Discrete Gradient Flows for Shape Optimization and Applications

@inproceedings{Dogan2007DiscreteGF,
  title={Discrete Gradient Flows for Shape Optimization and Applications},
  author={Gunay Dogan and Pedro Morin and Ricardo H. Nochetto and Marco Verani},
  year={2007}
}
We present a variational framework for shape optimization problems that establishes clear and explicit connections among the continuous formulation, its full discretization and the resulting linear algebraic systems. Our approach hinges on the following essential features: shape differential calculus, a semi-implicit time discretization and a finite element method for space discretization. We use shape differential calculus to express variations of bulk and surface energies with respect to… CONTINUE READING

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