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In this article, we propose a shape optimization algorithm which is able tohandle large deformations while maintaining a high level of mesh quality. Basedon the method of mappings we introduce a nonlinear extension operator, whichlinks a boundary control to domain deformations, ensuring admissibility ofresulting shapes. The major focus is on comparisons between well-establishedapproaches involving linear-elliptic operators for the extension and the effectof additional nonlinear advection on the set of reachable shapes. It ismoreover discussed how the computational complexity of the proposed algorithmcan be reduced. The benefit of the nonlinearity in the extension operator issubstantiated by several numerical test cases of stationary, incompressibleNavier-Stokes flows in 2d and 3d.

Mesh quality preserving shape optimization using nonlinear extension operators