author = {Geihe, Benedict and Lenz, Martin and Rumpf, Martin and Schultz, R{\"{u}}diger},
  title = {Risk averse elastic shape optimization with parametrized fine scale
  journal = {Mathematical Programming},
  year = {2013},
  volume = {141},
  pages = {383-403},
  number = {1-2},
  abstract = {Shape optimization of the fine scale geometry of elastic objects is
	investigated under stochastic loading. Thus, the object geometry
	is described via parametrized geometric details placed on a regular
	lattice. Here, in a two dimensional set up we focus on ellipsoidal
	holes as the fine scale geometric details described by the semiaxes
	and their orientation. Optimization of a deterministic cost functional
	as well as stochastic loading with risk neutral and risk averse stochastic
	cost functionals are discussed. Under the assumption of linear elasticity
	and quadratic objective functions the computational cost scales linearly
	in the number of basis loads spanning the possibly large set of all
	realizations of the stochastic loading. The resulting shape optimization
	algorithm consists of a finite dimensional, constraint optimization
	scheme where the cost functional and its gradient are evaluated applying
	a boundary element method on the fine scale geometry. Various numerical
	results show the spatial variation of the geometric domain structures
	and the appearance of strongly anisotropic patterns.},
  doi = {10.1007/s10107-012-0531-1},
  pdf = { 1},
  issn = {0025-5610},
  keywords = {SHAPE_OPT},
  language = {English},
  publisher = {Springer Berlin Heidelberg},
  url = {}