Optimization of piecewise smooth shapes under uncertainty using the example of Navier-Stokes flow

2023/08/15 by Caroline Geiersbach, Geiersbach, Caroline, Tim Suchan +3 · 2 citations
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Topology Optimization in Engineering #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2308.07742

Abstract

We investigate a complex system involving multiple shapes to be optimized in a domain, taking into account geometric constraints on the shapes and uncertainty appearing in the physics. We connect the differential geometry of product shape manifolds with multi-shape calculus, which provides a novel framework for the handling of piecewise smooth shapes. This multi-shape calculus is applied to a shape optimization problem where shapes serve as obstacles in a system governed by steady state incompressible Navier-Stokes flow. Numerical experiments use our recently developed stochastic augmented Lagrangian method and we investigate the choice of algorithmic parameters using the example of this application.

Cited by

• Fracture propagation by using shape optimization techniques based on outer Riemannian metrics
• Multilevel Stochastic Gradient Descent for Optimal Control Under Uncertainty

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