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Recent progress in PDE constrained optimization on shape manifolds is basedon the Hadamard form of shape derivatives, i.e., in the form of integrals atthe boundary of the shape under investigation, as well as on intrinsic shapemetrics. From a numerical point of view, domain integral forms of shapederivatives seem promising, which rather require an outer metric on the domainsurrounding the shape boundary. This paper tries to harmonize both points ofview by employing a Steklov-Poincar\'e type intrinsic metric, which is derivedfrom an outer metric. Based on this metric, efficient shape optimizationalgorithms are proposed, which also reduce the analytical labor, so farinvolved in the derivation of shape derivatives.

Efficient PDE constrained shape optimization based on Steklov-Poincar\'e type metrics