Shape optimisation with nearly conformal transformations

Understand

In shape optimisation it is desirable to obtain deformations of a given mesh without negative impact on the mesh quality.

• We propose a new algorithm using least square formulations of the Cauchy-Riemann equations.
• Our method allows to deform meshes in a nearly conformal way and thus approximately preserves the angles of triangles during the optimisation process.
• The performance of our methodology is shown by applying our method to some unconstrained shape functions and a constrained Stokes shape optimisation problem.