A Discretize-then-Optimize Approach to PDE-Constrained Shape Optimization
Roland Herzog,
Estefanía Loayza-Romero
Abstract:We consider discretized two-dimensional PDE-constrained shape optimization problems, in which shapes are represented by triangular meshes. Given the connectivity, the space of admissible vertex positions was recently identified to be a smooth manifold, termed the manifold of planar triangular meshes. The latter can be endowed with a complete Riemannian metric, which allows large mesh deformations without jeopardizing mesh quality; see [14]. Nonetheless, the discrete shape optimization problem of finding optima… Show more
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