numerical & computational mathematics Optimal control EQUAÇÕES DIFERENCIAIS PARCIAIS PARABÓLICAS 01 natural sciences Computer Science Applications 010101 applied mathematics Computational Mathematics Flow (mathematics) Modeling and Simulation Trajectory Sensitivity (control systems) 0101 mathematics Mathematics |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| Popis: | We develop a framework and numerical method for controlling the full space-time tube of a geometrically driven flow. We consider an optimal control problem for the mean curvature flow of a curve or surface with a volume constraint, where the control parameter acts as a forcing term in the motion law. The control of the trajectory of the flow is achieved by minimizing an appropriate tracking-type cost functional. The gradient of the cost functional is obtained via a formal sensitivity analysis of the space-time tube generated by the mean curvature flow. We show that the perturbation of the tube may be described by a transverse field satisfying a parabolic equation on the tube. We propose a numerical algorithm to approximate the optimal control and show several results in two and three dimensions demonstrating the efficiency of the approach. |
| Databáze: | OpenAIRE |
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