Geometric Gradient Flows for Interface Optimization in Transmission and Contact Problems

Geometric Gradient Flows for Interface Optimization in Transmission and Contact Problems Full article

Journal

Proceedings in Applied Mathematics and Mechanics (PAMM)
ISSN: 1617-7061

Output data

Year: 2025, Volume: 25, Number: 4, Article number : 70036, Pages count : 11 DOI: 10.1002/pamm.70036

Tags

elliptic transmission problem, geometric gradient flow, Kohn–Vogelius functional, shape optimization, Signorini contact

Authors

Tan Yixin ^1,2 , Plotnikov Pavel I. ³ , Sokolowski Jan ²

Affiliations

1	Department of Mathematics East China Normal University Shanghai China
2	Systems Research Institute of the Polish Academy of Sciences Warszawa Poland
3	Lavrentyev Institute of Hydrodynamics of the Russian Academy of Sciences Novosibirsk Russia

This paper investigates the evolution of interfaces in two-phase systems governed by elliptic transmission problems and linearelasticity. In the first part, we address a shape optimization problem in which an internal interface is identified by minimizing theKohn–Vogelius functional, comparing solutions arising from different boundary conditions. The interface evolves according to ageometric gradient flow that combines the shape derivative of the functional with curvature-based regularization. In the secondpart, we extend the framework to elastic contact problems with Signorini-type boundary conditions. Using material derivatives,we derive the shape derivative of the compliance functional and develop a regularized gradient flow governing the interfacemotion. The application of a gradient-flow-based strategy to contact problems in elasticity provides a new and efficient approachto this significant shape and topology optimization setting. Numerical experiments for both transmission and elasticity modelsdemonstrate the stability, efficiency, and accuracy of the proposed method in recovering optimal interface geometries under avariety of conditions.

Tan Y. , Plotnikov P.I. , Sokolowski J.
Geometric Gradient Flows for Interface Optimization in Transmission and Contact Problems
Proceedings in Applied Mathematics and Mechanics (PAMM). 2025. V.25. N4. 70036 :1-11. DOI: 10.1002/pamm.70036 OpenAlex

Submitted:	Jul 31, 2025
Accepted:	Nov 25, 2025
Published print:	Dec 16, 2025

≡ OpenAlex:

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