A shape optimization algorithm for cellular composites

Abstract

We propose and investigate a mesh deformation technique for PDE constrained shape optimization. Introducing a gradient penalization to the inner product for linearized shape spaces, mesh degeneration can be prevented within the optimization iteration allowing for the scalability of employed solvers. We illustrate the approach by a shape optimization for cellular composites with respect to linear elastic energy under tension. The influence of the gradient penalization is evaluated and the parallel scalability of the approach demonstrated employing a geometric multigrid solver on hierarchically distributed meshes.

References in corpus (1)

• Algorithmic aspects of multigrid methods for optimization in shape spaces

Cited by in corpus (4)

• Parallel 3d shape optimization for cellular composites on large distributed-memory clusters
• Fluid dynamic shape optimization using self-adapting nonlinear extension operators with multigrid preconditioners
• Shape optimization in $W^{1,\infty }$ with geometric constraints: a study in distributed-memory systems
• Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds