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Shape optimization by pursuing diffeomorphisms

by R. Hiptmair and A. Paganini

(Report number 2014-27)

Abstract
We consider PDE constrained shape optimization in the framework of finite element discretization of the underlying boundary value problem. We present an algorithm tailored to preserve and exploit the approximation properties of the finite element method, and that allows for arbitrarily high resolution of shapes. It employs (i) B-spline based representations of the deformation diffeomorphism, and (ii) superconvergent domain integral expressions for the shape gradient. We provide numerical evidence of the performance of this method both on prototypical well-posed and ill-posed shape optimization problems.

Keywords: Shape Optimization, Optimal Control, Finite Element Method, B-Splines

@Techreport{HP14_577,
  author = {R. Hiptmair and A. Paganini},
  title = {Shape optimization by pursuing diffeomorphisms},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2014-27},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2014/2014-27.pdf },
  year = {2014}
}

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