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The space mapping technique is used to efficiently solve complex optimizationproblems. It combines the accuracy of fine model simulations with the speed ofcoarse model optimizations to approximate the solution of the fine modeloptimization problem. In this paper, we propose novel space mapping methods forsolving shape optimization problems constrained by partial differentialequations (PDEs). We present the methods in a Riemannian setting based onSteklov-Poincar\'e-type metrics and discuss their numerical discretization andimplementation. We investigate the numerical performance of the space mappingmethods on several model problems. Our numerical results highlight the methods'great efficiency for solving complex shape optimization problems.

Space Mapping for PDE Constrained Shape Optimization