Ivan Hlaváček, Jan Chleboun (1996)
Applications of Mathematics
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A new postprocessing technique suitable for nonuniform triangulations is employed in the sensitivity analysis of some model optimal shape design problems.
Samuel Amstutz (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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This paper deals with topology optimization of domains subject to a pointwise constraint on the gradient of the state. To realize this constraint, a class of penalty functionals is introduced and the expression of the corresponding topological derivative is obtained for the Laplace equation in two space dimensions. An algorithm based on these concepts is proposed. It is illustrated by some numerical applications.
Piotr Fulmański, Antoine Laurain, Jean-Francois Scheid, Jan Sokołowski (2007)
International Journal of Applied Mathematics and Computer Science
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The level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed...