Topology Optimization Problems

In this part of the tutorial, we investigate how topology optimization problems can be treated with cashocs.

List of all topology optimization demos:

• Topology Optimization with a Poisson Equation
• Documentation of the Config Files for Topology Optimization Problems
• Topology Optimization with Linear Elasticity - Cantilever
• Topology Optimization with Stokes Flow - Pipe Bend
• Topology Optimization with a Volume Constraint
• Computing Multiple Local Minimizers of Topology Optimization Problems - Five-holes Double-pipe

Note

As topology optimization problems are very involved from a theoretical point of view, it is, at the moment, not possible to automatically derive topological derivatives. Therefore, cashocs cannot be used as “black-box” solver for topology optimization problems in general.

Moreover, our framework for topology optimization of using a level-set function is quite flexible, but requires a lot of theoretical understanding. In Topology Optimization with a Poisson Equation, we briefly go over some theoretical foundations required for using cashocs’ topology optimization features. We refer the reader, e.g., to Sokolowski and Novotny - Topological Derivatives in Shape Optimization for an exhaustive treatment of these topics.