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math.OC2015★ 77 cited
Computational comparison of surface metrics for PDE constrained shape optimization
Volker Schulz, Martin Siebenborn
We compare surface metrics for shape optimization problems with constraints, consisting mainly of partial differential equations (PDE), from a computational point of view. In parti…
math.OC2015★ 97 cited
Efficient PDE constrained shape optimization based on Steklov-Poincaré type metrics
Volker Schulz, Martin Siebenborn, Kathrin Welker
Recent progress in PDE constrained optimization on shape manifolds is based on the Hadamard form of shape derivatives, i.e., in the form of integrals at the boundary of the shape u…