Shape optimization

Some examples of the optimization of the shape of a bifurcation

(viscous dissipation of the fluid flowing inside the bifurcation is minimized at constant bifurcation volume)

Dirichlet boundary conditions at tree leaves

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Neumann boundary conditions at tree leaves

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Reference:

Shape minimization of the dissipated energy in dyadic trees (HAL link)
X. Dubois De La Sablonnière, B. Mauroy and Y. Privat.
Discrete Contin. Dyn. Syst. (B), 2010.