Speaker
Description
Shape optimization problems are ill-posed in general because of the lack of convexity. Therefore, the appropriate regularization is required for the existence of an optimal shape in applications to solid mechanics, as well as fluid and gas mechanics. In the lecture the mathematical model of shape optimization problem is considered. The convergence of the associated gradient flow dynamical system is established. In this way the convergence of the gradient method in shape optimization is shown for the first time in the literature. Numerical examples are presented for the shape and topology optimization in elasticity.
References:
[1] Plotnikov, P.I., Sokolowski, J. Gradient Flows in Shape OptimizationTheory. Dokl. Math. 108, 387 391 (2023).
[2] Plotnikov, P. I. ; Sokolowski, J. Gradient flow for Kohn-Vogeliusfunctional. Sib. Elektron. Mat. Izv. 20 (2023), no. 1, 524–579.
[3] Plotnikov, P. I. ; Sokolowski, J. Geometric aspects of shapeoptimization. J. Geom. Anal. 33 (2024), no. 7, Paper No. 206, 57 pp.
[4] Plotnikov, P. I. ; Sokolowski, J. Geometric Framework for GradientFlow in Shape Optimization, Springer Briefs, submitted.
[5] Sokolowski, J. ; Yixin, Tan. Shape and Topology Optimization of Control Problems in Elasticity, submitted.
