Shape Optimization Under Uncertainty---A Stochastic Programming Perspective

@article{Conti2008ShapeOU,
  title={Shape Optimization Under Uncertainty---A Stochastic Programming Perspective},
  author={Sergio Conti and Harald Held and Martin Pach and Martin Rumpf and R{\"u}diger Schultz},
  journal={SIAM J. Optim.},
  year={2008},
  volume={19},
  pages={1610-1632}
}
We present an algorithm for shape optimization under stochastic loading and representative numerical results. Our strategy builds upon a combination of techniques from two-stage stochastic programming and level-set-based shape optimization. In particular, usage of linear elasticity and quadratic objective functions permits us to obtain a computational cost which scales linearly in the number of linearly independent applied forces, which often is much smaller than the number of different… 

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