Seminar in Numerical Analysis: Ralf Hiptmair (ETH Zürich)

Adaptive Approximation of Shapes

We consider scalar-valued shape functionals on sets of shapes which are small perturbations of a reference shape. The shapes are described by parameterizations and their closeness is induced by a Hilbert space structure on the parameter domain. We justify a heuristic for finding the best low-dimensional parameter subspace with respect to uniformly approximating a given shape functional. We also propose an adaptive algorithm for achieving a prescribed accuracy when representing the shape functional with a small number of shape parameters.

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