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Adaptive Approximation of Shapes

by A. Buffa and R. Hiptmair and P. Panchal

(Report number 2020-60)

Abstract
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.

Keywords: Model reduction, shape calculus, shape gradient, shape Hessian, low-rank approximation, power iteration

@Techreport{BHP20_933,
  author = {A. Buffa and R. Hiptmair and P. Panchal},
  title = {Adaptive Approximation of Shapes},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2020-60},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2020/2020-60.pdf },
  year = {2020}
}

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